October 2016
Evaluating Sovereign Disaster
Risk Finance Strategies: Case
Studies and Guidance
© 2016 International Bank for Reconstruction and
Development / International Development Association or
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Evaluating Sovereign Disaster
Risk Finance Strategies: Case
Studies and Guidance
ii EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Acknowledgements
This report was written by a joint team comprising Daniel
Clarke and Naomi Cooney of the Disaster Risk Financing
and Insurance Program of The World Bank Group and
Anna Edwards and Andrew Jinks of the UK Government
Actuary’s Department. Overall guidance was provided by
Olivier Mahul (World Bank-GFDRR Disaster Risk Financing
and Insurance Program) and Ian Rogers (UK Government
Actuary’s Department).
The report is an output of the Disaster Risk Finance Impact
Analytics Project, and it greatly benefited from the inputs
and reviews from Cora Ciechanowicz, Mareile Drechsler,
Ruth Hill, Oscar Ishizawa, Barry Maher, Catherine Porter,
Richard Poulter, Wolter Soer, and Charles Stutley. The team
has made every attempt to verify the contents presented,
but the information should be interpreted with due
consideration to its limitations.
The Disaster Risk Financing and Insurance Program—a
joint initiative of The World Bank Group’s Finance and
Markets Global Practice and the Global Facility for Disaster
Reduction and Recovery (GFDRR)—and The World Bank
Group’s Poverty and Equity Global Practice are grateful for
the financial support received from GFDRR and the U.K.
Department for International Development’s Humanitarian
Innovation and Evidence Programme.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
01
Table of Contents
Acknowledgements
05 Overview
09 Country V Case Study
15 Country W Case Study
21 Country X Case Study
27 Country Y Case Study
33 Country Z Case Study
39 Guidance Note
43 Country V Annexes
52 Country W Annexes
60 Country X Annexes
68 Country Y Annexes
73 Country Z Annexes
83 Glossary
02 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
List of Tables
9 Table V1.1 – Strategies Considered
10 Table V2.1 – Assumptions Summary - Base Parameters and Sensitivity Analysis
15 Table W1.1 – Strategies Considered
16 Table W2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis
21 Table X1.1 – Strategies Considered
22 Table X2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis
28 Table Y1.1 – Strategies Considered
28 Table Y2.1 – Key Assumptions Summary, Base Parameters and Sensitivity Analysis
31 Table Y4.2 – Sensitivity Analysis: Cheapest and Most Expensive Strategies by Return Period
33 Table Z1.1 – Strategies Considered
34 Table Z2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis
71 Table AY2.2 – Diagnostics of Insurance Pricing Assumptions, Base Case
72 Table AY3.1 – Diagnostics of Insurance Pricing Assumptions, Sensitivities
72 Table AY3.2 – Assumptions with Sensitivity Analysis Not Considered
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
03
List of Figures
11 Figure V3.1 – Relative Cost Saving of Strategy B and C Compared to A
11 Figure V3.2 – Cost of Finance Strategies, Base Case Assumptions
17 Figure W3.1 – Relative Cost Saving of Strategy B and C compared to A
17 Figure W3.2 – Cost of Finance Strategies, Base Case Assumptions
23 Figure X3.1 – Relative Cost Saving of Strategy B and C Compared to A
23 Figure X3.2 – Cost of Finance Strategies, Base Case Assumptions
29 Figure Y3.1 – Costs of Risk Transfer Strategies, Base Case Scenario Assumptions
30 Figure Y4.1 – Cost of Risk Transfer Strategies, Including Sensitivities
35 Figure Z3.1 – Relative Cost Saving of Finance Strategies, Base Case Scenario, Average Cost
36 Figure Z3.2 – Relative Cost Saving of Finance Strategies, 1 in 10 Year Return Period Loss
36 Figure Z3.3 – Relative Cost Saving of Finance Strategies, 1 in 30 Year Return Period Loss
37 Figure Z3.4 – Cost of Finance Strategies, Base Case Assumptions
43 Figure AV1.1 – Cumulative Distribution Function of the Poverty Cost Due to Drought
45 Figure AV3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions
46 Figure AV3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund
and Insurance Pricing Multiple
47 Figure AV3.3 – Marginal Cost as a Multiple of Loss – Sensitivity to the Post-Disaster Debt Delay
Factor and the Budget Reallocation Hurdle Rate
48 Figure AV4.1 – Relative Cost Saving of Strategies under Increased Reserve Fund
48 Figure AV4.2 – Total Cost of Increased Reserve Fund
49 Figure AV4.3 – Relative Cost Saving of Strategies under Increased Underlying Contingent Liability
50 Figure AV4.4 – Total Cost of Increased Underlying Contingent Liability
51 Figure AV4.5 – Relative Cost Saving of Strategies under Decreased Underlying Contingent Liability
51 Figure AV4.6 – Total Cost of Decreased Underlying Contingent Liability
52 Figure AW1.1 – Cumulative Distribution Function of the Poverty Cost Due to Flood
54 Figure AW3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions
55 Figure AW3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund
and Contingent Credit
56 Figure AW3.3 – Marginal Cost as a Multiple of Loss – Sensitivity to the Post-Disaster Debt Delay
Factor and the Insurance Multiple
57 Figure AW4.1 – Relative Cost Saving of Reduced Insurance Layer
04 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
57 Figure AW4.2 – Total Cost of Reduced Insurance Layer
58 Figure AW4.3 – Relative Cost Saving of Increasing Non-Insurance Layers
58 Figure AW4.4 – Total Cost of Increasing Non-Insurance Layers
60 Figure AX1.1 – Cumulative Distribution Function of the Yield Loss Due to All Perils
62 Figure AX3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions
63 Figure AX3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund
and budget Reallocation Hurdle Rate
64 Figure AX3.3 – Marginal Cost as a Multiple of Loss, Sensitivity to the Post-Disaster Debt Delay Factor
and the Insurance Multiple
65 Figure AX4.1 – Relative Cost Saving of Reduced Reserve Fund
65 Figure AX4.2 – Total Cost of Reduced Reserve Fund
67 Figure AX4.3 – Relative Cost Saving of Increased Reserve Fund
67 Figure AX4.4 – Total Cost of Increased Reserve Fund
68 Figure AY1.1 – Cumulative Distribution Function for Undiversified Total Payouts/Costs
69 Figure AY1.2 – Cumulative Distribution Functions for Pooled Cover (by Peril and in Aggregate)
73 Figure AZ1.1 – Cumulative Distribution Function of the Public Losses
76 Figure AZ3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions
78 Figure AZ3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund
and The Budget Reallocation
78 Figure AZ3.3 – Marginal Cost as a Multiple of Loss, Sensitivity to the Post-Disaster Debt Delay Factor
and the Insurance Multiple
79 Figure AZ3.4 – Marginal Cost as a Multiple of Loss, Sensitivity to the Contingent Credit Assumptions
80 Figure AZ4.1 – Relative Cost Saving of Reduced Insurance Layer
80 Figure AZ4.2 – Total Cost of Reduced Insurance Layer
81 Figure AZ4.3 – Relative Cost Saving of Increasing Non-Insurance Layers
81 Figure AZ4.4 – Total Cost of Increasing Non-Insurance Layers
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
05
Overview
The cost of disasters to governments, households, and of budgetary and financial instruments available to
businesses is increasing. Population growth, increasing governments and their development partners.2 The
concentration of assets, and climate change are increasing framework covers such instruments as:
exposure, hazards, and losses. Developing countries
• Risk transfer instruments including insurance,
typically lack financial protection against the impacts of
reinsurance, catastrophe swaps, and catastrophe bonds
these disasters and rely on ex-post measures (for example,
budget reallocations, donor assistance, tax increases, and • Reserves / ex-ante budget allocations
post-disaster loans) to attempt to meet financing needs.
• Contingent credit
Disaster risk finance is an important component of the
disaster risk management and climate change adaptation • Emergency ex-post budget reallocations
agenda. It aims to increase the financial resilience of
• Ex-post direct credit (post-disaster debt).
countries against natural hazards by strengthening public
financial management and promoting market-based disaster This framework has been designed for governments and
risk finance solutions (such as, sovereign catastrophe risk development partners to identify the most appropriate and
transfer solutions for governments or domestic catastrophe financially efficient strategies to fund disaster losses, based
risk insurance markets for public and private assets). on their country risk profile and political constraints. It uses
the economic notion of opportunity cost to quantify the
However, when designing disaster risk finance solutions,
costs and benefits of alternative instruments for funding
details matter. Catastrophe risk data and information lay
disaster-induced losses.
the ground for disaster risk finance solutions, but they
need to be processed in order to inform financial decision This report complements the more theoretical framework
making. Despite an increasing amount of disaster risk paper with a demonstration of how the framework can
data made available from historical databases on disaster be applied in practice. Five case studies illustrate a range
losses and catastrophe risk models, countries often lack of questions that policy makers might ask, potential
the capacity, resources, and experience to properly analyze instruments to be considered, and economic conditions, and
this information for informed financial decision making. a Guidance Note presents principles for such analyses.
Without such analysis governments do not have the
quantitative tools to evaluate: (i) whether the proposed The structure of the report is as follows: the proposed
instrument would offer effective financial protection framework is presented, outlining the approach of the
against natural disaster and how it would complement their opportunity-cost framework and its limitations. The five
existing strategy, if any, and (ii) whether the price of the case studies are introduced and the contingent liability
proposed instrument is cost-effective compared to other and finance strategies considered in each are outlined.
financial options. Subsequently, the five case studies are presented in five
chapters, each standalone with relevant annexes (including
To respond to this, the Disaster Risk Finance Impact at the back of the report). Finally, a Guidance Note outlines
Analytics Project developed a comprehensive framework how the framework may be applied in a practical manner to
for assessing the costs1 and benefits of the full range
1 Where there are references to costs, these refer to the opportunity cost of 2 Clarke, D. J., O. Mahul, R. Poulter, and T.-L. The. 2016. “Evaluating
providing the payouts defined in the contingent liability through the various Sovereign Disaster Risk Finance Strategies: A Framework.” Policy Research
financing instruments. Working Paper, The World Bank Group, Washington DC.
06 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
another country’s plans for the disaster risk financing of a The currency considered is US$ and all figures have been
contingent liability. Lastly, a Glossary is provided. approximately converted to US$ at average 2015 exchange
rates.
The purpose of the entire report is to illustrate how to apply
the framework to a country-specific question. All formulae
and calculations applied in these case studies follow those in
the technical framework paper.2 It does not aim to make any
Limitations of the Analysis
generalized conclusion about which finance mechanisms are The analysis makes multiple assumptions on disaster risk,
cheapest or how disaster risk finance should be structured. economic environment, and risk transfer instruments,
and focuses solely on a finance structure assuming perfect
knowledge of a contingent liability and a mechanism to
Introduction to Case Studies measure this contingent liability. The analysis is based on
the framework presented in Clarke et al. (2016) and is also
In order to demonstrate this framework in a practical
subject to the limitations of the framework.3
manner, this report presents five sample country case
studies as in the table below. The case studies are based on The analysis is based on information from various sources
real countries that are exposed to the perils described, but including World Bank country specialists and economic
the countries have been anonymized. The finance strategies information available online. Generally speaking, this
considered were selected to reflect questions that were information was of a high quality and broadly sufficient
being asked in the country at the time of writing. for the present purposes. Information received was both
quantitative (for example, modelled distribution of losses
Country Contingent Liability Considered Disaster Risk Finance Instruments Considered
Ex-ante Ex-ante Ex-ante Ex-post Ex-post debt
reserve contingent risk transfer budget (post-
(reserve credit (insurance) reallocation disaster debt)
fund) (contingent (budget
credit) reallocations)
Country V Country-wide response costs due
to drought
Country W Country-wide response costs due
to flood
Country X Insured losses of two main crops
in several areas due to multiple
perils
Country Y Insurance program covering
public emergency losses in
multiple regions of a country
due to earthquake and tropical
cyclone events
Country Z Public losses (emergency and
reconstruction) due to tropical
cyclone events
3 Clarke, D. J., O. Mahul, R. Poulter, and T.-L. Teh. 2016. "Evaluating
Sovereign Disaster Risk Finance Strategies: A Framework." Policy Research
Working Paper, The World Bank Group, Washington DC.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
07
from a particular peril) and qualitative (such as, description
of the potential insurance coverage that might be available
in the country). Where possible and relevant, sensitivity
analyzes on the assumptions resulting from this information
have been performed.
While the analysis provides a sufficient basis for comparing
the opportunity costs of financing instruments, its use has
limitations, including:
1. Dependence on assumptions: Each case study involves
multiple assumptions relating to the disaster risk
faced, the economic environment, and the risk transfer
instruments available.
2. Limited to financial structure: The analysis focuses only on
evaluating the opportunity cost of alternative disaster risk
finance strategies to finance a well-defined contingent
liability. The analysis does not consider whether or not an
investment should be made in the first place (that is, there
may be wider political considerations such that a country
is content to avoid planning and instead rely on aid from
donors following any disaster; this is not considered in this
report).
3. Financial considerations only: The focus is on the
monetary comparisons only and does not consider other
considerations that are more difficult to quantify, such as
the degree to which the instrument supports or requires
strong public financial management (for example, if a
country holds a sizable reserve fund to cover the most
extreme potential disasters, it may be at risk of being fully
spent on a small disaster due to political considerations).
4. Source of finance: There is no discrimination on the source
of the finance as this might come from the regional
government, national government, or development
partners. Only the total overall opportunity cost
is considered.
08 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
09
Country V Case Study
Following that, the results in the base case scenario
0. Country V – Introduction (Section 3) and sensitivity scenario (Section 4) are
0.1. Country V is a country in Africa vulnerable to drought. presented. Supporting diagrams and comments are
The contingent liability considered is defined as included for the underlying contingent liability (Annex
follows: V1), the base case assumptions (Annex V2), and the
sensitivity analysis (Annexes V3 and V4).
• Peril: Drought
• Country area: Whole country
1. Country V – Risk
• Contingent liability: The costs associated with
supporting vulnerable households in districts affected Finance Strategies
by drought. 1.1. The analysis for Country V looks at the cost of
0.2. The focus of the Country V case study is to consider the alternative finance strategies.
relative cost saving of different risk finance strategies 1.2. All of the finance strategies considered are assumed to
to cover government expenditures to support drought- sit on top of a reserve fund that is established to meet
affected households. The contingent liability being approximately the 1 in 1.3 year contingent liability4 (a
considered for Country V arises from the financial costs loss equal to US$50m). All strategies also assume that
of supporting the population that is estimated to have if the additional measure being considered is exhausted
fallen below the poverty line as a result of drought. then post-disaster debt will be issued by Country V.
0.3. This chapter is structured with results presented in The source of the funding has not been considered
the main body for three different strategies. First and the conclusions could apply to any combination of
the chapter sets out the risk finance strategies under government or donor funding.
consideration (Section 1) and the base assumptions 1.3. Table V1.1 outlines the three finance strategies
and approach used to assess the strategies (Section 2). considered for Country V.
Table V1.1 – Strategies Considered
Layer Strategy A Strategy B Strategy C
First Reserve fund Reserve fund Reserve fund
Post-disaster debt Insurance Budget reallocations
Post-disaster debt Post-disaster debt
Last
4 A 1 in 1.3 year financing cost refers to the cost to finance a loss with
a return period of 1.3 years, equivalent to a 77 percent probability of
occurrence. See Glossary for further details.
10 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
2. Country V – Approach Economic and risk transfer assumptions
and Assumptions 2.1. Key assumptions, base parameters, and sensitivity
analysis performed are summarized in Table V2.1 below.
Natural hazard assumptions
2.2. Further details on the sources of the base assumptions,
• A Pareto distribution has been fitted to the number as well as other parameters not material for sensitivity
of people falling below the poverty line as a result analysis, are outlined in Annex V2.
of drought.
• It is assumed that part of the population – those falling
below the poverty line even in years of adequate rainfall
3. Country V – Base Case
– is covered by an existing social protection program. Scenario Results
The contingent liability considers the costs of transitory
poverty due to drought only. 3.1. This section outlines the total costs for the three
strategies considered. Costs are shown at different
• It is assumed that supporting an affected individual costs return periods to highlight which strategies are
US$45 per person. cheapest at covering the average loss, loss events of a
lower magnitude, and more extreme loss events. For the
• From the fitted Pareto distribution, 5,000 drought events
Country V case study, the cost of the three strategies
have been simulated.
over the following return periods are considered:
• The simulated loss distribution is presented in Annex V1.
