A Methodology for Calculating the Opportunity Cost of Layered Sovereign DRFI Strategies

Transcription

1 IMPACT APPRAISAL FOR SOVEREIGN DISASTER RISK FINANCING AND INSURANCE PROJECT: PHASE 1 ACTUARIAL AND REINSURANCE, PAPER 1 A Methodology for Calculating the Opportunity Cost of Layered Sovereign DRFI Strategies Daniel Clarke Richard Poulter

2 Abstract This paper proposes a framework to assess the economic opportunity cost of various budgetary and financial instruments available to governments for funding disaster-induced losses. The framework presented in this paper can be used by governments to identify the most appropriate and financially efficient strategies to fund disaster losses, based on their country risk profile and political constraints faced. Formulae and a theoretical rationale for calculating the opportunity cost of layered strategies including each of the following SDRFI instruments are presented: Risk transfer instruments including insurance, reinsurance, cat swaps, and cat bonds. Reserves / ex-ante budget allocations Contingent credit Emergency ex-post budget reallocations Ex-post direct credit Following this the concepts are brought together and an example provided of the total cost of three different layered sovereign SDRFI strategies for a lower-middle income country facing earthquake risk. Finally the paper concludes with a summary of the findings and recommendations for key decision makers, showing that financing low layers with risk transfer is costly where reserves and contingent credit are more cost efficient, and reliance on ex-post credit is costly but the only realistic solution for very high losses as the cost of insurance becomes prohibitive. This paper makes a contribution to the literature in this area by suggesting implementable, calculable, simple formulae for capturing the cost of risk financing, allowing governments to directly compare the relative costs of different SDRFI instruments when designing and implementing layered SDRFI programs. About the Project The UK Department for International Development (DFID), the World Bank Group and the Global Facility for Disaster Reduction and Recovery (GFDRR) have partnered to improve evaluation and evidence for sovereign disaster risk financing and insurance (DRFI). The $3.2 million, 3-year ( ) project was launched in 2013, and will develop and test a quantitative impact appraisal framework for sovereign DRFI. The project aims to meet this need by developing a methodology to evaluate a range of DRFI programs and provide quantitative results based on five country-specific case studies, and seeks to understand whether forward-looking impact appraisals can help effectively target support for disaster risk activities. The results will help better target and prioritize future investments from national governments and international donors in sovereign DRFI programs. This paper forms part of the background research underpinning the draft operational framework, to be pilot tested in the case studies in Phase 2 of the project.

3 A METHODOLOGY FOR CALCULATING THE OPPORTUNITY COST OF LAYERED SOVEREIGN DRFI STRATEGIES SOVEREIGN DRFI IMPACT APPRAISAL PROJECT ACTUARIAL AND REINSURANCE, PAPER 1 CONTENTS 1 Introduction Opportunity Cost Formulae Amount of risk financed by each tool Counterfactuals Risk transfer Reserve fund / ex-ante budget allocation Contingent line of credit Ex-post emergency budget reallocation Ex-post direct credit Example SDRFI programs for a given risk profile Selected risk profile Parameter assumptions Strategy opportunity costs Conclusion References... 18

4 ACKNOWLEDGEMENTS The authors would like to thank members of the core team of the SDRFI Impact Appraisal Project, along with members of the joint World Bank / GFDRR DRFI Program, for their comments and suggestions on the methodology discussed within this paper. We would also like to thank the generous support of the UK s Department for International Development (DFID) of the SDRFI Impact Appraisal Project itself, and also the continued support of Switzerland s State Secretariat for Economic Affairs (SECO) which has supported the development of the DRFI tools and methodology discussed in this paper. ABSTRACT This paper proposes a framework to assess the economic opportunity cost of various budgetary and financial instruments available to governments for funding disaster-induced losses. The framework presented in this paper can be used by governments to identify the most appropriate and financially efficient strategies to fund disaster losses, based on their country risk profile and political constraints faced. Formulae and a theoretical rationale for calculating the opportunity cost of layered strategies including each of the following SDRFI instruments are presented: Risk transfer instruments including insurance, reinsurance, cat swaps, and cat bonds. Reserves / ex-ante budget allocations Contingent credit Emergency ex-post budget reallocations Ex-post direct credit. Following this the concepts are brought together and an example provided of the total cost of three different layered sovereign SDRFI strategies for a lower-middle income country facing earthquake risk. Finally the paper concludes with a summary of the findings and recommendations for key decision makers, showing that financing low layers with risk transfer is costly where reserves and contingent credit are more cost efficient, and reliance on ex-post credit is costly but the only realistic solution for very high losses as the cost of insurance becomes prohibitive. This paper makes a contribution to the literature in this area by suggesting implementable, calculable, simple formulae for capturing the cost of risk financing, allowing governments to directly compare the relative costs of different SDRFI instruments when designing and implementing layered SDRFI programs. 1