• On average
• 1 in 5 year return period
• 1 in 30 year return period.
Table V2.1 – Assumptions Summary - Base Parameters and Sensitivity Analysis
Assumption Base Parameter Sensitivity Analysis Reference
Amount of reserve fund US$50m Increase to US$132m (which is the Figure AV4.1 –
average expenditure) Figure AV4.2
Spread between interest rate 3% Increase the spread from 3% to 5% Figure AV3.2
& investment return (interest rate = 6.625%;
investment return = 3.625%) Reduce the spread from 3% to 1%
Maximum insurance 1 in 30 year (US$433m) Not considered
Insurance pricing multiple 1.35 Increase the insurance pricing Figure AV3.2
multiple from 1.35 to 2
Maximum amount of budget US$100m Not considered
reallocation
Budget reallocation hurdle 10% Increase to 20% and 40% Figure AV3.3
rate
Post-disaster debt delay factor 3 (US$1 now = US$3 post-event) Reduce the delay factor from 3 to 1.5 Figure AV3.3
Contingent liability Pareto distribution for the number Loss distribution increased by 25% Figure AV4.3 –
of people falling below the Figure AV4.6
poverty line as a result of drought Loss distribution reduced by 25%
Per person cost US$45 Not considered
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
11
3.2. Figure V3.1 presents the relative cost saving of 3.4. While Figure V3.1 compares the relative cost saving of
Strategies B and C compared to Strategy A, under the the strategies at different return periods, it does not
base assumptions on average and at the 1 in 5 and 1 in allow a direct comparison of the magnitude of the costs.
30 year return periods. Figure 3.2 shows the cost in monetary terms of the
different strategies at the different return periods.
3.3. For example, on average across the 5,000 simulations,
Strategy B is 43 percent cheaper than Strategy A.
Figure V3.1 – Relative Cost Saving of Strategy B and C Compared to A
100%
90% 87%
80%
Percentage cost decrease
(relative to Strategy A)
70% 66%
60%
50%
43% 43%
40%
31%
30%
20% 16%
10%
0%
B C B C B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure V3.2 – Cost of Finance Strategies, Base Case Assumptions
1,400
1,200
Total cost (US$m)
1,000
800
600
400
200
0
A B C A B C A B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Reserve Fund Insurance Budget reallocation Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016). Return period of loss
12 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
3.5. The main conclusions from the base case scenario as Sensitivity Results: Varying the Economic and
demonstrated in Figures V3.1 and V3.2 are: Financial Assumptions
• On average, Strategy B is the cheapest; insurance 4.2. A marginal cost analysis for each finance instrument is
is more cost-effective than post-disaster debt due used to demonstrate their features and benefits over
to the assumption of an insurance pricing multiple varying return periods. The marginal cost analysis in
of 1.35 compared to a delay factor of 3.0 on post- Annex V3 demonstrates the intuitive notion that as
disaster debt. the economic cost of a finance source increases, the
attractiveness of that source decreases, namely:
• On average, Strategy C is only marginally more
expensive than Strategy B. This is because although • Reserve funds are marginally the cheapest finance
the assumed budget reallocation hurdle rate of 10 instrument up to approximately the 1 in 2.1 year
percent is lower than the assumed insurance pricing return period.
multiple of 1.35, this is more than offset by the fact
that budget reallocation is exhausted (at US$100m) • After the 1 in 2.1 year return period, budget
at a lower level than insurance (at US$433m) and reallocation becomes the cheapest instrument.
hence more expensive post-disaster debt covers However, the marginal cost analysis ignores that
more of the losses. there might be a limit on the extent to which
government budgets can be reallocated.
• Note that the costs at the 1 in 5 year period are
higher than the average costs for all strategies. 4.3. The results indicated by the marginal costs analysis
This is because the average loss under the assumed are dependent on the financial and other assumptions
distribution is smaller than the 1 in 5 year loss. (See selected. If these assumptions are varied, the outcomes
Annex V1 for the assumed distribution of losses.) can be materially different. Sensitivity to economic
parameters for each of these finance instruments is also
• At higher return periods, the costs of Strategy B demonstrated in Annex V3. The results vary intuitively
are significantly lower than the costs of the other as the economic parameters are adjusted and the
strategies as losses are passed onto the insurer. following can be noted:
• Strategy A always has the greatest cost due to the • Increasing the assumed budget reallocation hurdle
relatively higher post-disaster delay factor costs rate reduces the cost benefit of budget reallocation.
compared to other finance instruments.
• Similarly, increasing the insurance pricing multiple
decreases the cost benefit gained from insurance.
4. Country V – Sensitivity Results • Adjusting the delay factor downward makes post-
disaster debt more attractive.
4.1. The Country V case study considers sensitivity
analysis to: • Increasing the spread between the investment and
borrowing rates increases the marginal cost of the
• The economic and financial assumptions used to
reserves as it increases the cost of holding reserve
derive the costs of the strategies
funds that may not be called on.
• The maximum amount of losses covered by the
different finance strategies.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
13
Sensitivity Results: Varying Maximum Funding 5. Country V – Concluding Remarks
by Finance Instrument
5.1. The most cost-effective strategy will depend on the
4.4. The results shown in the base case scenario are risk tolerance of policy makers. The analysis shows that
dependent on the amount of funding assumed to when considering drought events, losses that are of a
be available by each finance instrument and the lower impact and occur more frequently are likely to be
assumed loss distribution. Sensitivity to the size of the most cost-effectively financed by holding a reserve fund
reserve fund layer and underlying loss distribution is and reallocating from existing budgets.
demonstrated through examination of the total cost
analysis. The results vary intuitively with the following 5.2. Given the likely limitations on the amount of the
key results (see Annex V4 for details): reserve fund and the budget reallocation that will
be available, insurance is a cost-effective alternative.
• Increasing the size of the reserve fund decreases Insurance may result in an overall cheaper strategy as
the costs of all strategies as more losses are met by although it is marginally more expensive at lower return
the reserve fund, which is the most cost-effective periods, it can likely cover a greater layer of loss before
strategy at lower return periods. the most expensive post-disaster debt finance kicks in.
• Increasing the assumed losses increases the costs of 5.3. Additionally, strategies involving insurance are likely to
all strategies. It also reduces the cost-effectiveness be attractive at the higher return periods when losses
of the strategies if the size of the layers are are ceded to the insurer.
unchanged.
• Decreasing the assumed losses reduces the costs of
all strategies. It also increases the cost-effectiveness
of Strategies A and C as more losses are covered by
the reserve fund.
14 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
15
Country W Case Study
0. Country W – Introduction 1. Country W – Risk
0.1. Country W is a country in Africa vulnerable to flood. Finance Strategies
The contingent liability considered is defined as
1.1. The analysis for Country W looks at the cost of
follows:
alternative finance strategies.
• Perils: Flood
1.2. All of the finance strategies considered are assumed to
• Country area: Majority of the regions in the country sit on top of a reserve fund that is established to meet
approximately the 1 in 2.3 year contingent liability (a
• Contingent liability: Planned Government loss equal to US$100m). All strategies assume that if
social protection expenditures to support flood- the additional finacial instrument being considered
affected households. is exhausted then post-disaster debt will be issued by
0.2. The focus of the Country W case study is to consider Country W. The source of the funding has not been
the relative cost saving of different risk finance considered and the conclusions could apply to any
strategies to cover government expenditures to support combination of government or donor funding.
flood-affected households. The contingent liability 1.3. Table W1.1 outlines the three finance strategies
being considered for Country W arises from the considered for Country W.
financial costs of social protection transfers to flood-
affected households.
0.3. This chapter is structured with results presented in the 2. Country W – Approach and
main body for three different strategies. First the report
Assumptions
sets out the risk finance strategies under consideration
(Section 1) and the base assumptions and approach Natural hazard assumptions
used to assess the strategies (Section 2). Following
that, the results in the base case scenario (Section 3) • Based on over 30 years of historic data of the number of
and sensitivity scenario (Section 4) are presented. people in poverty due to flood.
Supporting diagrams and comments are included for
• Approximately 25 percent of historical years showed no-
the underlying contingent liability (Annex W1), the
one affected by flood. A 25 percent probability of nobody
base case assumptions (Annex W2) and the sensitivity
being affected by flood is therefore assumed.
analysis (Annexes W3 and W4).
Table W1.1 – Strategies Considered
Layer Strategy A Strategy B Strategy C
First Reserve fund Reserve fund Reserve fund
Post-disaster debt Insurance Contingent credit
Post-disaster debt Post-disaster debt
Last
16 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
• The remaining 75 percent of historical years have been 2.2. Further details on the sources of the base assumptions,
fitted to an exponential distribution with mean of 1.8m as well as other parameters not material for sensitivity
people affected (that is, when there is a flood, on average analysis, are outlined in Annex W2.
1.8m people are affected with flood events following an
exponential distribution).
• Combining the years in which people are affected and the
3. Country W – Base Case
years in which no-one is affected, the total mean number Scenario Results
of people in poverty is 1.35m. Monetary losses are derived
by multiplying the assumed number of people affected by 3.1. This section outlines the total costs for the three
a per person cost of US$100. strategies considered. Costs are shown at different
return periods, to highlight which strategies are
• The fit to the data is demonstrated in Annex W1. cheapest at covering the average loss, loss events of a
lower magnitude, and more extreme loss events. For the
Economic and risk transfer assumptions Country W case study, the cost of the three strategies
2.1. Key assumptions, base parameters, and sensitivity over the following return periods are considered:
analysis performed are summarized in Table W2.1.
Table W2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis
Assumption Base Parameter Sensitivity Analysis Reference
Amount of reserve US$100m Increase to US$150m Figure AW4.3
available – AW4.4
Spread between interest 10% Increase the spread from 10% to 15% Figure AW3.2
rate & investment return (interest rate = 13%;
investment return = 3%) Decrease the spread from 10% to 5%
Amount of contingent US$100m Increase to US$150m Figure AW4.3
credit available – AW4.4
Contingent credit interest 2.5% Increase to 5% Figure AW3.2
rate
Contingent credit facility 0.5% of maximum loan Not considered
arrangement fee amount
Maximum insurance 1 in 30 Not considered
(US$559m)
Proportion of losses 100% Decrease to 50% (with remainder covered by Figure AW4.1
ceded to insurance post-disaster debt) – AW4.2
Insurance pricing 1.5 Increase the insurance pricing multiple from Figure AW3.3
multiple 1.5 to 2
Post-disaster debt delay 3 (US$1 now = US$3 post- Reduce the delay factor from 3 to 1.4 Figure AW3.3
factor event)
Contingent liability Exponential distribution Not considered
for the number of people
affected by flood
Per person cost US$100 Not considered
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
17
• On average 3.3. While Figure W3.1 compares the relative cost saving of
the strategies at different return periods, it does not
• 1 in 5 year return period
allow a direct comparison of the magnitude of the costs.
• 1 in 30 year return period. Figure W3.2 shows the cost, in monetary terms of the
different strategies at the different return periods.
3.2. Figure W3.1 presents the relative cost saving of
Strategies B and C compared to Strategy A, under the 3.4. The main conclusions from the base case scenario as
base assumptions on average and at the 1 in 5 and 1 in demonstrated in Figures W3.1 and W3.2 are:
30 year return periods.
Figure W3.1 – Relative Cost Saving of Strategy B and C compared to A
100%
90% 85%
80%
Percentage cost decrease
(relative to Strategy A)
70%
59%
60%
50%
40%
40% 36%
30%
23%
20% 14%
10%
0%
B C B C B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure W3.2 – Cost of Finance Strategies, Base Case Assumptions
1,600
1,400
1,200
Total cost (US$m)
1,000
800
600
400
200
0
A B C A B C A B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Reserve Fund Contingent Credit Insurance Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
18 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
• On average, Strategy B is the cheapest; insurance is Sensitivity Results: Varying the Economic and
more cost-effective than post-disaster debt due to Financial Assumptions
the assumption of an insurance pricing multiple of
1.5 compared to a delay factor of 3 on post-disaster 4.2. A marginal cost analysis for each finance instrument is
debt. used to demonstrate their features and benefits over
varying return periods. The marginal cost analysis in
• Strategy C, although including contingent credit Annex W3 demonstrates the intuitive notion that as
financing which at lower return periods is more the economic cost of a finance source increases, the
cost-effective than insurance, is not cheaper than attractiveness of that source decreases, namely:
Strategy B because contingent credit covers only
a relatively small amount of loss. The remainder Reserves are marginally the cheapest finance
is financed by post-disaster debt, which drives the instrument (though contingent credit is only very
overall cost of Strategy C. marginally more expensive) up to approximately the 1
in 7 year return period, after which insurance becomes
• Note that the costs at the 1 in 5 year period are the cheapest instrument.
higher than the average costs for all strategies.
This is because the average loss under the assumed 4.3. The results indicated by the marginal costs analysis
distribution is smaller than the 1 in 5 year loss (see are dependent on the financial and other assumptions
Annex W1 for the assumed distribution of losses). selected. If these assumptions are varied the outcomes
can be materially different. Sensitivity to economic
• At higher return periods, the costs of Strategy B parameters for each of these finance instruments is also
are significantly lower than the costs of the other demonstrated in Annex W3.The results vary intuitively
strategies as finance costs are passed onto the as the economic parameters are adjusted and the
insurer. following can be noted:
• Strategy A always has the greatest cost due to the • Increasing the insurance pricing multiple decreases
relatively higher post-disaster delay factor costs the cost benefit gained from insurance.
compared to other finance instruments.
• Adjusting the post-disaster debt delay factor
downward makes post-disaster debt more attractive.
4. Country W – Sensitivity Results • Increasing the spread between the investment and
borrowing rates increases the marginal cost of the
4.1. The Country W case study considers sensitivity
reserves as it increases the cost of holding reserve
analysis to:
funds which may not be called on.
• The economic and financial assumptions used to
• Similarly, increasing the interest rate charged on
derive the costs of the strategies
contingent credit reduces the cost benefit of the
• The maximum amount of losses covered by the contingent credit.
different finance strategies.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
19
Sensitivity Results: Varying Maximum Funding 5. Country W – Concluding Remarks
by Finance Instrument
5.1. The most cost-effective strategy will depend on the
4.4. The results shown in the base case scenario are risk tolerance of policy makers. The analysis shows
dependent on the amount of funding assumed to be that when considering flood events, losses that are of a
available by each finance instrument. Sensitivity to the lower impact and occur more frequently are likely to be
size of the layers is demonstrated through examination most cost-effectively financed by holding reserves and
of the total cost analysis. The results (see Annex W4 contingent credit.
for details) vary intuitively as the amounts available
from each finance instruments are adjusted, with the 5.2. Given the likely limitations on the amount of reserves
following key results: and contingent credit that will be available, insurance
is a cost-effective alternative. Insurance may result in
• Decreasing the percentage of loss covered by an overall cheaper strategy as although it is marginally
insurance demonstrates that on average Strategy C, more expensive at lower return periods, it is assumed to
which includes contingent credit, is the cheapest. cover a greater layer of loss before the most expensive
This is due to the fact that the proportion in post-disaster debt finance kicks in.
Strategy B not ceded to insurance is covered by the
more costly post-disaster debt. 5.3. Additionally, strategies involving insurance are likely to
be attractive at the higher return periods when losses
• Increasing the amount of financing available from are ceded to the insurer.
reserves and contingent credit reduces the cost
savings of Strategies B and C (relative to Strategy
A) because more loses are met by reserves and
contingent credit which are both cheaper than post-
disaster debt.
20 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
21
Country X Case Study
consideration (Section 1) and the base assumptions
0. Country X – Introduction and approach used to assess the strategies (Section 2).
0.1. Country X is a country in Asia vulnerable to flood, Following that, the results in the base case scenario
drought, and other perils. The contingent liability (Section 3) and sensitivity scenario (Section 4) are
considered is defined as follows: presented. Supporting diagrams and comments are
included for the underlying contingent liability (Annex
• Perils: All natural perils affecting maize crops X1), the base case assumptions (Annex X2) and the
(flood, drought, tropical cyclone, pests) sensitivity analysis (Annexes X3 and X4).
• Country area: Three regions of the country
(covering less than 5 percent of the country’s
population) that are vulnerable to several perils and 1. Country X – Risk
rely heavily on the yield from maize produced in Finance Strategies
the regions
1.1. The analysis for Country X looks at the cost of
• Contingent liability: Insured losses (in US$) due to alternative finance strategies.
a reduction in yield from crop failure for two maize
varieties. 1.2. All of the finance strategies considered are assumed to
sit on top of a reserve fund that is established to meet
0.2. The focus of the Country X case study is to consider approximately the 1 in 2.5 year contingent liability (a
the relative cost saving of different risk finance loss equal to US$20m). All strategies also assume that
strategies to cover the insured losses from publicly- if the additional measure being considered is exhausted
supported maize insurance policies. The contingent then post-disaster debt will be issued by Country X.
liability being considered for Country X arises from the The source of the funding has not been considered
money that would be required if crop losses triggered and the conclusions could apply to any combination of
insurance payouts. government or donor funding.
0.3. This chapter is structured with results presented in 1.3. Table X1.1 outlines the three finance strategies
the main body for three different strategies. First considered for Country X.
the chapter sets out the risk finance strategies under
Table X1.1 – Strategies Considered
Layer Strategy A Strategy B Strategy C
First Reserve fund Reserve fund Reserve fund
Post-disaster debt Insurance Budget reallocations
Post-disaster debt Post-disaster debt
Last
22 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
2. Country X – Approach and 3. Country X – Base Case
Assumptions Scenario Results
Natural hazard assumptions 3.1. This section outlines the total costs for the three strategies
considered. Costs are shown at different return periods,
• Based on a third party model, which simulates the to highlight which strategies are cheapest at covering the
reduction in maize yields caused by all perils. average loss, loss events of a lower magnitude, and more
extreme loss events. For the Country X case study, the cost
• Yields are projected in the local currency for two types of
of the three strategies outlined above over the following
maize in each of the three regions considered.
return periods are considered:
• The distribution is based on 5,000 simulations of yield
• On average
loss.
• 1 in 5 year return period
• The corresponding yield loss cost is converted to US$
using average recent exchange rates. • 1 in 30 year return period.
• The simulated loss distribution is demonstrated in Annex 3.2. Figure X3.1 presents the relative cost savings of
X1. Strategies B and C compared to Strategy A, under the
base assumptions.
Economic and risk transfer assumptions
3.3. While Figure X3.1 compares the relative cost saving of
2.1. Key assumptions, base parameters, and sensitivity
the strategies at different return periods, it does not
analysis performed are summarized in Table X2.1 below:
allow a direct comparison of the magnitude of the costs.
2.2. Further details on the sources of the base assumptions, Figure X3.2 shows the cost, in monetary terms of the
as well as other parameters not material for sensitivity different strategies at the different return periods.
analysis, are outlined in Annex X2.
Table X2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis
Assumption Base Parameter Sensitivity Analysis Reference
Amount of reserve US$20m Decrease to US$10m Figure AX4.1 –
available Increase to US$30m Figure AX4.4
Spread between interest 2% Increase the spread from 2% to 4% Figure AX3.2
rate & investment return (interest rate = 5%;
investment return =
3%)
Maximum insurance 1 in 30 Not considered
(US$52.4m)
Insurance pricing multiple 1.35 Increase the insurance pricing multiple from 1.35 to 2 Figure AX3.3
Amount of budget US$20m Not considered
reallocation
Budget reallocation 20% Decrease to 10% Figure AX3.2
hurdle rate
Increase to 40%
Post-disaster debt 3 (US$1 now = US$3 Increase the delay factor from 3 to 5 Figure AX3.3
delay factor post-event) Reduce the delay factor from 3 to 1.5
Contingent liability Third party model of Not considered
reduction in maize yields
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
23
Figure X3 .1 – Relative Cost Saving of Strategy B and C Compared to A
100%
90%
80% 77%
Percentage cost decrease
(relative to Strategy A)
70%
60%
50% 46%
40% 37%
32%
30% 27% 26%
20%
10%
0%
B C B C B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure X3.2 – Cost of Finance Strategies, Base Case Assumptions
140
120
Total cost (US$m)
100
80
60
40
20
0
A B C A B C A B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Reserve Fund Insurance Budget reallocation Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
24 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
3.4. The main conclusions from the base case scenario as Sensitivity Results: Varying the Economic and
demonstrated in Figures X3.1 and X3.2 are: Financial Assumptions
On average, Strategy B is the cheapest; insurance is
• 4.2. A marginal cost analysis for each finance instrument is
more cost-effective than post-disaster debt due to the used to demonstrate their features and benefits over
assumption of an insurance pricing multiple of 1.35 varying return periods. The marginal cost analysis in
compared to a delay factor of 3.0 on post-disaster debt. Annex X3 demonstrates the intuitive notion that as
the economic cost of a finance source increases, the
• On average, Strategy C is only marginally more
attractiveness of that source decreases, namely:
expensive than Strategy B. This is because although
the assumed hurdle rate of 20 percent is lower than • Reserves are marginally the cheapest finance
the assumed insurance pricing multiple of 1.35, this is instrument up to approximately the 1 in 8.5 year
more than offset by the fact that budget reallocation return period.
is exhausted (at US$40m) at a lower level than
insurance (at US$52.4m) and hence more expensive • After the 1 in 8.5 year return period, budget
post-disaster debt covers more of the losses. reallocation becomes the cheapest instrument.
However, the marginal cost analysis ignores that
• Note that the costs at the 1 in 5 year period are there might be a limit on the extent to which
higher than the average costs for all strategies. government budgets can be reallocated.
This is because the average loss under the assumed
distribution is smaller than the 1 in 5 year loss (see 4.3. The results indicated by the marginal costs analysis
Annex X1 for the assumed distribution of losses). are dependent on the financial and other assumptions
selected. If these assumptions are varied, the outcomes
• At higher return periods, the costs of Strategy B can be materially different. Sensitivity to economic
are significantly lower than the costs of the other parameters for each of these finance instruments is also
strategies as finance costs are passed onto the insurer. demonstrated in Annex X3. The results vary intuitively
as the economic parameters are adjusted and the
• Strategy A always has the greatest cost due to the
following can be noted:
relatively higher post-disaster delay factor costs
compared to other finance instruments. • Increasing the assumed hurdle rate for budget
reallocation reduces the cost benefit of budget
reallocation.
4. Country X – Sensitivity Results
• Similarly, increasing the insurance pricing multiple
4.1. The Country X case study considers sensitivity decreases the cost benefit gained from insurance.
analysis to:
• Adjusting the delay factor downward makes post-
• The economic and financial assumptions used to disaster debt more attractive.
derive the costs of the strategies
• Increasing the spread between the investment and
• The maximum amount of losses covered by the borrowing rates increases the marginal cost of the
different finance strategies. reserves as it increases the cost of holding reserve
funds which may not be called on.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
25
Sensitivity Results: Varying Maximum Funding
by Finance Instrument
4.4. The results shown in the base case scenario are
dependent on the amount of funding assumed to be
available by each finance instrument. Sensitivity to
the size of the reserve layer is demonstrated through
examination of the total cost analysis. The results (see
Annex X4 for details) vary intuitively as the reserve is
adjusted, with the following key results:
• Decreasing the size of the reserve fund increases the
costs of all strategies as fewer losses are met by the
reserves which is the most cost-effective strategy at
lower return periods.
• Increasing the size of the reserve fund decreases
the costs of all strategies as more losses are met by
the reserves, and is the most cost-effective strategy
at lower return periods. If the reserve is increased
to US$30m then Strategy A becomes the cheapest
strategy at lower return periods.
5. Country X –
Concluding Remarks
5.1. The most cost-effective strategy will depend on the
risk tolerance of policy makers. The analysis shows that
when considering maize losses due to multiple perils,
losses which are of a lower impact and occur more
frequently are likely to be most cost-effectively financed
by holding reserves.
5.2. Budget reallocation is assumed to have the lowest
marginal cost at the higher loss events. However, there
may be a limit on the extent to which government
budgets can be reallocated. As a result, strategies
involving insurance are likely to be attractive,
particularly at the higher return periods when losses are
ceded to the insurer.
26 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
27
Country Y Case Study
function of wind speed (tropical cyclone coverage) and
0. Country Y – Introduction ground acceleration (earthquake coverage). The model
0.1. Country Y is a country with a large diversified economy has been designed to try to proxy emergency losses
and has regions that have very high recurrent risk of incurred by the government in the local regions.
disasters from both earthquakes and tropical cyclones.
Insurance payouts
0.2. Thirteen regions in Country Y are assumed to have
• The insurance contract has a two-step payout
selected parametric insurance coverage for earthquake
function with defined partial and full payouts.
and tropical cyclone risk, with claim payments based
on modelled loss, as determined by a pre-agreed • The attachment point (trigger point) for partial
catastrophe risk model. payouts is the 1 in 10 year emergency loss. Partial
payouts are assumed to be US$16m across
0.3. The focus of the Country Y case study is to evaluate the
tropical cyclone and earthquake (allocated either
costs of potential disaster risk finance structures that
US$8m/$8m if the risk of losses from each peril is
could provide the desired insurance coverage, where
considered roughly equal or US$12m/$4m if the
regions either act independently or work together in
region is more vulnerable to tropical cyclone).
different ways.
• The attachment point for full payouts is the 1 in 30
0.4. This case study is structured with results presented in
year emergency loss. Full payouts are assumed to
the main body for two main scenarios – the base case
be US$40m across tropical cyclone and earthquake
scenario and the sensitivity scenario. The case study is
(allocated either US$20m/$20m or US$30m/$10m
structured as follows. First the risk finance strategies
under the same rationale as the partial payouts.
(Section 1) and relevant assumptions (Section 2) are
outlined. Then the results in the base case scenario • More than 1 partial payout can be made in a year
(Section 3) and sensitivity scenario (Section 4) are subject to a maximum annual payout equal to the
presented. Supporting diagrams and comments are full payout.
included for the underlying contingent liability (Annex
Y1), the base case assumptions (Annex Y2) and the 1.2. The contingent liability considered in the opportunity
sensitivity analysis (Annex Y3). cost analysis are the cumulative insurance payouts (or
costs) for all individual insurance policies (for the 13
regions) as defined above.
1. Country Y – Risk 1.3. Three alternative insurance placement arrangements
Finance Strategies with different pooling mechanisms were considered as
outlined in Table Y1.1.
1.1. The analysis for Country Y looks at the cost of
financing regional insurance policies through
alternative insurance placement arrangements (see
Table Y1.1). The underlying insurance contracts are
parametric in nature with insurance premiums and
payouts defined through a catastrophe risk model as a
28 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Table Y1.1 – Strategies Considered
Insurance Strategy A Insurance Strategy B Insurance Strategy C
Individual insurance Regions jointly approach the Regional Insurance Facility
contracts for each region. reinsurance market with a
portfolio of region-specific Regions establish a catastrophe risk insurance facility, acting
insurance policies. as a joint reserve mechanism, where smaller payouts are
retained through reserves and excess losses are transferred
to the reinsurance market.
Retention level (smaller losses)
Up to first 1 in 10 year aggregate loss of the portfolio
Reinsurance (excess losses)
All losses beyond the 1 in 10 year aggregate loss of the portfolio
2.2. The base case scenario assumptions and sensitivity
2. Country Y – Approach and
analysis performed on these are outlined below in Table
Assumptions 2.1, with supporting detail in Annex Y2. All sensitivity
analyses are presented in section 4 with supporting
Natural hazard assumptions detail in Annex Y3.
2.1. The analysis is based on 10,000 simulated years of
emergency losses caused by tropical cyclone and
earthquake events across 13 regions, many of which
years have multiple events. On average, there are a total
of 3.4 events per year per region. The average tropical
cyclone impacts 3.8 regions and the average earthquake
impacts 2.1 regions.
Table Y2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis
Assumption Base Parameter Sensitivity Analysis
Strategy A pricing multiple 1.64 N/A
Strategy B pricing multiple 1.47 (= 90% * 1.64) where there 1.31 (= 80% * 1.64) where there is a 20%
is a 10% diversification benefit diversification benefit compared to
compared to Strategy A Strategy A
Strategy C Pricing multiple (paid for excess 2.0 Decrease to 1.47 for comparison against
losses above the first 1 in 10 year event in a Strategy B
year for Strategy C)
Spread between interest rate & investment 0% Increase the spread from 0% to 5%
return (interest rate = 4%;
investment return = 4%)
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
29
• On average, the cost of Strategy C is lower than
3. Country Y – Base Case
Strategy A and B. This is because on average, it is
Scenario Results cheaper to finance the cost of the relevant payouts
through a reserve fund (with no charge applied)
3.1. Figure Y3.1 presents the costs of the three risk transfer
than to pay a pricing premium (through a pricing
strategies at various return periods in the base case
multiple) for insurance placement.
scenario assumptions.
• For greater payouts at the 1 in 5 year return and
3.2. The cost of Strategy B is always lower than Strategy A,
beyond, the cost of Strategy C becomes higher than
due to the diversification benefit in Strategy B. Strategy
Strategy A and B, since the payouts retained increase
A and B have all underlying assumptions identical
and have to be financed by the reserve funds.
except Strategy B has a diversification benefit of 10
percent (decreasing the cost) and a market fee of 2.5 • Beyond the 1 in 10 year return period, Strategy C
percent (increasing the cost). The result is a constant cost levels off because only up to the 1 in 10 year
net decrease at all return periods in the cost of Strategy payout is retained in the reserve fund, as defined in
B compared to Strategy A. the mechanism for Strategy C.
3.3. The cost of Strategy C is driven by the cost of risk
retention. In the base case scenario, there is no
foregone investment return on reserve funds held since
4. Country Y – Sensitivity Results
the investment return is assumed to be equal to the 4.1. Figure Y4.1 presents the costs of the three risk transfer
discount rate, and the cost of financing the retained strategies at various return periods in the base case
payouts is equal to the retained payouts themselves at scenario, as well as the following sensitivity scenarios:
all return periods:
Figure Y3.1 – Costs of Risk Transfer Strategies, Base Case Scenario Assumptions
120
Strategy A
100
Strategy B
80
Strategy C - risk retention
60
Strategy C -
40 reinsurance (premium)
20
0
Average 1 in 3 1 in 5 1 in 10 1 in 50
Source: Clarke, Cooney, Edwards, and Jinks (2016).
30 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
• Increasing the Strategy B diversification benefit 4.4. For payouts at the 1 in 3 year return period, the results
from 10 percent to 20 percent are dependent on the sensitivities:
• Reducing the Strategy C pricing multiple from 2.0 to • Strategy C is again the cheapest if the spread
1.47 between investment return and discount rate is
zero, but Strategy B with a greater diversification
• Increasing the spread (between the interest rate and
benefit is only marginally more expensive.
investment return) from 0 percent to 5 percent for
Strategy C retained risk. • If Strategy C is considered with a greater spread (of
5 percent), then it becomes the most expensive, with
4.2. Annex Y3 outlines the rationale for selecting these
a greater cost than Strategy A and B.
sensitivities and presents the resulting diagnostics
(pricing multiples and risk volatility factors) for each 4.5. For higher payouts at or greater than the 1 in 5 year
strategy as a comparison. return period, Strategy B with a greater diversification
benefit has a significantly cheaper cost than any other
4.3. On average, Strategy C is the cheapest strategy if the
strategy. A summary of the cheapest, second cheapest,
spread between the investment return and discount rate
and most expensive strategies is presented in Table Y4.2.
is kept minimal. This is consistent with the conclusions
in the base case scenario, where on average it is cheaper
to finance the cost of the relevant payouts through a
reserve fund (with no charge applied) than to pay a pricing
premium (through a pricing multiple) for insurance
placement. However, when a spread is introduced such
that there is a charge on the reserves held, Strategy C
becomes more expensive than Strategy B.
Figure Y4.1 – Cost of Risk Transfer Strategies, Including Sensitivities
120
Strategy A
100 Strategy B
Strategy B w/ greater diversi ication
80
Strategy C w/ greater spread
60
Strategy C - risk retention
40
Strategy C - reinsurance (premium)
20
0 Strategy C w/ lower pricing multiple
Average 1 in 3 1 in 5 1 in 10 1 in 50
Source: Clarke, Cooney, Edwards, and Jinks (2016).