5 1 INTRODUCTION This paper proposes a framework to assess the economic opportunity cost of various budgetary and financial instruments available to governments for funding disaster-induced losses. The increasing frequency and severity of climate extremes has forced governments to consider new ways of meeting the financial consequences of natural disasters, and there is a growing interest in implementing Sovereign Disaster Risk Financing and Insurance (SDRFI) programs in an attempt by governments to be financially prepared for when disasters occur. This has resulted in tremendous growth in the number and type of financial and budgetary instruments available, ranging from disaster reserve funds and lines of contingent credit to insurance instruments, but to date there has been no attempt to quantify the true economic cost of these various instruments in a single coherent framework. Therefore at present, governments have no way of determining whether the programs and financial strategies they are employing are appropriate and efficient bearing in mind the risks they face. The framework presented in this paper can be used by governments to identify the most appropriate and financially efficient strategies to fund disaster losses, based on their country risk profile and political constraints faced. Formulae and a theoretical rationale for calculating the opportunity cost of each of the following SDRFI instruments are presented: Risk transfer instruments including insurance, reinsurance, cat swaps, and cat bonds. Reserves / ex-ante budget allocations Contingent credit Emergency ex-post budget reallocations Ex-post direct credit. In addition to calculating the opportunity cost of each instrument, this paper addresses the question of how these instruments should best be combined to finance disaster losses given defined country risk profiles. A small amount of literature exists regarding the theoretical costs of individual instruments, for example Clarke and Mahul (2011) provide a model to analyse the use of contingent credit in addition to reserves and/or insurance as part of a SDRFI strategy. However, until now there has been no coherent methodology for governments to assess the true economic cost of alternative risk financing strategies. First the proposed opportunity cost formulae for each instrument are presented, along with the economic rationale underpinning the formulae. Following this in Section 3 the concepts are brought together and examples provided of different sovereign SDRFI programs, with an indication of the varying costs of each programs for specific loss distributions. Finally the paper concludes with a summary of the findings and recommendations for key decision makers. 2

6 2 OPPORTUNITY COST FORMULAE 2.1 AMOUNT OF RISK FINANCED BY EACH TOOL The following formulae describe the opportunity cost of using each instrument to finance losses based on the amount of risk (or layer ) each instrument is financing. A typical risk financing strategy is formed of a combination of the various instruments discussed below, layered in such a way that more instruments provide payments when losses are more extreme. The diagram below shows an example SDRFI strategy which utilises a reserve fund; a contingent line of credit; risk transfer; ex-post emergency budget reallocation; and reliance on ex-post borrowing from capital markets for the most extreme losses Ex-post credit Insurance Attachment (A) Risk Transfer Exhaustion (E) Ceding % (C) Maximum Loss (E A) x C $15m $75m 60% $36m 60 $m Emergency budget reallocation Contingent credit Reserve fund / ex-ante annual budget allocation Figure 1: Example SDRFI strategy showing layer structure Other instruments Attachment Exhaustion Maximum Loss Reserves $0m $5m $5m Contingent Credit $5m $15m $10m Emergency Budget $15m $32.5m $7m Reallocation Ex Post Credit $32.5m In the strategy shown in Figure 1: Losses up to $5m are financed through a reserve fund A line of contingent credit is then available for losses between $5m and $15m. Risk transfer (for example an insurance policy) has been purchased covering losses from $15m to $75m, with a ceding percentage of 60%. Losses that occur within the attachment and exhaustion of the insurance policy must therefore be funded 40% by other instruments. Emergency budget reallocation of up to $7m is available. Note in the example above, emergency budget reallocation finances losses from $15m alongside the insurance coverage (therefore the exhaustion point above is calculated as: exhaustion point = attachment point + maximum loss (1 ceding % of risk transfer) Ex Post direct credit is used for: o 40% of losses above $32.5m where insurance coverage is still available but emergency budget reallocation has been exhausted. o 100% of losses above $75m, the exhaustion point of the risk transfer. Note that while the diagram above shows only losses up to $100m for presentation purposes, it is assumed that ex post credit is used to fund losses of any size (i.e. the final layer is infinite). 3