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
31
Table Y4.2 – Sensitivity Analysis: Cheapest and Most Expensive Strategies by Return Period
Average 1 in 3 1 in 5 and greater
Strategy A Most expensive
Strategy B Second cheapest
Strategy B w/ greater diversification Only marginally more Cheapest
expensive than Strategy C
Strategy C Second cheapest Second cheapest Overall Strategy C is more
Strategy C w/ lower pricing multiple Cheapest Cheapest expensive than Strategy A and B
beyond the 1 in 5 year return period,
Strategy C w/ greater spread Most expensive under all sensitivities considered
Source: Clarke, Cooney, Edwards, and Jinks (2016).
5. Country Y –
Concluding Remarks
5.1. Strategy C, which includes a portion of risk retention, is
cheapest on average due to the low or non-existent cost
charge on the reserves required to fund the retained
level of payout (compared to the pricing premium
charge of placing insurance coverage).
5.2. The greater the diversification benefit that can be
achieved in Strategy B and the greater the charge
(spread) on the reserves held for Strategy C, the lower
the payouts at which Strategy B will become the most
cost-effective strategy. This likely happens at some
point between payouts at the 1 in 3 year and the 1 in 5
year return period.
5.3. The most cost-effective strategy will depend on the
risk tolerance of policy makers. If the focus is on losses
at lower return periods, or a long-term average cost,
retaining a layer of payouts as in Strategy C may be the
optimal choice. For increasingly greater payouts and
when considering catastrophic tail risk, Strategy B is
likely the most cost-effective strategy beyond the 1 in 5
year payout.
32 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
33
Country Z Case Study
used to assess the strategies (Section 2). Following
0. Country Z – Introduction that, the results in the base case scenario (Section 3)
• Country Z is a small island developing state, with the and sensitivity scenario (Section 4) are presented.
entire country vulnerable to the damage caused by Supporting diagrams and comments are included for
tropical cyclones. the underlying contingent liability (Annex Z1), the base
case assumptions (Annex Z2) and the sensitivity analysis
• The focus of the Country Z case study is to consider the (Annexes Z3 and Z4).
relative cost saving of different risk finance strategies
to cover the losses caused by tropical cyclones. The
contingent liability being considered for Country Z is the 1. Country Z – Risk
required public expenditure to finance reconstruction of
public capital infrastructure destroyed or damaged due to Finance Strategies
tropical cyclones.
• The analysis for Country Z looks at the cost of alternative
• Since the primary focus of the analysis is in assessing the finance strategies.
relative costs and benefits of the finance strategies, this
• All of the finance strategies considered are assumed to
case study assumes that government finance strategies
sit on top of a reserve fund that is established to meet
are exhausted at the 1 in 50 year return period. Beyond
approximately the 1 in 6 year contingent liability (a loss
this point, it is assumed that donor support would be
equal to roughly 0.2 percent of GDP or US$25m). All
provided, and rather than model this cost that would be
strategies also assume that if the additional measure
the same in all strategies, the contingent liability losses
being considered is exhausted then post-disaster debt will
are capped at the 1 in 50 year return period.
be issued by Country Z.
• This chapter is structured with results presented in the
• The alternative strategies and finance instruments
main body for four different strategies. First the report
considered for Country Z analysis are summarized in
sets out the risk finance strategies under consideration
Table 2.1 below.
(Section 1) and the base assumptions and approach
Table Z1.1 – Strategies Considered
Layer Strategy A Strategy B Strategy C Strategy D
First Reserve fund Reserve fund Reserve fund Reserve fund
↓ Post-disaster debt Insurance Budget reallocations Contingent credit
Post-disaster debt Post-disaster debt Post-disaster debt
Last
34 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
• Public capital losses have been capped at the 1 in 50 year
2. Country Z – Approach and
return period (approximately US$300m or 2.5 percent of
Assumptions GDP). Losses beyond this magnitude are assumed to be
financed by donor support in any finance strategy – the
Natural hazard assumptions cost of this donor support would be consistent for all
• The analysis is based on 10,000 simulated years of losses strategies and is excluded from this analysis.
caused by tropical cyclone events across the entire
Economic and risk transfer assumptions
country. These simulated losses were extrapolated from
an extract of return period losses from a third-party 2.1. Key assumptions, base parameters, and sensitivity
catastrophe modelling report. Annex Z1 includes further analysis performed are summarized in Table Z2.1:
detail on the underlying distribution of losses.
2.2. Further details on the sources of the base assumptions,
• Since our analysis is only interested in public capital as well as other parameters not material for sensitivity
losses, it is assumed that 30 percent of the losses are analysis, are outlined in Annex Z2.
public capital losses, in line with the proportion of
exposure assumed to be public capital in the underlying
catastrophe model.
Table Z2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis
Assumption Base Parameter Sensitivity Analysis Reference of
Where Results
Are Presented
Reserve fund US$25m Double the maximum to US$50m Figure AZ4.3 –
maximum Figure AZ4.4
Spread between 3% Increase in the spread from 3% to 5% Figure AZ3.2
interest rate & (interest rate = 6.75%; Decrease in the spread from 3% to 1%
investment return investment return = 3.75%)
Contingent credit US$30m Double the maximum to US$60m Figure AZ4.3 –
maximum Figure AZ4.4
Contingent credit 2.5% interest on used funds, 0.5% Consider reduced interest (1%) Figure AZ3.4
arrangements arrangement fee
Insurance 1 in 30 year loss 1 in 15 year loss Figure AZ4.1 –
maximum limit Figure AZ4.2
Risk volatility 25% (broadly equivalent to an Decrease to 12.5% (multiple of 1.4) and Figure AZ3.3
loading insurance pricing multiple of 1.85) increase to 45% (multiple of 2.5)
Amount of budget US$100m Double the maximum to US$200m Figure AZ4.3 –
reallocation Figure AZ4.4
Budget 37% Decrease to 10% and increase to 50% Figure AZ3.2
reallocation hurdle
rate
Post-disaster debt 18.4%, based on underlying Increase to 38% (equivalent to a post- Figure AZ3.3
delay factor assumptions outlined in Annex Z2 disaster borrowing rate of 8%, rather
than 6.75% ex ante rate)
Contingent liability Third party model of losses caused Not considered
by tropical cyclone events
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
35
3.2. Figures Z3.1, Z3.2, and Z3.3 show the cost savings of
3. Country Z – Base Case
Strategies B, C, and D relative to Strategy A. In other
Scenario Results words, they show the relative cost saving or cost from
having a finance instrument that sits between the
3.1. This section outlines the total costs for the four
reserve fund and Country Z’s post-disaster debt.
strategies considered. Costs are shown at different
return periods, to highlight which strategies are 3.3. Figure Z3.1 presents the relative cost savings of
cheapest at covering the average loss, loss events of a Strategies B, C, and D on average, under the base
lower magnitude, and more extreme loss events. For assumptions.
the Country Z case study, the cost of the four strategies
outlined above over the following return periods
are considered:
• On average
• 1 in 10 year return period
• 1 in 30 year return period.
Figure Z3 .1 – Relative Cost Saving of Finance Strategies, Base Case Scenario, Average Cost
50% • The average cost of Strategy B (insurance) is around 30
Percentage cost decrease (increase) relative to Strategy A
percent higher than the average cost of Strategy A. This is
40%
because the insurance premium payable covers for higher
30% loss scenarios.
20% • The average cost of Strategy C (budget reallocation) is
around 3 percent higher than the average cost of Strategy
10%
A. This is because the hurdle rate is higher than the
-29% -3% 1%
0% assumed cost of post-disaster debt.
-10% • The average cost of Strategy D (contingent credit) is
around 1 percent lower than the average cost of Strategy
-20% A. This is because the contingent credit interest rate is
-30%
lower than the government borrowing rate.
-40%
-50%
B C D
Average
Source: Clarke, Cooney, Edwards, and Jinks (2016).
36 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Figure Z3 .2 – Relative Cost Saving of Finance Strategies, 1 in 10 Year Return Period Loss
50% 3.4. Figures Z3.2 and Z3.3 demonstrate the same analysis at
Percentage cost decrease (increase) relative to Strategy A
the 1 in 10 and 1 in 30 return periods.
40%
• At the 1 in 10 return period, Strategies B, C, and D do
30%
not require post-disaster debt to be issued because
20% the finance instrument are sufficient to meet the
losses.
10% 6%
1% -4% • Strategy B starts to appear cheaper (relative to
0%
Strategy A) as the size of the premium relative to the
-10% size of the loss reduces.
-20% • The cost of Strategy C (with budget reallocation)
continues to be the higher than Strategy A because
-30%
of the high hurdle rate.
-40%
• The cost of Strategy D (with contingent credit)
-50% is the cheapest because of the relatively low
B C D contingent credit interest rate.
1 in 10 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure Z3 .3 – Relative Cost Saving of Finance Strategies, 1 in 30 Year Return Period Loss
90% • For greater losses at higher return periods, Strategy B is
Percentage cost decrease (increase) relative to Strategy A
81%
80% significantly (at the 1 in 30 year, 81 percent) cheaper than
70% other strategies because a significant proportion of the
60% large losses are ceded to the insurer.
50% • Strategy C (with budget reallocation) has the highest cost
40% because of the high hurdle rate.
30%
• The cost of Strategy D (with contingent credit) is slightly
20%
lower than the costs of Strategies A and C because of the
10%
2% relatively low contingent credit interest rate.
-4%
0%
-10%
-20%
-30%
-40%
-50%
B C D
1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
37
Figure Z3.4 – Cost of Finance Strategies, Base Case Assumptions
300
250
Total cost (US$m)
200
150
100
50
0
A B C D A B C D A B C D
Average 1 in 10 year return period of loss 1 in 30 year return period of loss
Reserve Fund Contingent Credit Insurance Budget reallocation Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
3.5. While Figures Z3.1, Z3.2, and Z3.3 compare the relative
4. Country Z – Sensitivity Results
cost saving of the strategies at different return periods,
it does not allow a direct comparison of the magnitude 4.1. Country Z case study considers sensitivity analysis to:
of the costs. Figure Z3.4 shows the cost, in monetary
• The economic and financial assumptions used to
terms of the different strategies at the different return
derive the costs of the strategies
periods.
• The maximum amount of losses covered by the
3.6. The main conclusions from the base case scenario are:
different finance strategies.
• The costs of Strategy B (insurance) are highest
at lower return periods because the insurance Sensitivity Results: Varying the Economic and
premium exceeds the average loss (which is roughly Financial Assumptions
at the 1 in 7 year return period).
4.2. A marginal cost analysis for each finance instrument is
• At higher return periods, the costs of Strategy B used to demonstrate their features and benefits over
are significantly lower than the costs of the other varying return periods. The marginal cost analysis in
strategies as losses are passed onto the insurer. Annex Z3 demonstrates the intuitive notion that as
the economic cost of a finance source increases, the
• Strategy C always has the greatest cost due to the attractiveness of that source decreases, namely:
relatively higher budget reallocation costs compared
to other finance instruments. • Reserves are marginally the cheapest finance
instrument up to approximately the 1 in 7.6 year
• At the return periods shown, the cost of Strategy D return period, after which post-disaster debt
is lower than the cost of Strategies A and C because becomes the cheapest instrument.
the assumed interest rate of contingent credit is
much lower than the costs associated with budget 4.3. The results indicated by the marginal costs analysis
reallocation or post-disaster debt issuance. are dependent on the financial and other assumptions
38 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
selected. If these assumptions are varied the outcomes
5. Country Z –
can be materially different. Sensitivity to economic
parameters for each of these finance instruments is also Concluding Remarks
demonstrated in Annex Z3. The results vary intuitively
5.1. The analysis shows that when considering tropical
as the economic parameters are adjusted and the
cyclone events, losses which are of a lower impact
following can be noted:
and occur more frequently are likely to be most cost-
• Increasing the insurance risk volatility loading effectively financed by contingent credit. However,
decreases the cost benefit gained from insurance. there is unlikely to be sufficient contingent credit
available to provide cover for larger losses and hence
• Increasing the delay factor makes post-disaster debt post-disaster debt is likely to be required.
less attractive.
5.2. Post-disaster debt is assumed to have the lowest
• Increasing the spread between the investment and marginal cost at the higher loss events. However,
borrowing rates increases the marginal cost of the strategies with insurance attaching at a lower return
reserves as it increases the cost of holding reserve period had a much lower total cost – reflecting the fact
funds which may not be called on. that using insurance results in losses being ceded to the
• Similarly, increasing the interest charged on insurer.
contingent credit reduces the cost benefit of the 5.3. The most cost-effective strategy will depend on the
contingent credit. risk tolerance of policy makers and realistic amounts
• Decreasing the budget reallocation hurdle rate available from each financial instrument. In practice,
increases the cost-effectiveness of the budget the government may wish to combine insurance with
reallocation layer. another instrument such that only a percentage of
the layer is ceded out for reinsurance, and the rest is
Sensitivity Results: Varying Maximum Funding financed through other instruments. The impact of only
by Finance Instrument ceding a percentage of the layer would be similar to that
of reducing the insurance exhaustion point.
4.4. The results shown in the base case scenario are
dependent on the amount of funding assumed to be
available by each financial instrument. Sensitivity to the
size of the layers is demonstrated through examination
of the total cost analysis. The results (see Annex Z4
for details) vary intuitively as the amounts available
from each financial instrument are adjusted, with the
following key results:
• Increasing the amount of financing available from
reserve and budget instruments reduces the cost at
higher return periods because fewer finance costs
are met by budget reallocation and post-disaster
debt, which are typically more expensive.
• Decreasing the exhaustion point (maximum loss
covered) of insurance demonstrates that at higher
return periods, post-disaster debt is now required,
hence increasing the total cost.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
39
Guidance Note
The purpose of this Guidance Note is to give guidance • Contingent credit
on the steps that should normally be taken to conduct
• Emergency ex-post budget reallocations
an evaluation of alternative of sovereign disaster risk
finance strategies. This note should be read in conjunction • Ex-post direct credit (borrowing/ post-disaster debt)
with the formulae and descriptions in the World Bank
Policy Research Working Paper, “Evaluating Sovereign Define which instruments will act to finance the contingent
Disaster Risk Finance Strategies: A Framework,” by D.J. liability, in which order, and to what extent.
Clarke, O. Mahul, R. Poulter, and T.-L. Teh (hereafter, the
• The minimum and maximum point at which each
Framework Paper).
instrument will finance the liability, as well as the total
maximum funding available from each instrument should
be defined.
1. Define Contingent Liability
• The source of the financing may be from national or
Define the expenditures (or losses) that would be financed subnational government, or from development partners.
by government and/or development partners in the Any application of the framework should include a
aftermath of potential future natural disasters (for example, suitable caveat about how much reliance can be placed
tropical cyclones, earthquakes, floods, droughts). on the results by a government if the funding sources
The underlying expenditures considered should have a clear is unspecified.
element of uncertainty and a way to probabilistically model • One of the instruments will require an assumption that it
this uncertainty through a set of simulated expenditures. is unlimited so that the entire contingent liability can be
Typically expenditures are simulated over a 12 month fully financed. This is usually assumed to be post-disaster
period, to coincide with agricultural or tropical cyclone debt.
seasons, or the annual budgeting period of government.
This data on simulated expenditures might come from a Each combination of one or more instruments that in
natural catastrophe model, from a distribution fitted to aggregate can precisely finance the entire contingent
historic loss data, or from other sources. The contingent liability is then considered a strategy. Typically comparing
liability being considered for financing could be a truncation three to four overall strategies yields the most insight
or a layer of the underlying expenditures (losses). without introducing too many considerations or
assumptions.
2. Define Finance Strategies
3. Set Base Assumptions
and Layers
Assumptions about the economic and
Select potential financial instruments to be considered and
commercial environment
in which combination, such as:
• Interest rates (that is, borrowing rates) should normally
• Risk transfer instruments including insurance,
be taken to be consistent with market-implied interest
reinsurance, catastrophe swaps, and catastrophe bonds
rates for sovereign debt, consistent with the currency
• Reserves / ex-ante budget allocations
40 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
used for analysis (that is, for analysis in US$, Eurobond
4. Calculate Results under
debt rates issued in US$ should be used).
Base Assumptions
• The discount rate used to discount costs incurred in
the future into present day terms should normally be
chosen to equal the marginal interest rate on pre-disaster Calculate the opportunity cost for each strategy for each
sovereign debt. simulation of the contingent liability:
• The investment return on undisbursed contingency funds • Refer to the Framework Paper for formulae to calculate
or budgets should normally be chosen to be consistent the opportunity cost of each financial instrument
with the asset classes the funds or budget lines are depending on the quantum of the layer financed by the
invested in. This is expected to be lower than the market- instrument. These formulae may be adjusted where
implied interest rate. appropriate, for example, to allow for a different rule of
thumb for pricing risk transfer instruments.