7 The formulae below provide the opportunity cost of each of these instruments following a given loss amount to the layer that each instrument is financing. It is possible to run a large number of simulations of losses, and then take the average of the calculated costs to provide an indication of the Average Annual Cost (AAC) of each SDRFI instrument. The AAC of each SDRFI instrument for the example programs illustrated in section 3 are based on 10,000 losses taken from a specified loss distribution. 2.2 COUNTERFACTUALS The following formulae calculate the economic cost of using each instrument to fund a particular layer of disaster losses compared with the counterfactual of not financing the particular layer of disaster losses at all. 2.3 RISK TRANSFER The cost formula below is based on an indicative risk transfer pricing rule. COST FORMULA The risk transfer pricing rule is defined in terms of the following: % ceded = percentage ceded to insurer AAL = annual average loss to layer, with layer defined by the attachment and exhaustion points and the ceding percentage of the risk transfer policy St.Dev =standard deviation of annual simulated losses in layer IPRF = Insurance Premium Risk Factor (IPRF). The IPRF will depend on the assumed correlation between the risk transfer policy definition of loss and the actual loss incurred, thereby capturing the notion that the higher the correlation the more costly the policy. Specifically: - Indemnity insurance contracts have 100% correlation between the policy definition of the loss and the actual losses incurred, and are assumed to be the most expensive form of insurance policy. - An index-based or parametric risk transfer contract (where for example there may be a 60% correlation between the losses under the policy definition and the actual losses incurred) will have a lower IPRF figure and is therefore cheaper. It is assumed there are allowances within the IPRF to cover expenses, profit, and an insurer s cost of holding reserves. Cost of financing fiscal disaster losses through risk transfer = % ceded x {AAL + (IPRF x St. Dev)} ECONOMIC RATIONALE The cost of risk transfer is simply the price of the policy, which is assumed to be dependent on both the expected annual loss to the policy and the variability of those losses. 4

8 The cost of the policy is calculated using the AAL added to the standard deviation of the losses multiplied by the IPRF the loading that insurers add to the expected losses to cover the cost of bearing risk. The resulting premium is linear in the ceding percentage. Moreover, the premium multiple will be higher for higher layers of risk, where the St.Dev is greater as a proportion of AAL. The formula above is consistent with standard reinsurance pricing techniques, although the value of the IPRF can vary widely based on the (re)insurers risk perception, capital position, level of diversification of risk offered by the contract, recent large losses, and by market conditions. Flower et al. (2006) suggest the figure could lie in the range of 30% 70%. 2.4 RESERVE FUND / EX-ANTE BUDGET ALLOCATION SIMPLIFYING ASSUMPTIONS 1. A government must borrow from the commercial market at their marginal ex-ante borrowing rate in order to fund reserves. 2. All losses occur at the start of the year. 3. Investment return is earned throughout the year on the amount not used to fund losses. 4. It is assumed that the debt used to finance the reserve fund can be repaid at the end of the year at no frictional cost, for example by restructuring debt. The cost of the reserve fund therefore only includes one year of the spread between interest payable on debt and investment return on reserves. 5. The interest rate charged on amounts borrowed ex-ante is independent of outstanding debt. This is in contrast to the interest rate charged for amounts borrowed ex-post (discussed in section 2.7 below) which is assumed to increase with increasing levels of outstanding debt. 6. Any reserve fund or ex-ante budget allocation is available immediately to fund losses following a disaster event, and thus the cost is not subject to a delay factor. This is in contrast to ex-post direct credit where it is assumed that funds would not be available immediately following a disaster event. COST FORMULA The formula is defined in terms of the following: L = Loss amount in layer R = Total amount of reserves / ex-ante budget allocation i = Interest rate charged on amounts borrowed ex-ante r = Investment return earned on amounts not used to fund losses d = Discount rate used to calculate the cost at the start of the year 5

9 Cost of financing fiscal disaster losses through reserves = R x 1 i 1d (1) (R L) x 1r 1d (2) ECONOMIC RATIONALE With using a reserve fund or ex-ante budget allocation, the government: 1. Has to borrow the amount required to fund the reserves, and pays a year s interest on this amount at the marginal ex-ante borrowing rate. 2. Receives investment return on amounts not used to fund disaster losses. It is assumed that the government will continue borrow money and invest in projects until the marginal interest rate of ex-ante borrowing and the marginal internal rate of return on projects are equal. The marginal interest rate of ex-ante borrowing, i, is therefore used as the discount rate to calculate the cost of holding reserves in present values, d. The interest rate and discount rate being equal indicates that a government borrowing an additional $1 for the current year s budget costs $1 in present-value economic terms. With the assumption that i=d, the above formula simplifies somewhat with the first term (1) reducing to only the full amount of reserves, R. It is assumed that all disaster losses occur at the beginning of the fiscal year, (i.e. the point at which the funds are borrowed). The reserves not used to fund disaster losses generate a positive investment return, treated as negative cost in the above formula (2). The investment returns generated have the effect of reducing the cost to the government of borrowing to fund the reserves / ex-ante allocation only when there is not a full loss to the layer. 2.5 CONTINGENT LINE OF CREDIT SIMPLIFYING ASSUMPTIONS 1. Any loan facility at a favourable interest rate (for example a World Bank loan facility) is fully utilised under the counterfactual, and when a contingent line of credit is used this loan facility is reduced by the amount of the contingent line of credit. It is therefore assumed that the government must 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 other expenditures. 2. All losses occur at the start of the year. 3. It is assumed that contingent credit arrangements can be renegotiated at the end of the year at no frictional cost, for example by restructuring debt. The cost of contingent credit therefore only includes one year of the spread between the favourable interest rate which would have been paid under the counterfactual and the interest rate payable on amounts borrowed in order to finance the same portfolio of other expenditures as the counterfactual. 6

10 4. Any amounts drawn down to fund losses are subject to interest, and are repaid at the end of the fiscal year (for example through debt restructuring). 5. Any arrangement fee is annualised and is payable at the start of the year. 6. Funds from a contingent line of credit are available immediately to fund losses following a disaster event, and thus the cost is not subject to a delay factor. COST FORMULA The formula is defined in terms of the following: L = Loss amount in layer C = Total amount of contingent credit available i = Interest rate charged on amounts borrowed ex-ante c = Interest rate charged on amounts drawn down as contingent credit d = Discount rate used to calculate the cost at the start of the year F = Annualised arrangement fee Cost of financing fiscal disaster losses through contingent credit = L x 1 c 1d (3) + C x ic 1d (4) + F (5) ECONOMIC RATIONALE The first term (3) in the above formula reflects the interest charged on the amount drawn down, discounted for a single year (as it is assumed any amounts drawn down are repaid at the end of the year). The second term (4) reflects the opportunity cost of utilising a contingent line of credit. It is assumed that utilising a line of contingent credit reduces the government s ability to borrow funds at a favourable interest rate, c, and in order to maintain the same fiscal position as the counterfactual the government must borrow the amount of the line of contingent credit, C, from the commercial market at the government s ex-ante borrowing rate, i. It is assumed that i > c. As an example, the following diagram shows that under the counterfactual there exists a World Bank loan facility of $100m which is fully utilised. If a contingent line of credit of $10m is used this loan facility is reduced to $90m, and the government is required to borrow a further $10m to maintain the same fiscal position as the counterfactual. 7

11 $10m $10m Amount required to maintain fiscal position $m $100m $90m Contingent line of credit World Bank loan facility 20 0 Counterfactual Utilising contingent credit Figure 2: Reduced ability of borrowing funds at a favourable interest rate when utilising contingent credit The opportunity cost of using a contingent line of credit is calculated as the difference between the rate the government must now borrow at, i, and the favourable interest rate, c, which the government borrows at under the counterfactual. It is assumed all amounts are repaid at the end of the fiscal year. The final term in the cost formula (5) is the annualised arrangement fee payable. For example where there is a structured arrangement fee usually payable over a number of years this is recalculated into one single up-front fee. 2.6 EX-POST EMERGENCY BUDGET REALLOCATION SIMPLIFYING ASSUMPTIONS 1. All losses occur at the start of the year. 2. It is assumed that a government project not implemented due to diverting funds toward disaster losses would be implemented in the following year, thus the government only forgoes one year of social returns which would have been gained under the counterfactual. 3. Funds from ex-post budget reallocations are available immediately to fund losses following a disaster event, and thus the cost is not subject to a delay factor. COST FORMULA The formula is defined in terms of the following: L = Loss amount in layer h =Government hurdle-rate used to fund investment projects d = Discount rate used to calculate the cost at the start of the year 8