• The hurdle rate of return for projects that would have
funding cut in the case of budget reallocations can be • Demonstrating the savings of certain alternative
taken from any government rules on the social rate of strategies compared to a base strategy is a helpful way to
return required on projects, or other economic studies present results.
of the internal rate of return of public expenditure.
• This will typically be for 10,000 or more simulated
The hurdle rate may vary for different tranches of
annual expenditures; however, 5,000 simulations is likely
reallocations (that is, the first few US$m of reallocations
sufficient to consider lower return periods.
might be subject to a lower hurdle rate than the next few
US$m). For simplicity, it is usually best to set one hurdle Present the resulting opportunity cost results at
rate and assume a limit on the maximum amount of return periods that are relevant for or requested by the
budget reallocation available that might be subject to this stakeholders of the analysis.
hurdle rate.
• For example, for catastrophic natural disasters
• Where possible, ex-post borrowing rates and delay factors (tropical cyclone, earthquake), at the mean, 1 in 10
should be taken from economic studies. and 1 in 50 year results may be relevant.
• Rules of thumb for pricing risk transfer instruments • For disasters such as flood or drought, at least the
should be designed to approximate market pricing as mean, 1 in 5 and 1 in 30 year results may be relevant.
closely as possible.
In some circumstances it may be appropriate to make
different assumptions depending on the source of funds, for
example, if some parts of government or some development
partners are able to offer budget reallocations at lower
opportunity cost than others. However, typically it may
be reasonable to set assumptions that are neutral to the
source of the funding – that is, such that they could apply to
funding from the government or from external development
partners.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
41
5. Consider Relevant Sensitivities 6. Conclude on Risk
and Re-Calculate Results Finance Implications
Sensitivities involve considering alternative parameters A combination of base result and sensitivity analysis
for the layers, economic assumptions, or risk should demonstrate:
transfer assumptions.
• Which strategies tend to have the lowest opportunity
• Sensitivities may be driven by the uncertainty of certain costs on average and at various return periods
parameters (for example, discount rate) or by the
• Which assumptions and parameters have the greatest
political landscape of the country (such as, available
impact on the results.
emergency budget reallocation may be very limited, but it
is insightful to consider what significantly increasing this Reporting should summarise the conclusions, and also
might do to the risk finance strategies). consider any limitations of the analysis or any additional
implicit assumptions that have been made.
• Economic assumption sensitivities can be succinctly
presented through the use of marginal opportunity The most cost-effective strategy will depend on the
cost charts. assumptions, the risk tolerance of policy makers, and
potentially other considerations. Any conclusions and
Re-calculate the results as in (4) and consider how the
results also need to be interpreted in the context of the
assumptions changes impact which strategies are the most
objectives of the stakeholders of the analysis.
cost-effective at various return periods.
42 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
43
Country V Annexes
Annex V1 – Contingent Liability
Figure AV1.1 demonstrates the cumulative distribution function of the costs associated with supporting food insecure
households in districts across the country affected by drought. This cumulative distribution function of the contingent
liability demonstrates a long tail of extreme potential losses.
The sensitivity of the assumed loss distribution is considered further in Annex V4 and the alternative loss distributions
considered are also shown in Figure V1.1.
Figure AV1.1 – Cumulative Distribution Function of the Poverty Cost Due to Drought
3000
2500
2000
Loss (US$m)
1500
1000
500 Baseline
Sensitivity: Increased Contingent Liability
0 Sensitivity: Decreased Contingent Liability
0% 20% 40% 60% 80% 100%
Cumulative Probability
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Annex V2 – Assumptions
Reserve fund assumptions (all strategies)
Under all strategies, initial losses are retained through a reserve fund. The base case assumes that the reserve fund is
assumed to be equal to US$50m, which is equal to a 1 in 1.3 year event.
The cost of reserve funds reflects the assumption that Country V has to borrow to fund the reserves and has to pay interest
on the amount borrowed. While this is offset by the investment returns achieved on the reserves, the investment returns are
typically assumed to be lower than the borrowing rate. The economic assumptions required for calculating the cost of reserve
fund are therefore:
44 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
• Discount rate used to discount costs incurred in the future into present day terms
• Interest rate on amounts that are borrowed to fund reserve fund
• Investment return earned on reserve funds not used to finance costs.
The interest rate charged on amounts borrowed to fund the reserve fund is assumed to be 6.625 percent.
The reserve fund is assumed to be invested in low risk assets, hence it is assumed that the investment return earned is equal
to the borrowing rate, minus a spread of 3 percent.
For simplicity, it is assumed that the discount rate is the same as the borrowing rate – varying this assumption does not have
a material effect on any conclusions drawn in this case study.
Post-disaster debt assumptions (all strategies)
Delay factor for post-disaster debt response: This is the impact on benefit costs due to a delay in providing response (for
example, due to reliance on slow finance instruments such as post-disaster debt). Currently this is assumed to be equivalent
to a factor of 3, such that US$1 early (immediate financing of drought losses) is equivalent to US$3 late (post-disaster debt-
financed), based on a review of literature on this topic for this country.
Insurance assumptions (Strategy B)
Strategy B assumes that insurance will start to payout once the reserve fund has been exhausted. The base case insurance
contract structure is defined as follows:
• Insurance Coverage: The attachment point is 1 in 1.3 year losses when the reserve fund is exhausted. The insurance layer
is assumed to cover losses up to the 1 in 30 year event (equivalent to US$433.4m).
• Insurance Premium: The annual premium payable is US$105m for drought cover. The assumed premium was set using
a pricing multiple of 1.35, which is representative of the drought peril insured at the time of writing this paper. Fees and
expenses associated with insurance mechanisms are assumed to be included within the premium.
Budget reallocation assumptions (Strategy C)
Strategy C assumes that once the reserve fund has been exhausted, Country V will reallocate existing budgets to fund the
finance costs. The base case assumes that Country V is able to reallocate budgets equal to US$100m, such that, together with
the reserve fund, the maximum budget available to finance costs is US$150m (equivalent to a 1 in 3.6 year event).
It is assumed that the cost of reallocating budgets is a hurdle rate of 10 percent.
Annex V3 – Sensitivity Analysis: Economic and Financial Assumptions
Marginal cost – base case scenario
Figure AV3.1 compares the marginal cost (as a multiple of expected loss in layer) for the various finance sources under the
base case assumptions. The marginal cost represents the additional cost of each risk finance instrument per unit of annual
average loss in layer, for a specific return period.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
45
Figure AV3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions
3.5
per $1 of annual average scale up expenditure
Annual average economic cost of nancing,
3.0
2.5
2.0
1.5
1.0 Post Disaster Debt - Delay actor o 3
Insurance multiple o 1.35
0.5
Budget reallocation - 10% hurdle rate
Reserve Fund - 3% spread
0.0
0 5 10 15 20 25 30 35 40 45 50
Return period of scale up expenditure
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• The reserve fund has a marginal cost increasing in the return period due to the difference between the cost of borrowing
funds (the interest rate) and the investment return earned on unspent reserves, which is lower. At losses at higher return
periods, the reserve fund is less likely to be called on and therefore more likely to incur a cost of holding funds.
• Post-disaster debt has a cost of exactly 3 times the loss at all return periods by definition of the delay factor of 3. It is
assumed that US$1 of aid provided early costs US$3 when the response is provided late.
• Insurance has a cost of 1.35, reflecting the constant assumed 1.35 insurance pricing multiple.
• Budget reallocation has a constant marginal cost of 1.03 under the base case scenario, representing the spread between the
hurdle rate (10 percent) and the discount rate (6.625 percent).
The marginal cost does not reflect the limitations and budgetary constraints of various finance sources – most notably
funds available through some instruments are cost-effective but very limited. The graph implies that theoretically, budget
reallocation is most cost-effective for high finance cost return periods. However, this ignores the fact that there might be a
limit on the extent to which government budgets can be reallocated.
Where the different lines of marginal cost intersect is where one finance strategy becomes marginally more cost-effective
than another:
• Reserve funds are the cheapest finance instrument up the 1 in 2.1 year return period.
• For losses greater than the 1 in 2.1 year loss, budget reallocation is always marginally the cheapest finance instrument.
• Reserve funds remain the second cheapest between the 1 in 2.1 year and the 1 in 13.4 year loss, after that insurance is the
second cheapest.
46 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Marginal cost - sensitivities
Figures AV3.2 and AV3.3 consider the impact on the marginal cost of adjusting the following economic and
financial assumptions:
Figure AV3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund
and Insurance Pricing Multiple
3.5
per $1 of annual average scale up expenditure
Annual average economic cost of nancing,
3.0
2.5
2.0
Post Disaster Debt - Delay actor o 3
1.5
Insurance multiple o 1.35
Insurance multiple o 2.0
1.0
Reserve Fund - 3% spread
Reserve Fund - 5% spread
0.5
Reserve Fund - 1% spread
Budget reallocation - 10% hurdle rate
0.0
0 5 10 15 20 25 30 35 40 45 50
Return period of scale up expenditure
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Increasing the spread between the interest rate and investment return of the reserve fund increases the slope of the
marginal cost line, such that the reserve fund becomes less cost-effective.
• Similarly, increasing the insurance pricing multiple increases the point at which insurance becomes marginally the least
cost-effective strategy compared to reserve fund.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
47
Figure AV3.3 – Marginal Cost as a Multiple of Loss – Sensitivity to the Post-Disaster Debt Delay
Factor and the Budget Reallocation Hurdle Rate
3.5
per $1 of annual average scale up expenditure
Annual average economic cost of nancing,
3.0
2.5
2.0
Insurance multiple o 1.35
1.5
Post Disaster Debt - Delay actor o 3
Post Disaster Debt - Delay actor o 1.5
1.0
Budget reallocation - 10% hurdle rate
Budget reallocation - 20% hurdle rate
0.5
Budget reallocation - 40% hurdle rate
Reserve Fund - 3% spread
0.0
0 5 10 15 20 25 30 35 40 45 50
Return period of scale up expenditure
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Reducing the post-disaster finance delay factor shifts down the horizontal line showing the post-disaster finance cost, such
that it is significantly cheaper.
• Increasing the budget reallocation hurdle rate reduces the cost-effectiveness of budget reallocation and increases the
period over which contingency funds are the most cost-effective strategy.
Annex V4 – Sensitivity Analysis: Varying Maximum Funding by
Finance Instrument
Increased reserve fund coverage
Figures AV4.1 and AV4.2 show the cost of the three strategies over different return periods, assuming that the reserve fund is
increased to US$132.1m (the average loss). For the alternative finance strategies considered:
• For Strategy B, it is assumed that insurance still attaches after the reserve fund and is assumed to cover losses up to the
1 in 30 year event.
• For Strategy C, it is assumed that the government is still able to reallocate budgets equal to US$100m, such that, together
with the reserve fund, the maximum budget available to finance losses is US$232.1m (equivalent to a 1 in 7.4 year event).
48 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Figure AV4 .1 – Relative Cost Saving of Strategies under Increased Reserve Fund
100%
90%
83%
80%
Percentage cost decrease
(relative to Strategy A)
70%
60%
50%
40% 38% 36%
30% 27%
20% 19% 19%
10%
0%
B C B C B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure AV4.2 – Total Cost of Increased Reserve Fund
1,200
1,000
Total cost (US$m)
800
600
400
200
0
A B C A B C A B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Reserve Fund Insurance Budget reallocation Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Increasing the reserve fund decreases the average costs for all three strategies as there are more losses met from the
reserve fund, which is the most cost-effective strategy.
• Strategy B is still the cheapest, both on average and at the return periods considered. Increasing the reserve fund decreases
the cost savings of Strategy B relative to Strategy A as there are additional losses covered by the reserve fund in both
strategies; hence the costs under both strategies are closer.
• Strategy C is still cheaper than Strategy A, but the relative savings at the higher return periods are increased. This is
because there is the same absolute cost saving (in US$ terms) between Strategies A and C.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
49
Increased underlying contingent liability
Figures AV4.3 and AV4.4 show the cost of the three strategies over different return periods, assuming that contingent losses
are 25 percent higher. For the alternative finance strategies considered:
• In all strategies it is assumed that the level of reserve fund is unchanged at US$50m (note that this is exhausted in all
simulations as the minimum loss is US$128m).
• Strategy B assumes that insurance still attaches after the reserve fund and is assumed to cover finance costs up to the
higher 1 in 30 year event (which is now US$634m).
• Strategy C assumes that the government is still able to reallocate budgets equal to US$100m, such that, together with the
reserve fund, the maximum budget available to finance costs is US$150m (equivalent to a 1 in 1.2 year event).
Figure AV4 .3 – Relative Cost Saving of Strategies under Increased Underlying Contingent Liability
100%
90%
82%
80%
Percentage cost decrease
(relative to Strategy A)
70% 64%
60%
49%
50%
40%
30% 29%
23%
20%
11%
10%
0%
B C B C B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
50 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Figure AV4.4 – Total Cost of Increased Underlying Contingent Liability
2,000
1,800
1,600
Total cost (US$m)
1,400
1,200
1,000
800
600
400
200
0
A B C A B C A B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Reserve Fund Insurance Budget reallocation Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Increasing the contingent liabilities increases the average costs for all strategies and the costs at all return periods
considered.
• The cost savings of Strategy C relative to Strategy A is reduced, particularly at higher return periods because the size of the
layers is unchanged and hence more losses are covered by post-disaster debt.
Decreased underlying contingent liability
Figures AV4.5 and AV4.6 show the cost of the three strategies over different return periods, assuming that contingent losses
are 25 percent lower. For the alternative finance strategies considered:
• In all strategies it is assumed that the size of the reserve fund is unchanged at US$50m (equivalent to a 1 in 5.2 year event).
• Strategy B assumes that insurance still attaches after the reserve fund and is assumed to cover finance costs up to the
lower 1 in 30 year event (which is now US$233m).
• Strategy C assumes that the government is still able to reallocate budgets equal to US$100m, such that, together with the
reserve fund, the maximum budget available to finance costs is US$150m (equivalent to a 1 in 14.5 year event).
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
51
Figure AV4 .5 – Relative Cost Saving of Strategies under Decreased Underlying Contingent Liability
100%
88%
80%
Percentage cost decrease
(relative to Strategy A)
60%
40% 34% 33%
30%
20%
-46% 0%
0%
-20%
-40%
-60%
B C B C B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure AV4.6 – Total Cost of Decreased Underlying Contingent Liability
700
600
500
Total cost (US$m)
400
300
200
100
0
A B C A B C A B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Reserve Fund Insurance Budget reallocation Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Decreasing the contingent liabilities decreases the average costs for all strategies at all return periods considered.
• Strategy B is still the most cost-effective strategy on average and at higher return periods.
• At lower return periods, Strategy B is more expensive than Strategy A. This is because at these low return periods, losses
are met from the reserve fund. However the insurance premium is still payable.
• The cost savings of Strategy C relative to Strategy A is reduced at lower return periods and on average. This is because at
these low return periods, losses are met from the reserve fund and hence the costs are identical under Strategies A and
C. At higher return periods, the cost savings of Strategy C is more pronounced as a higher share of the loss is met from
budget reallocation.
52 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Country W Annexes
Annex W1 – Contingent Liability
Figure AW1.1 demonstrates the cumulative distribution function of the public capital losses relating to the cost of poverty
due to flood. This cumulative distribution function of the contingent liability demonstrates a long tail of extreme potential
losses. Both historical data and the fitted distribution assume a US$100 per person cost.
Figure AW1.1 – Cumulative Distribution Function of the Poverty Cost Due to Flood
1,600
1,400
1,200
1,000
USD Millions
800
600
400
200
Fitted distribution
0 Historic data
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Annex W2 – Assumptions
Reserve fund assumptions (all strategies)
Under all strategies, initial intial losses are retained through a reserve fund. The base case assumes that the reserve fund is
assumed to be equal to US$100m, which is equal to a 1 in 2.3 year event.
The cost of reserve funds reflects the assumption that Country W has to borrow to fund the reserves and has to pay interest
on the amount borrowed. While this is offset by the investment returns achieved on the reserves, the investment returns are
typically assumed to be lower than the borrowing rate. The economic assumptions required for calculating the cost of reserve
fund are therefore:
• Discount rate used to discount costs incurred in the future into present day terms
• Interest rate on amounts that are borrowed to fund reserves
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
53
• Investment return earned on reserve not used to fund the losses.