12 Cost of financing fiscal disaster losses through budget reallocation = L x 1 h 1d (6) ECONOMIC RATIONALE The interest rate applied to the average loss incurred is taken as the hurdle rate required by the government to fund investment projects. It is assumed that a government project not implemented due to diverting funds toward disaster losses would be implemented in the following year, thus only one year of interest is charged on the annual average loss (6). 2.7 EX-POST DIRECT CREDIT SIMPLIFYING ASSUMPTIONS 1. The amount of ex-post credit available is infinite. 2. The interest rate charged is an increasing function of outstanding sovereign debt at the start of the year (i.e. a higher interest rate is payable if outstanding sovereign debt is higher). 3. All losses occur at the start of the year. 4. The total amount of ex-post direct credit borrowed is repaid in annual equal repayments at the end of each year over a specified term. There is an initial grace period during which repayments are not payable; however any amounts borrowed are still subject to interest during the grace period. 5. Ex-post direct credit is not available to fund losses immediately following a disaster event. Losses which relate to expenditure on disaster relief and recovery are therefore inflated by a delay factor. Estimating a suitable value for this parameter is discussed below. COST FORMULA The formula is defined in terms of the following: L = Loss amount in layer p = Proportion of losses relating to disaster relief and recovery D = Delay factor applied to loss e =Interest rate charged on amounts borrowed d = Discount rate used to calculate the cost at the start of the year t = Term of repayment including grace period g = Grace period a n i =The present value of an annuity-immediate is with term n and interest rate i 9

13 Cost of financing fiscal disaster losses through ex post credit = L x p x D x (1e) g a tg e x a tg d (1d) g (7) + L x 1 p x 1+e g a t g e x a t g d (1+d) g (8) ECONOMIC RATIONALE The formula considers the proportion of losses to the layer that relate to disaster relief and recovery (7), and those that relate to longer-term expenses such as reconstruction (8). Based on the assumptions listed above, the formula is explained as follows. Equation (7): 1. L x p x D x (1 + e) g : The amount borrowed (the loss amount to the layer, L), multiplied by the proportion of costs relating to disaster relief and recovery, multiplied by the delay factor D (discussed below), and inflated by the interest rate payable, e, for the grace period, g. 2. a tg e : This amount is then divided by the formula for an annuity-immediate at the rate payable on the amount borrowed, e, for the remainder of the term, t g. This gives the annual amount payable, assuming equal repayments at the end of each year for the remainder of the term. 3. a tg d : Multiplying the annual payment amount by an annuity-immediate at the discount rate, d, for the remainder of the term, t g, gives the value of the accumulated annual payments at the end of the grace period, assuming equal repayments at the end of each year for the remainder of the term. 4. (1 + d) g : Dividing the by 1 + the discount rate for the grace period gives the present value of the annual repayments. Equation (8): All terms are the same as equation (7), except the losses not relating to disaster relief and recovery are not inflated by the delay factor. ESTIMATING THE DELAY FACTOR In the above formula it is assumed that ex-post direct credit cannot be obtained immediately to fund losses following a disaster event. It is proposed that in the absence of disaster response efforts (due to the unavailability of funds) the losses that relate to relief and recovery expenditure will increase, and so the amount required to fund the losses is greater than if the funds had been available immediately. This 10