The interest rate charged on amounts borrowed to fund the reserves is assumed to be 13 percent.
The fund is assumed to be invested in low risks assets, hence it is assumed that the investment return earned is equal to the
borrowing rate, minus a spread of 10 percent.
For simplicity, it is assumed that the discount rate is the same as the borrowing rate – varying this assumption does not have
a material effect on any conclusions drawn in this case study.
Post-disaster debt assumptions (all strategies)
Delay factor for post-disaster debt response: This is the impact on benefit costs due to a delay in providing response (for
example, due to reliance on slow finance instruments such as post-disaster debt). Currently this is assumed to be equivalent
to a factor of 3, such that US$1 early (immediate financing of response costs) is equivalent to US$3 late (post-disaster debt-
financed). A factor of 3 is assumed in line with recent World Bank research.
Insurance assumptions (Strategy B)
Strategy B assumes that insurance will start to pay out once the reserve fund has been exhausted. The base case insurance
contract structure is defined as follows:
• Insurance Coverage: The attachment point is the 1 in 2.3 year losses when the reserve fund is exhausted. The insurance
layer is assumed to cover losses up to the 1 in 30 year event.
• Insurance Premium: The annual premium payable is US$101.7m for flood cover. The assumed premium was set using
a pricing multiple of 1.5, which is representative of the flood perils insured at the time of writing this paper. Fees and
expenses associated with insurance mechanisms are assumed to be included within the premium.
Contingent credit assumptions (Strategy C)
Strategy C assumes that Country W has contingent credit arrangements to provide immediate liquidity in the aftermath of a
flood event.
It is assumed that Country W can secure contingent credit of up to a maximum of US$100m, set equal to the reserve fund
maximum for easier comparison.
To derive the opportunity cost of contingent credit, it is assumed that Country W would otherwise have to borrow the
amount of the line of contingent credit from the commercial market (at the government’s ex-ante borrowing rate) in order to
finance the same portfolio of expenditures.
As a result, the opportunity cost of contingent credit depends not only on the assumed contingent credit interest rate but
also the spread between the interest rate on amounts borrowed and the contingent credit interest rate.
The economic assumptions required for calculating the cost of contingent credit are therefore:
• Discount rate used to discount costs incurred in the future into present day terms
• Interest rate on amounts that are borrowed (the ex-ante borrowing rate)
• The interest rate charged on contingent credit.
54 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Contingent credit interest rates, such as catastrophe risk deferred drawdown options, are set based on a spread over LIBOR.
Based on current US$ LIBOR rates and IBRD lending rates, a contingent credit interest rate of 2.5 percent is assumed.
In addition to the contingent credit interest rate, contingent credit arrangements such as catastrophe risk deferred
drawdown options charge fees for establishing these lines of credit. For simplicity, it is assumed that there is a single front-
end fee of 0.5 percent of the maximum loan amount.
Annex W3 – Sensitivity Analysis: Economic and Financial Assumptions
Marginal cost – base case scenario
Figure AW3.1 compares the marginal cost (as a multiple of expected loss in layer) for the various finance sources under the
base case assumptions. The marginal cost represents the additional cost of each risk finance instrument per unit of annual
average loss in layer, for a specific return period.
Figure AW3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions
3.5
per $1 of annual average scale up expenditure
Annual average economic cost of nancing,
3.0
2.5
2.0
1.5
1.0
Reserves - 10% spread
Post Disaster Financing Delay actor o 3.0
0.5
Contingent Credit - 2.5% interest
Insurance pricing multiple o 1.5
0.0
0 5 10 15 20 25 30 35 40 45 50
Return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• The reserve fund has an increasing marginal cost due to the difference between the cost of borrowing funds (the interest
rate) and the investment return earned on funds held in reserves, which is lower. At higher return periods, the reserve
fund is less likely to be called on and therefore more likely to incur a cost of holding funds.
• Contingent credit similarly has an increasing marginal cost due to the difference between the cost of borrowing funds
(interest/discount rate) and the investment return earned on the amount of contingent credit unused, which is lower. This
spread (10.5 percent being the difference between 13.0 percent and 2.5 percent) is greater than for the reserve fund and so the
marginal cost increases more sharply.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
55
• Post-disaster debt has a cost of exactly 3 times the loss at all return periods by definition of the delay factor of 3. It is
assumed that US$1 of aid provided early costs US$3 when the response is provided late.
• Insurance has a cost of 1.5, reflecting the constant assumed 1.5 insurance pricing multiple.
The marginal cost does not reflect the limitations and budgetary constraints of various finance sources – most notably funds
available through some instruments are cost-effective but very limited. The graph implies insurance is most cost-effective at
high return periods.
Where the different lines of marginal cost intersect is where one finance strategy becomes marginally more cost-effective
than another:
• Reserves are the cheapest finance instrument up the 1 in 7 year return period.
• For losses greater than the 1 in 7 year loss, insurance is always marginally the cheapest financing instrument.
• Reserves remain the second cheapest between the 1 in 7 year and the 1 in 24 year loss, after that post-disaster debt is the
second cheapest.
Marginal cost - sensitivities
Figure AW3.2 and AW3.3 consider the impact on the marginal cost of adjusting the following economic and
financial assumptions:
• Increasing (decreasing) the spread between the interest rate and investment return of the reserve increases (decreases)
the slope of the marginal cost line, such that the reserve becomes less (more) cost-effective.
• Similarly, increasing the interest earned on contingent credit facilities not used to fund losses reduces the “spread” of this
instrument, reducing the slope of this line and making contingent credit more cost-effective.
Figure AW3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund
and Contingent Credit
3.5
per $1 of annual average scale up expenditure
Annual average economic cost of nancing,
3.0
2.5
2.0
1.5 Insurance pricing multiple o 1.5
Post Disaster Financing Delay actor o 3.0
1.0 Contingent Credit - 2.5% interest
Contingent Credit - 5.0% interest
0.5 Reserves - 10% spread
Reserves - 5% spread
0.0 Reserves - 15% spread
0 5 10 15 20 25 30 35 40 45 50
Return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
56 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
• Increasing the insurance pricing multiple increases the point at which insurance becomes marginally the least cost-
effective strategy compared to reserves and contingent credit financing.
• Decreasing the post-disaster finance delay factor shifts down the vertical line showing the post-disaster finance cost, such
that it becomes a more cost-effective option – if the delay factor is lower than the insurance pricing multiple, then post-
disaster debt becomes the cheapest strategy beyond a certain return period.
Figure AW3.3 – Marginal Cost as a Multiple of Loss – Sensitivity to the Post-Disaster Debt Delay
Factor and the Insurance Multiple
3.5
per $1 of annual average scale up expenditure
Annual average economic cost of nancing,
3.0
2.5
2.0
1.5
Insurance pricing multiple o 1.5
Insurance pricing multiple o 2.0
1.0
Post Disaster Financing Delay actor o 3.0
0.5 Post Disaster Financing Delay actor o 1.4
Contingent Credit - 2.5% interest
0.0 Reserves - 10% spread
0 5 10 15 20 25 30 35 40 45 50
Return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Annex W4 – Sensitivity Analysis: Varying Maximum Funding by
Finance Instrument
Reduced insurance coverage
FIgures AW4.1 and AW4.2 show the cost of the three strategies over different return periods, assuming that the insurance
layer covers only 50 percent of the losses between the reserve fund (1 in 2.3 year return period) and the 1 in 30 year return
period loss. The remaining 50 percent is assumed to be funded by post-disaster debt.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
57
Figure AW4 .1 – Relative Cost Saving of Reduced Insurance Layer
45% 43%
40%
40%
Percentage cost decrease
35%
(relative to Strategy A)
30%
30%
25% 23%
20% 18%
15% 14%
10%
5%
0%
B C B C B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure AW4.2 – Total Cost of Reduced Insurance Layer
1,600
1,400
1,200
Total cost (US$m)
1,000
800
600
400
200
0
A B C A B C A B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Reserve Fund Contingent Credit Insurance Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• On average and at lower return periods, the total cost of Strategy B is now higher compared to Strategy C. This is because
fewer losses are covered by insurance and more losses are covered by the more expensive post-disaster debt. On average,
however, Strategy B is still cheaper than Strategy A.
• Decreasing the insurance layer shows that at higher return periods, post-disaster debt is now required, hence increasing
the total cost of Strategy B. While it is still cheaper than the other strategies at the 1 in 30 year return period, the saving is
not as great due to the requirement for post-disaster debt.
58 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Increase layers of non-insurance finance arrangements
Figures AW4.3 and AW4.4 demonstrate the cost of the three strategies above over different return periods, assuming that the
layers of non-insurance instruments are increased by 50 percent.
Figure AW4 .3 – Relative Cost Saving of Increasing Non-Insurance Layers
100%
90%
82%
80%
Percentage cost decrease
(relative to Strategy A)
70%
60%
50%
43%
40%
40%
31%
30% 25% 23%
20%
10%
0%
B C B C B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure AW4.4 – Total Cost of Increasing Non-Insurance Layers
1,400
1,200
Total cost (US$m)
1,000
800
600
400
200
0
A B C A B C A B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Reserve Fund Contingent Credit Insurance Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
59
• In this sensitivity scenario, the reserve covers losses up to the 1 in 3.1 year return period and contingent credit covers
losses between the 3.1 year and 7.2 year return period.
• Strategy B is still the cheapest on average and at the 1 in 5 and 1 in 30 year return periods, because the layer of losses
financed by contingent credit (up to the 7.2 year loss) is still significantly lower than the layer of losses financed by
insurance (up to the 30 year loss), with the remainder financed by the more expensive post-disaster debt.
• However, compared to the base scenario, the savings offered by Strategy B compared to Strategy A are decreased, because
there is not as much post-disaster debt required in Strategy A (which drove up the overall cost in the base scenario).
• Similarly, the savings offered by Strategy C compared to Strategy A are decreased compared to the base scenario, due to
the lower level of post-disaster debt required.
60 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Country X Annexes
Annex X1 – Contingent Liability
Figure AX1.1 demonstrates the cumulative distribution function of poverty losses caused by reduced crop yields that arise from
all perils. This cumulative distribution function of the contingent liability demonstrates a long tail of extreme potential losses.
Figure AX1.1 – Cumulative Distribution Function of the Yield Loss Due to All Perils
120
100
80
Loss (US$m)
60
40
20
0
0% 20% 40% 60% 80% 100%
Cumulative Probability
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Annex X2 – Assumptions
Reserve fund assumptions (all strategies)
Under all strategies, initial losses are retained through a reserve fund. The base case assumes that the reserve fund is
assumed to be equal to US$20m, which is equal to a 1 in 2.5 year event.
The cost of reserve funds reflects the assumption that Country X has to borrow to fund the reserves and has to pay interest
on the amount borrowed. While this is offset by the investment returns achieved on the reserves, the investment returns are
typically assumed to be lower than the borrowing rate. The economic assumptions required for calculating the cost of reserve
fund are therefore:
• Discount rate used to discount costs incurred in the future into present day terms
• Interest rate on amounts that are borrowed to fund reserves
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
61
• Investment return earned on reserve not used to fund losses.
The interest rate charged on amounts borrowed to fund the reserves is assumed to be 5 percent.
The fund is assumed to be invested in low risks assets, hence it is assumed that the investment return earned is equal to the
borrowing rate, minus a spread of 2 percent.
For simplicity, it is assumed that the discount rate is the same as the borrowing rate – varying this assumption does not have
a material effect on any conclusions drawn in this case study.
Post-disaster debt assumptions (all strategies)
Delay factor for post-disaster debt response: This is the impact on costs due to a delay in providing response (for example,
due to reliance on slow finance instruments such as post-disaster debt). Currently this is assumed to be equivalent to a factor
of 3, such that US$1 early (immediate financing of flood losses) is equivalent to US$3 late (post-disaster debt-financed). A
factor of 3 is assumed in line with recent World Bank research.
Insurance assumptions (Strategy B)
Strategy B assumes that insurance will start to pay out once the reserve fund has been exhausted. The base case insurance
contract structure is defined as follows:
• Insurance Coverage: The attachment point is 1 in 2.5 year loss when the reserve fund is exhausted. The insurance layer is
assumed to cover losses up to the 1 in 30 year event (equivalent to US$52.4m).
• Insurance Premium: The annual premium payable is US$6.7m for all perils cover. The assumed premium was set using a
pricing multiple of 1.35, which is representative of the perils insured at the time of writing this paper. Fees and expenses
associated with insurance mechanisms are assumed to be included within the premium.
Budget reallocation assumptions (Strategy C)
Strategy C assumes that once the reserve fund has been exhausted, Country X will reallocate existing budgets to fund the
losses. The base case assumes that Country X is able to reallocate budgets equal to US$20m, such that, together with the
reserve fund, the maximum budget available to finance losses is US$40m (equivalent to a 1 in 10.7 year event).
It is assumed that the cost of reallocating budgets is 20 percent.
62 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Annex X3 – Sensitivity Analysis: Economic and Financial Assumptions
Marginal cost – base case scenario
Figure AX3.1 compares the marginal cost (as a multiple of expected loss in layer) for the various finance sources under the
base case assumptions. The marginal cost represents the additional cost of each risk finance instrument per unit of annual
average loss in layer, for a specific return period.
Figure AX3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions
3.5
per $1 of annual average scale up expenditure
Annual average economic cost of nancing,
3.0
2.5
2.0
1.5
1.0
Budget reallocation - 20% hurdle rate
Insurance Multiple o 1.35
0.5
Post Disaster Financing Delay actor o 3
0.0 Reserves -2% spread
0 5 10 15 20 25 30 35 40 45 50
Return period of scale up expenditure
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• The reserve fund has an increasing marginal cost due to the difference between the cost of borrowing funds (the interest
rate) and the investment return earned on funds held in reserves, which is lower. At losses at higher return periods, the
reserve fund is less likely to be called on and therefore more likely to incur a cost of holding funds.
• Post-disaster debt has a cost of exactly 3 times the loss at all return periods by definition of the delay factor of 3. It is
assumed that US$1 of aid provided early costs US$3 when the response is provided late.
• Insurance has a cost of 1.35, reflecting the constant assumed 1.35 insurance pricing multiple.
• Budget reallocation has a constant marginal cost of 1.14 under the base case scenario, representing the spread between the
hurdle rate (20 percent) and the discount rate (5 percent).
The marginal cost does not reflect the limitations and budgetary constraints of various finance sources – most notably
funds available through some instruments are cost-effective but very limited. The graph implies that theoretically, budget
reallocation is most cost-effective for high finance cost return periods. However, this ignores the fact that there might be a
limit on the extent to which government budgets can be reallocated.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
63
Where the different lines of marginal cost intersect is where one finance strategy becomes marginally more cost-effective
than another:
• Reserves are the cheapest finance instrument up the 1 in 8.5 year return period.
• For losses greater than the 1 in 8.5 year loss, budget reallocation is always marginally the cheapest finance instrument.
• Reserves remain the second cheapest between the 1 in 8.5 year and the 1 in 19.4 year loss, after that insurance is the second
cheapest.
Marginal cost - sensitivities
Figures AX3.2 and AX3.3 consider the impact on the marginal cost of adjusting economic and financial assumptions:
Figure AX3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund
and budget Reallocation Hurdle Rate
3.5
per $1 of annual average scale up expenditure
Annual average economic cost of nancing,
3.0
2.5
2.0
Insurance Multiple o 1.35
1.5
Post Disaster Financing Delay actor o 3
Reserves -2% spread
1.0
Reserves -4% spread
Budget reallocation - 20% hurdle rate
0.5
Budget reallocation - 10% hurdle rate
Budget reallocation - 40% hurdle rate
0.0
0 5 10 15 20 25 30 35 40 45 50
Return period of scale up expenditure
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Increasing the spread between the interest rate and investment return of the reserve increases the slope of the marginal
cost line, such that the reserve becomes less cost-effective.
• Similarly, increasing (decreasing) the budget reallocation hurdle rate increases (decreases) the marginal cost of budget
reallocation and increases (decreases) the point to which the reserves remain the cheapest instrument.