14 is represented by the factor D, applied to the loss amounts relating to relief and recovery expenditure, L x p in the above formula (7). There are several factors which can impact the delay factor, such as further degradation of assets in the absence of reconstruction and the consequences of lack of income due to asset damages (Hallegatte, 2014). In this paper we propose the delay factor D can be calculated based the internal rate of return (IRR) for public service or government projects which are delayed due to the occurrence of a disaster event. As the IRR is an effective annual rate, and benefits are assumed to accumulate continuously, we define the continuous IRR, δ as: δ = In(1 + IRR) If we assume the government receives a continuous benefit stream of 1 per year for a particular program of expenditure, then the present value of this discounted at the continuous IRR is: Present value of benefit stream of 1 discounted at continuous IRR = 1 δ (9) If this benefit stream is instead delayed by t, then: Present value of benefit stream of 1 discounted at continuous IRR starting after a delay of t = = 1 δ x 1 (10) e (δt) Taking the ratio of these two values gives the amount lost due to the delay in the income stream in present value terms, which can be used as an estimate of the delay factor: Delay factor = 1 δ x 1 δ = 1 e(δt) e (δt) As a numerical example, consider the following: Annual effective IRR for government projects = 40% Continuous IRR, δ = In(1.4) = Time delay in funding = 9 months Delay factor = e (0.3365)x( 9 12 ) = This indicates the losses in the layer due to disaster response and relief which are funded by ex-post direct credit will be 28.7% higher, due to the effect of the delay in arranging the funds (based on these assumptions). While this offers a methodology for calculating the delay factor using the IRR as a proxy for the social discount rate, S, we also note the following: 11

15 In practice, the IRR may not be equal to the social discount rate, S, and may be significantly less, where a dollar invested at the IRR would have a Net Present Value (NPV) of IRR/S. This indicates the delay factor D is likely to be understated when calculated in the way proposed above. In addition the formula above assumes full optimaisation and no frictional costs. In reality an unplanned and disruptive interruption to an investment programme is likely to be substantially more costly than the IRR, so again the factor D is likely to be understated when calculated as above. 3 EXAMPLE SDRFI PROGRAMS FOR A GIVEN RISK PROFILE In this section we explore the relative costs of three different SDRFI strategies for a defined country risk profile, described in section 3.1. Following this the assumptions for each of the parameters in the cost formulae are given in section 3.2, and the opportunity costs of each strategy are analysed in section SELECTED RISK PROFILE The chosen example country is a lower-middle-income economy (based on the World Bank country classification). For simplicity only earthquake risk is analysed here, although the described methodology could be applied to different types of perils, or an all-perils approach could also be used. The figures described below are based on the results of 10,000 simulations from a catastrophe risk model calibrated for the example country. Presented losses are on an annual aggregate basis (and so losses from events occurring in the same year are summed to give the total annual loss). 8,000 7,000 6,000 5,000 Annual aggregate 4,000 loss ($m) 3,000 2,000 1, Return period (years) Annual losses for selected return periods Return period (years) Loss ($m) , ,000 4, ,000 7,240.5 Key statistics GDP ($m) 67,738.8 Annual average loss (AAL, $m) 64.6 AAL / GDP 0.1% 100 year loss / GDP 1.6% Figure 3: Loss exceedance curve for simulated earthquake losses in example country 3.2 PARAMETER ASSUMPTIONS The following assumptions are made in order to calculate the opportunity cost for each instrument using the formulae described in section 2 of this paper. 12

16 RISK TRANSFER The AAL and standard deviation of losses are calculated based on the defined risk profile and the selected attachment and exhaustion points within each strategy. The ceding % is selected for each strategy. The insurance product is assumed to be indemnity insurance and therefore the IPRF is expected to be higher than for parametric insurance. In the calculations below we have assumed a value of 30% for the IPRF. RESERVES The amount of reserves available (R) is selected for each strategy. The interest rate on long-term government borrowing (i) is selected as 10% The discount rate (d) is selected to be the same as the interest rate on long-term borrowing (i) and so is also 10%. The investment return earned on amounts not used to fund losses (r) is selected as 8%. CONTINGENT CREDIT The amount of contingent credit available (C) is selected for each strategy. The interest rate on long-term government borrowing (i) is selected as 10% The discount rate (d) is selected to be the same as the interest rate on long-term borrowing (i) and so is also 10%. The interest rate charged on amounts drawn down as contingent credit (c) is selected as 7%. The annualised arrangement fee (F) is selected as 0.1% of the amount of contingent credit available (C). EX-POST EMERGENCY BUDGET REALLOCATION The amount of budget reallocation available is defined in terms of a selected % of annual government expenditure. Government expenditure is assumed to be 20% of GDP. The government hurdle-rate used to fund investment projects (h) is selected as 20%. The discount rate (d) is selected to be the same as the interest rate on long-term borrowing (i) and so is 10%. EX-POST DIRECT CREDIT The amount of ex-post direct credit available is assumed to be infinite. The proportion of losses relating to disaster relief and recovery (p) is selected as 20%. The delay factor (D) applied to losses relating to disaster relief and recovery is 1.3. The term of repayment including grace period (t) is 5 years. The grace period (g) is 2 years. The discount rate (d) is selected to be the same as the interest rate on long-term borrowing (i) and so is 10%. 13