64 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Figure AX3.3 – Marginal Cost as a Multiple of Loss, Sensitivity to the Post-Disaster Debt Delay Factor
and the Insurance Multiple
5.0
per $1 of annual average scale up expenditure
Annual average economic cost of nancing,
4.5
4.0
3.5
3.0
2.5
Insurance Multiple o 1.35
2.0
Insurance Multiple o 2
1.5 Post Disaster Financing Delay actor o 3
Post Disaster Financing Delay actor o 1.5
1.0
Post Disaster Financing Delay actor o 5
0.5 Budget reallocation - 20% hurdle rate
Reserves -2% spread
0.0
0 5 10 15 20 25 30 35 40 45 50
Return period of scale up expenditure
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Increasing the insurance pricing multiple increases the point at which insurance becomes marginally the least cost-
effective strategy compared to reserves and budget reallocation. In fact, increasing the multiple to 2 means that the reserve
fund and budget reallocation always has a lower marginal opportunity cost than insurance.
• Increasing the post-disaster finance delay factor shifts up the horizontal line showing the post-disaster finance cost, such
that it is now significantly more expensive than the other strategies.
Annex X4 – Sensitivity Analysis: Varying Maximum Funding by
Finance Instrument
Reduced reserve fund coverage
Figure AX4.1 and AX4.2 show the cost of the three strategies above over different return periods, assuming the reserve fund is
reduced to US$10m (1 in 1.4 year return period). For the alternative finance strategies considered:
• Strategy B assumes that insurance still attaches after the reserve fund and is assumed to cover losses up to the 1 in 30
year event.
• Strategy B assumes that the government is still able to reallocate budgets equal to US$20m, such that, together with the
reserve fund, the maximum budget available to finance losses is US$30m (equivalent to a 1 in 5.1 year event).
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
65
Figure AX4 .1 – Relative Cost Saving of Reduced Reserve Fund
100%
90%
82%
80%
Percentage cost decrease
(relative to Strategy A)
70% 65%
60%
53%
50%
42%
40% 37%
30% 27%
20%
10%
0%
B C B C B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure AX4.2 – Total Cost of Reduced Reserve Fund
160
140
120
Total cost (US$m)
100
80
60
40
20
0
A B C A B C A B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Reserve Fund Insurance Budget reallocation Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Decreasing the reserve fund increases the average costs for all three strategies as there are more losses met from post-
disaster debt in Strategies A and C (which is the least cost-effective strategy) and there is an increase in the premium in
Strategy B.
• Strategy B is still the cheapest, both on average and at the return periods considered. Decreasing the reserve fund increases
the cost savings of Strategy B relative to Strategy A as the additional losses previously covered by the reserve fund are
ceded to the insurer (at the marginal cost of the assumed insurance price multiple of 1.35), which is cheaper than the
additional losses covered by post-disaster debt (at a marginal cost of the assumed delay factor of 3).
• Strategy C is still cheaper than Strategy A, but the relative savings at the higher return periods are reduced as post-disaster
debt begins to dominate the total cost of both strategies.
66 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Increased reserve fund coverage
Figure AX4.3 and AX4.4 show the cost of the three strategies above over different return periods, assuming that the reserve
fund is increased to US$30m (1 in 1.4 year return period). For the alternative finance strategies considered:
• Strategy B assumes that insurance still attaches after the reserve fund and is assumed to cover losses up to the 1 in 30
year event.
• Strategy C assumes that the government is still able to reallocate budgets equal to US$20m, such that, together with the
reserve fund, the maximum budget available to finance losses is US$50m (equivalent to a 1 in 24.7 year event).
• Increasing the reserve reduces the average costs for all three strategies as there are more losses met from the reserve in all
strategies, which is the most cost-effective strategy at lower return periods.
• While Strategy B is still the cheapest on average, at the 1 in 5 return period Strategy A is now more cost-effective. This is
because the reserve is sufficient to meet 1 in 5 year events and hence the insurance is not called on but the premium is still
payable.
• As in the baseline assumptions, costs at the 1 in 5 year period are higher than the average costs for all strategies. This is
because the average loss under the assumed distribution is smaller than the 1 in 5 year loss (see Annex 1 for the assumed
distribution of losses).
• At the 1 in 5 return period, the cost of Strategy A and C are identical because there is no need for budget reallocation.
• At higher return periods, Strategy B is still the cheapest strategy.
EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
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Figure AX4 .3 – Relative Cost Saving of Increased Reserve Fund
70% 66%
60%
Percentage cost decrease
50%
(relative to Strategy A)
40% 28%
30%
20% 15%
14%
10%
-10% 0%
0%
-10%
-20%
B C B C B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure AX4.4 – Total Cost of Increased Reserve Fund
120
100
Total cost (US$m)
80
60
40
20
0
A B C A B C A B C
Average 1 in 5 year return period of loss 1 in 30 year return period of loss
Reserve Fund Insurance Budget reallocation Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
68 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Country Y Annexes
Annex Y1 – Underlying Contingent Liability
Figure AY1.1 represents the undiversified total payout/cost function in Strategy A. There is a discrete increase at
approximately 90 percent to a multiple of 4 times the premium. This is consistent with the fact the initial payout is triggered
at the 1 in 10 return period, which corresponds to a 90th percentile (slightly greater for some regions due to multiple events
occurring in one year). There is a plateau at payouts of 10 times the premium after approximately the 96.7th percentile
(corresponding to 1 in 30), with a step in between of 8 times the premium for years with multiple events.
Figure AY1.1 – Cumulative Distribution Function for Undiversified Total Payouts/Costs
10
9
Payment as a multiple of premium
8
7
6
5
4
3
2
1
0 - region perils (undiversi ed)
Sum all
70% 75% 80% 85% 90% 95% 100%
Probability
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure AY1.2 demonstrates the diversified individual distributions, summed by simulated year. Some correlation exists
between neighbouring regions, as expected, but there is an overall diversification benefit.
The pooled portfolio demonstrates an overall smoother loss function profile, with sharp increase to a total aggregate 10 times
the premium loss; that is, even the 1 in 200 loss at the 99.5th percentile is significantly lower than the maximum loss (unlike
in Figure AY1.1, where the 1 in 200 loss is also the maximum loss).
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Figure AY1.2 – Cumulative Distribution Functions for Pooled Cover (by Peril and in Aggregate)
Individual Pooled Pooled Fully
Insurance Earthquake Tropical Pooled 10
Payment as a multiple of premium
Contracts Only Cyclone 9
Only
8
1 in 200 10 6.3 5.4 3.8
loss 7
6
(as multiple
of base 5
premium) 4
Maximum 10 8.1 8.0 5.9 3
simulated
(1 in 10,000) 2
loss 1
(as multiple 0
of base 70% 75% 80% 85% 90% 95% 100%
premium) Probability
Sum Tropical Cyclone Sum Earthquake Sum All
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Annex Y2 – Base Case Scenario Assumptions
Economic assumptions
Initial payouts (in Strategy C) are retained through a reserve fund.
The cost of reserve funds reflects the assumption that Country Y has to borrow to fund the reserves and has to pay interest
on the amount borrowed. While this is offset by the investment returns achieved on the reserves, the investment returns are
typically assumed to be lower than the borrowing rate. The economic assumptions required for calculating the cost of reserve
fund are therefore:
• Discount rate used to discount costs incurred in the future into present day terms
• Interest rate on amounts that are borrowed to fund reserves
• Investment return earned on reserve not used to fund payouts.
The retained payouts are assumed to be fully capitalised; that is, the pooled facility is assumed to hold capital reserves at a
level equal to the maximum expected payout in the retained layer. For simplicity and because the focus of this case study
is on different insurance strategies, the discount rate, interest rate, and investment return are assumed to all be equal. The
simplifying result of this combination of assumptions is that the cost of financing the retained payouts is equal to the costs
occurred in the retained layer, with no cost charged on the capital reserves held in excess of the loss incurred.
Risk transfer assumptions
Under Strategy A the average insurance pricing multiple based on the individual insurance contracts is 1.64 (determined
based on the premium divided by the average annual loss).
70 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Two key assumptions were made in comparing the insurance price of Strategies B and C:
• Diversification benefit (Strategy B): The diversification benefit that can be achieved by moving from Strategy A to Strategy
B and pooling the risks of all regions
• Reinsurance pricing (Strategy C): The (re)insurance pricing multiple applied to excess losses in Strategy C.
Strategy B diversification benefit
Based on a pool of the cumulative underlying risk, the resulting cumulative distribution function (CDF) follows a smoother
distribution (than the individual risks) and there is a diversification benefit arising from the pooling of all risks. This is
demonstrated in Figure AY1.2 in Annex Y1.
With the evidence that a diversification benefit exists, assumptions were made about the size of this benefit (that is, the
discount on premiums charged) through consideration of the following metrics:
• The insurance pricing multiple (premium divided by average annual loss)
• The implied risk volatility loading to demonstrate the premium charged to compensate for the level of volatility in the
underlying losses (see Glossary).
Strategy A assumes a summation of all CDFs across all regions and perils with no diversification benefit (see Figure AY1.1 in
Annex Y). Strategy B has an inherent diversification benefit incorporated, as it is summing across 13 regions by simulated
year rather than by CDF ranked from best scenario (no losses) to worst scenario (maximum payout for each region). Some
correlation exists between neighbouring regions, as expected, but there is an overall diversification benefit (see Figure AY1.2
in Annex Y1). Therefore, as a starting point, comparing Strategy B with Strategy A, it is intuitively expected that:
• The risk volatility loading to be higher: This is because Strategy A would have a relatively high standard deviation value
due to the nature of the defined payouts being a step function with a more extreme maximum than any pooled loss
distributions in Strategies B. A relatively greater standard deviation value would result in a relatively lower risk volatility
loading base amount.
• The pricing multiple to be lower, due to the diversification benefit achieved in Strategy B.
The initial parameter for the diversification benefit from Strategy B was set as 10 percent:
• It is evident that there should be some level of diversification, but without real-time market pricing insight it is difficult to
set an initial parameter. Ten percent was chosen for simplicity and to demonstrate the difference in cost between Strategy
A and B.
• It is intuitive that any diversification benefit greater than 2.5 percent (which is the additional fee charged for pooling) will
result in Strategy B being more cost-effective.
• While this approach may not be robust enough for market pricing purposes, it is sufficient for the purposes of the
evaluation of the finance strategies in this case study and will allow us to reach a reasonable conclusion, keeping the
limitation on parameter robustness in mind.
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Strategy C pricing multiple
The resulting assumption for the pricing multiple in Strategy C was set based on a reasonable level of the risk volatility
loading compared to Strategy B. The pricing multiple is expected to be greater in Strategy C than Strategy B due to the higher
layer of risk being written and the greater volatility in the layer.
A summary of the base case scenario assumptions and diagnostics are outlined in Table AY2.2.
Table AY2.2 – Diagnostics of Insurance Pricing Assumptions, Base Case
Strategy A Strategy B Strategy C
Diversification benefit 10%
Pricing multiple 1.64 1.47 2.00
Risk volatility loading 52% 38% 25%
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Market and administration fees
There are fees assumed to be placed on the risk transfer mechanisms:
• Strategy B and C both have a 2.5 percent market fee charged on the premium for the layer placed in the insurance market.
• Strategy C has a 5 percent administrative fee charged on the retained layer.
Annex Y3 – Sensitivity Analysis
The analysis considered sensitivities to key assumptions as follows:
• Strategy B diversification benefit: increase from 10 percent to 20 percent
• Strategy C insurance pricing multiple: reduce from 2.0 to 1.47
• Strategy C economic assumptions relevant to the risk retention: increase the spread (between the interest rate and
investment return) from 0 percent to 5 percent.
For the first two sensitivities, the insurance pricing assumptions are considered, in Table AY3.1 were considered which
decrease the cost of insurance premiums in both Strategy B and C, as outlined by the resulting pricing multiples in Table
AY3.1.
72 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Table AY3.1 – Diagnostics of Insurance Pricing Assumptions, Sensitivities
Strategy A Strategy B - sensitivity Strategy C - sensitivity
Diversification benefit N/A 20% N/A
Pricing multiple 1.64 1.31 1.47
Risk volatility loading 52% 25% 12%
Source: Clarke, Cooney, Edwards, and Jinks (2016).
For the third sensitivity, the following dynamics with the economic assumptions apply:
• Increasing the discount rate and/or decreasing the investment rate (that is, increasing the spread between the investment
rate and the discount rate) will increase the cost. To demonstrate this, a spread of 5 percent (such that the discount rate is
5 percent higher than the investment rate) is assumed.
Additional parameters and sensitivities that have not been considered are outlined in Table AY3.2.
Table AY3.2 – Assumptions with Sensitivity Analysis Not Considered
Assumption Base Parameter Justification for Not Considering Sensitivity Analysis
Spread between 0% No sensitivity analysis considered as a more material and relevant spread is
interest rate & (interest rate = 4%; the one between investment return and interest rate.
discount rate discount rate = 4%)
Market fee 2.5% The magnitude of how much these assumptions will vary is likely to be
significantly smaller than the assumptions around premium pricing for
Strategy B and C.
Administration 5%
fee The direction of movement in overall cost is intuitively obvious and there is
minimal additional insight to be gained in varying these assumptions – the
costs will increase proportionally and evenly for all return periods (since
premiums are consistent) as the fees increase.
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Country Z Annexes
Annex Z1 – Contingent Liability
Figure AZ1.1 demonstrates the cumulative distribution function of the public capital losses relating to tropical cyclone
damage. This cumulative distribution function of the contingent liability demonstrates a long tail of extreme potential losses,
which is the nature of catastrophic tropical cyclone exposure. It is the same shape as the underlying total tropical cyclone
losses (the losses are just a 30 percent proportion of total tropical cyclone losses).
Public capital losses have been capped at the 1 in 50 year return period (approximately US$300m or 2.5 percent of GDP).
Losses beyond this magnitude are assumed to require significant donor support in any finance strategy – the cost of this
donor support would be consistent for all strategies and is excluded from this analysis.
Figure AZ1.1 – Cumulative Distribution Function of the Public Losses
100%
90%
80%
70%
Cumulative probability
60%
50%
40%
30%
20%
10%
0%
0 50 100 150 200 250 300
Loss ($USD millions)
Source: Clarke, Cooney, Edwards, and Jinks (2016).
74 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Annex Z2 – Assumptions
Reserve fund assumptions (all strategies)
Under all strategies, initial losses are retained through a reserve fund. The base case assumes that the reserve fund is
assumed to be equal to 0.2 percent of GDP, which is broadly equivalent to a 1 in 6 year event.
The cost of reserve funds reflects the assumption that Country Z has to borrow to fund the reserves and has to pay interest
on the amount borrowed. While this is offset by the investment returns achieved on the reserves, the investment returns are
typically assumed to be lower than the borrowing rate. The economic assumptions required for calculating the cost of reserve
fund are therefore:
• Discount rate used to discount costs incurred in the future into present day terms
• Interest rate on amounts that are borrowed to fund reserves
• Investment return earned on reserve not used to fund finance costs.
The interest rate charged on amounts borrowed to fund the reserves is assumed to be 6.75 percent, which is the yield on long-
term bonds issued by Country Z in US$.
The fund is assumed to be invested in low risk assets, hence it is assumed that the investment return earned is equal to the
borrowing rate, minus a spread of 3 percent.
For simplicity, it is assumed that the discount rate is the same as the borrowing rate – varying this assumption does not have
a material effect on any conclusions drawn in this case study.
Post-disaster debt assumptions (all strategies)
All strategies assume that large losses (that is, those that exhaust the additional financial instruments described below)
are met by post-disaster debt issued by Country Z. A post-disaster debt delay factor of 18.44 percent is assumed based on
assumptions that:
• Emergency public losses account for 23 percent of losses.
• The internal rate of return for emergency public losses is 40 percent.
• The internal rate of return for non-emergency public losses is 12 percent.
• There is a one-year delay in building both emergency and non-emergency reconstruction.
Insurance assumptions (Strategy B)
Strategy B assumes that insurance will start to pay out once the reserve fund has been exhausted. The base case insurance
contract structure is defined as follows:
• Insurance Coverage: The attachment point is 1 in 6 year loss when the reserve fund is exhausted. The insurance layer is
assumed to cover losses up to the 1 in 30 year event.
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• Insurance Premium: The annual premium payable is US$23.5m for tropical cyclone cover. The assumed premium was set
with consideration of the following metrics:
• The pricing multiple (premium divided by annual average loss)
• The implied risk volatility loading to demonstrate the premium charged to compensate for the level of volatility in
the underlying losses (see Glossary).
The base case assumes a constant risk volatility loading of 25 percent. For the assumed attachment point and layer, this is
equivalent to a pricing multiple of 1.85. It should be noted that if the risk volatility loading is assumed to be constant then the
equivalent pricing multiple increases (decreases) as the assumed attachment point increases (decreases) and the assumed
layer decreases (increases). This is because the volatility of insured losses increases as the attachment point increases, and
hence insurers charge a higher premium for the extra volatility.
Fees and expenses associated with insurance mechanisms are assumed to be included within the premium.
Budget reallocation assumptions (Strategy C)
Strategy C assumes that once the reserve fund has been exhausted, Country Z will reallocate existing budgets to fund the
losses. The base case assumes that Country Z is able to reallocate budgets equating to 0.8 percent of GDP, such that, together
with the reserve fund, the maximum budget available to finance losses is 1 percent of GDP (roughly equivalent to a 1 in 17
year event).
It is assumed that the cost of reallocating budgets is 37 percent, based on economic modelling.
Contingent credit assumptions (Strategy D)
Strategy D assumes that Country Z has contingent credit arrangements to provide immediate liquidity in the aftermath of a
tropical cyclone event.
It is assumed that Country Z can secure contingent credit of up to a maximum of US$30m, which is approximately 0.25
percent of GDP, consistent with current World Bank arrangements.1
To derive the cost of contingent credit, it is assumed that Country Z would otherwise have to borrow the amount of the line
of contingent credit from the commercial market (at the government’s ex-ante borrowing rate) in order to finance the same
portfolio of expenditures.
As a result, the cost of contingent credit depends not only on the assumed contingent credit interest rate but also the spread
between the interest rate on amounts borrowed and the contingent credit interest rate.
The economic assumptions required for calculating the cost of contingent credit are therefore:
• Discount rate used to discount costs incurred in the future into present day terms
• Interest rate on amounts that are borrowed (the ex-ante borrowing rate)
• The interest rate charged on contingent credit.
Contingent credit interest rates, such as catastrophe risk deferred drawdown options are set based on a spread over LIBOR.
Based on current US$ LIBOR rates and IBRD lending rates, a contingent credit interest rate of 2.5 percent is assumed.
1 http://treasury.worldbank.org/bdm/pdf/Handouts_Finance/CatDDO_Product_Note.pdf
76 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
In addition to the contingent credit interest rate, contingent credit arrangements such as catastrophe risk deferred
drawdown options charge fees for establishing these lines of credit. For simplicity, a single front-end fee of 0.5 percent of the
maximum loan amount is assumed.
Annex Z3 – Sensitivity Analysis: Economic and Financial Assumptions
Marginal cost – base case scenario
Figure AZ3.1 compares the marginal cost (as a multiple of expected loss in layer) for the various financial instruments under
the base case assumptions. The marginal cost represents the additional cost of each risk finance instrument per unit of
annual average loss in layer, for a specific return period.
Figure AZ3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions
3.5
Annual average economic cost of nancing,
3.0
per $1 of annual average respose cost
2.5
2.0
1.5
Insurance Risk Volatility Loading o 25%
1.0
Post Disaster Financing Delay actor o 1.18
Contingent Credit - 2.50% interest
0.5
Budget reallocation - 37% hurdle rate
0.0 Reserves -3% spread
0 5 10 15 20 25 30 35 40 45 50
Return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• The reserve fund has an increasing marginal cost due to the difference between the cost of borrowing funds (the interest
rate) and the investment return earned on funds held in reserves, which is lower. For losses at higher return periods, the
reserve fund is less likely to be called on and therefore more likely to incur a cost of holding funds.
• Contingent credit similarly has an increasing marginal cost due to the difference between the cost of borrowing funds
(interest/discount rate) and the investment return earned on the amount of contingent credit unused, which is lower. This
spread (4.25 percent being the difference between 6.75 percent and 2.5 percent) is greater than for the reserve fund and so
the marginal cost increases more sharply.
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• Post-disaster debt has a cost of 1.18 times the loss at all return periods.
• Budget reallocation has a constant marginal cost of approximately 1.30 under the base case scenario, with 30 percent being
approximately the spread between the hurdle rate (37 percent) and the discount rate (6.75 percent).
• The marginal cost for insurance is derived from the change in insurance premium that results from insurance attaching
US$1 higher. Attaching insurance at a higher return period increases the marginal cost of insurance (note that the
unsmooth curve of the insurance marginal cost is a result of the number of simulations used). This is because a constant
risk volatility loading is assumed and as the attachment point increases, the uncertainty in the loss increases. When
expressed relative to the loss amount, it is therefore cheaper for insurance to attach at a lower level.
The marginal cost does not reflect the limitations and budgetary constraints of various financial instruments – most notably
funds available through some instruments (for example, contingent credit) are cost-effective but very limited. The graph
implies post-disaster debt is most cost-effective for high loss return periods.
Where the different lines of marginal cost intersect is where one finance strategy becomes marginally more cost-effective
than another:
• Reserves are the cheapest finance instrument up the 1 in 7.6 year return period.
• For losses greater than the 1 in 7.6 year loss, post-disaster debt financing is always marginally the cheapest
finance instrument.
• Reserves remain the second cheapest between the 1 in 7.6 year and the 1 in 11.1 year loss, after that budget reallocation is
the second cheapest.
• Beyond the 1 in 5 year, insurance and contingent credit are marginally the most expensive finance instruments (assuming
that insurance attaches at these higher return periods).
Note that the last bullet may at first sight appear inconsistent with Figure Z3.4, which shows that at higher return periods,
Strategy B (insurance) is the cheapest strategy. This is because the marginal cost presented in Figure AZ3.1 assumes that
insurance attaches at the return period shown on the x-axis.
In our baseline assumptions, Strategy B assumes that insurance attaches at the 1 in 6 year loss. As a result, Strategy B ‘locks
in’ the marginal cost of insurance at the 1 in 6 year level, which is much lower. Or alternatively, Figure AZ3.1 demonstrates
that it is much more cost-effective for insurance to attach at lower return periods.
Marginal cost - sensitivities
Figures AZ3.2, AZ3.3 and AZ3.4 consider the impact on the marginal cost of adjusting the following economic and
financial assumptions:
78 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Figure AZ3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund
and The Budget Reallocation
3.5
Annual average economic cost of nancing,
per $1 of annual average response cost
3.0
2.5
2.0
Insurance Risk Volatility Loading o 25%
Post Disaster Financing Delay actor o 1.18
1.5
Contingent Credit - 2.50% interest
Budget reallocation - 50% hurdle rate
1.0 Budget reallocation - 10% hurdle rate
Budget reallocation - 37% hurdle rate
0.5 Reserves -1% spread
Reserves -5% spread
0.0 Reserves -3% spread
0 5 10 15 20 25 30 35 40 45 50
Return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Increasing (decreasing) the spread between the interest rate and investment return of the reserve increases (decreases)
the slope of the marginal cost line, such that the reserve becomes less (more) cost-effective.
• Increasing (decreasing) the budget reallocation hurdle rate shifts up the horizontal line showing the budget reallocation
marginal cost, such that budget reallocation becomes less (more) cost-effective.
Figure AZ3.3 – Marginal Cost as a Multiple of Loss, Sensitivity to the Post-Disaster Debt Delay Factor and the
Insurance Multiple
3.5
Annual average economic cost of nancing,
per $1 of annual average response cost
3.0
2.5
2.0
Insurance Risk Volatility Loading o 25%
1.5 Insurance Risk Volatility Loading o 45%
Insurance Risk Volatility Loading o 12.5%
1.0 Post Disaster Financing Delay actor o 1.18
Post Disaster Financing Delay actor o 1.38
0.5 Contingent Credit - 2.50% interest
Budget reallocation - 37% hurdle rate
Reserves -3% spread
0.0
0 5 10 15 20 25 30 35 40 45 50
Return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
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• Increasing (decreasing) the risk volatility loading decreases (increases) the point at which insurance becomes marginally
the least cost-effective strategy.
• Increasing the post-disaster finance delay factor shifts up the horizontal line showing the post-disaster finance cost, such
that it becomes a less cost-effective option.
Figure AZ3.4 – Marginal Cost as a Multiple of Loss, Sensitivity to the Contingent Credit Assumptions
3.5
per $1 of annual average scale up expenditure
Annual average economic cost of nancing,
3.0
2.5
2.0
1.5 Insurance Risk Volatility Loading o 25%
Post Disaster Financing Delay actor o 1.18
1.0 Contingent Credit - 2.50% interest
Contingent Credit - 1.00% interest
Contingent Credit - 2.00% ee
0.5
Budget reallocation - 37% hurdle rate
Reserves -3% spread
0.0
0 5 10 15 20 25 30 35 40 45 50
Return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Reducing the interest rate charged on contingent credit investment return increases the slope of the marginal cost line,
such that contingent credit becomes less cost-effective.
• Increasing the fee to 2 percent of the contingent credit maximum, increases the marginal cost slightly, such that
contingent credit becomes less cost-effective.
Annex Z4 – Sensitivity Analysis: Varying Maximum Funding by
Finance Instrument
Reduced insurance layer
Figures AZ4.1 and AZ4.2 show the relative cost savings and overall costs of the four strategies over different return periods,
assuming that the insurance layer covers only finance costs up to the 1 in 15 year return period.
80 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Figure AZ4.1 – Relative Cost Saving of Reduced Insurance Layer
30%
27% 26%
25%
Percentage cost decrease
20%
(relative to Strategy A)
15%
10%
6%
5%
2%
-11% -3% 1% -4% -4%
0%
-5%
-10%
-15%
B C D B C D B C D
Average 1 in 10 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure AZ4.2 – Total Cost of Reduced Insurance Layer
300
250
Total cost (US$m)
200
150
100
50
0
A B C D A B C D A B C D
Average 1 in 10 year return period of loss 1 in 30 year return period of loss
Reserve Fund Contingent Credit Insurance Budget reallocation Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
• Decreasing the insurance layer shows that at higher return periods, post-disaster debt is now required, hence increasing
the total cost of Strategy B. While it is still cheaper than the other strategies at higher return periods, consistent with the
base case scenario results, the saving is not as great due to the requirement for post-disaster debt.
• On average and at lower levels of losses, the total cost of Strategy B is now lower compared to the base case scenario as the
premium has reduced. On average, Strategy B is still the most expensive (consistent with the base case scenario).
• At the 1 in 10 year return period Strategy B becomes more cost-effective strategy (contrary to the base case scenario where
Strategy D was cheapest at this level of loss) since losses are fully covered up to the 1 in 10 year loss, but the premium is
lower than the base case scenario premium (due to the overall reduced coverage).
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Increase layers of non-insurance finance arrangements
Figure AZ4.3 and AZ4.4 demonstrate the relative cost savings and overall costs of the four strategies over different return
periods, assuming that the layers of non-insurance arrangements are doubled.
Figure AZ4.3 – Relative Cost Saving of Increasing Non-Insurance Layers
80% 72%
60%
Percentage cost decrease
(relative to Strategy A)
40%
20%
2% 4%
-25% -4% -42% 0% -1% -7%
0%
-20%
-40%
-60%
B C D B C D B C D
Average 1 in 10 year return period of loss 1 in 30 year return period of loss
Source: Clarke, Cooney, Edwards, and Jinks (2016).
Figure AZ4.4 – Total Cost of Increasing Non-Insurance Layers
300
250
Total cost (US$m)
200
150
100
50
0
A B C D A B C D A B C D
Average 1 in 10 year return period of loss 1 in 30 year return period of loss
Reserve Fund Contingent Credit Insurance Budget reallocation Post-disaster debt
Source: Clarke, Cooney, Edwards, and Jinks (2016).
82 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
• In this sensitivity scenario, the average costs of Strategies A, C, and D increase slightly. This is because losses up to the 1
in 11 year return period are met by reserve funds which become marginally more expensive than post-disaster debt beyond
the 1 in 7.6 year loss (see Figure AZ3.1).
• The average cost of strategy B reduces slightly, because there is a reduction in the premium payable, due to the higher
attachment point (though this is partially offset by the higher equivalent pricing multiple that results from the assumed
constant risk volatility loading).
• At the 1 in 10 year return period, the cost of Strategies A and C are identical because losses are met by reserve funds
in both strategies. Although losses are also met by reserve funds in Strategies B and D, the cost is higher due to the
contingent credit arrangement fee and insurance premium. For Strategy D, the difference is small; however, for Strategy B,
the insurance premium means the cost is 42 percent higher than Strategy A.
• At the higher return periods, Strategy B continues to be the most cost-effective; however the cost savings of Strategy B
relative to Strategy A are reduced. This is because losses up to the 1 in 11 year return period are met by reserve funds,
which become marginally more expensive, and because it is less cost-effective to attach insurance at a higher level.
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Glossary
Average A number expressing the central or typical value in a set of data. In this report, average refers to
the mean, which is calculated by dividing the sum of the values in the set by the number of values
(data points) in the set.
Average Annual The average (mean) annual loss to a layer, calculated by summing all losses above the layer
Loss minimum and below the layer maximum in the relevant simulations and dividing by the total
number of simulations.
Budget The release of resources originally designated for a different purpose to cover costs associated
reallocation with financing losses due to disasters considered.
Capital reserves The funds held in respect of a potential contingent liability, typically held by insurers or any party
taking on an element of risk.
Contingent credit Financing credit available from a source to a recipient which is contingent on a trigger (for
example, a natural disaster occurring), and for which the recipient pays a set-up fee as a
percentage of the total credit available.
Contingent liability A potential payment obligation that may be incurred depending on the outcome of a future event.
Cost / Opportunity The cost of an alternative use of the finance that must be forgone in order to pursue a certain
cost strategy. Throughout this report, references to cost imply opportunity cost.
Delay factor The assumed cost increase due to delayed response. A delay factor of 1.5 corresponds to a
situation where delayed response of US$1.50 has the same impact as US$1 of fast response cost.
This delay factor is applied to financial or budgetary instruments assumed to be slow in situations
where slow response is less cost-effective than fast response.
Ex-ante Before an event – based on forecast results rather than actual results. For example, the ex-ante
investment return is the expected return on an investment portfolio.
Ex-post Subsequently to an event – based on actual results rather than forecast results. For example, the
ex-post investment return is the known investment return that was achieved on an investment
portfolio.
Hurdle rate Rate of return on foregone investments, specifically considered in the context of budget
reallocation. This rate is also used to calculate the (opportunity) cost of the insurance premiums
that will need to be paid by government or development partners.
Insurance (risk An arrangement by which a company undertakes to provide a guarantee of compensation for
transfer product) specified loss in return for payment of a specified premium.
Insurance The trigger point at which insurance will start to pay, for example an insurance attachment of
attachment US$5m, means that losses that are smaller than US$5m would not trigger a payout from the
insurance contract.
Insurance The maximum point to which insurance will cover losses, for example, phrased as up to the 1 in 30
exhaustion year loss or up to a loss of US$100m.
(insurance limit)
84 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE
Marginal cost The additional average opportunity cost of each risk finance instrument (such as, insurance) per
unit of annual average loss, for losses at a specific return period.
Opportunity cost The cost of an alternative use of the finance that must be forgone in order to pursue a certain strategy.
Parametric A type of insurance that does not indemnify the pure loss (that is, the pure response costs
insurance incurred), but ex ante agrees to make a payment upon the occurrence of a triggering event. This is
common for natural disaster insurance where the trigger might be the severity of a windstorm or
the magnitude of an earthquake on a Richter scale.
Pricing multiple Premium
Pricing multiple =
Average Annual Loss
A factor applied to expected losses by an insurance company to determine the premium required
for the insured risk. This factor would reflect the cost of capital and expense costs of the insurance
company.
Return period (of An indication of the likelihood of an event occurring; a recurrence interval demonstrating how
loss) frequently an event is expected to occur.
For example, an event or a loss with a return period of 5 years is statistically expected to recur
every 5 years on average over an extended period of time (or has a 20 percent probability of
occurrence).
Risk finance A set of finance instruments combined to provide funds to cover the financial effect of potential
strategy losses.
Risk volatility Premium charged - Average Annual Loss
loading Risk volatility loading =
Standard deviation of loss
The factor applied to the chosen measure of risk (in this case the standard deviation) by the party
accepting the risk (in this case insurers), in a set of simulated losses.
With Technical Input From