17 The interest rate charged on amounts borrowed (e) is an increasing function of outstanding sovereign debt at the start of the year, which is assumed to be 25% of GDP. The interest rate is defined as follows: Interest Rate 25% 20% 15% 10% 5% Interest on ex-post direct credit Level of borrowing (% of GDP) Interest rate Up to 40% 10% 40% - 100% 14% Over 100% 20% 0% 0% 20% 40% 60% 80% 100% 120% Level of borrowing (% of GDP) Figure 4: Interest rate on ex-post direct credit for different levels of borrowing Given the assumed outstanding level of sovereign debt (25% of GDP), if ex-post direct credit is required to fund losses of up to 15% of GDP (approximately $10bn) the interest rate applied will be 10%. For losses between 15% and 75% of GDP (making total sovereign debt between 40% and 100% of GDP) the interest rate will be 14%, while further losses will be paid at a 20% interest rate. 3.3 STRATEGY OPPORTUNITY COSTS In this section we first present the three selected SDRFI strategies. Following this the opportunity cost of each strategy is analysed. SELECTED STRATEGIES The three selected SDRFI strategies are described in the tables below, and shown graphically in figure 5. Attachment (A) Risk transfer Exhaustion (E) Ceding % (C) Maximum Loss (E A) x C Strategy 1 $30m $150m 60% $72m Strategy 2 $100m $250m 40% $60m Strategy 3 $0m $400m 20% $80m 14

18 Other instruments (amount available) Emergency budget reallocation (% of Reserves Contingent credit government expenditure) Ex-post credit Strategy 1 $10m $20m 10% Strategy 2 $25m $0m 20% Strategy 3 $2m $40m 5% 250 Ex-post credit 200 Insurance $m Emergency budget reallocation Contingent credit 0 Strategy 1 Strategy 2 Strategy 3 Reserve fund / ex-ante annual budget allocation Figure 5: Structure of selected strategies OPPORTUNITY COST OF EACH STRATEGY The cost formulae outlined in section 2 are calculated for each simulated loss, and the costs averaged over the 10,000 simulations. The annual average cost (AAC) of each instrument within each strategy is shown in Figure 6 below ,692,315 77,197,456 72,090,085 Ex-post credit Insurance $m Emergency budget reallocation Contingent credit Strategy 1 Strategy 2 Strategy 3 Figure 6: Annual average cost of each strategy Reserve fund / ex-ante annual budget allocation 15

19 As shown in Figure 6, the majority of the cost for each strategy is due to reliance on ex-post credit, although the annual average cost of the total strategy is highest for Strategy 1. A useful diagnostic is to take selected points from the cost exceedance curve for specified return periods from the distribution of costs for each strategy. Figure 7 shows strategies 2 and 3 relative to strategy 1 for the annual average, 1-in-10 year and 1-in-100 year costs. 180% 160% 140% 120% 100% 80% 60% 40% 20% 0% Strategy 1 Strategy 2 Strategy 3 Annual average cost 1-in-10 Year Cost 1-in-100 Year Cost Figure 7: Cost of strategies 2 and 3 relative to strategy 1 for the annual average cost and defined return periods Figure 7 shows that both strategies 2 and 3 are similar to strategy 1 when looking at the annual average cost or 1-in-100 year cost, but both are much more expensive when considering the 1-in-10 year costs. This is due to the fact that: All three strategies rely heavily on ex-post credit for high level losses, and so the costs of the strategies are similar at the 1-in-100 year return period. Strategy 2 has a much higher 1-in-10 year cost relative to strategy 1 due to the higher attachment point of the insurance, and the fact ex-post credit is relied upon for lower losses as contingent credit is not utilised. Strategy 3 also has a higher 1-in-10 year cost as contingent credit is utilised at an earlier stage due to the limited reserves. Another diagnostic we can assess is the probability that each instrument is exhausted under each strategy, as shown in Figure 8 below. 16

20 80% Insurance 70% Probability 60% 50% 40% 30% Emergency budget reallocation Contingent credit 20% 10% 0% Strategy 1 Strategy 2 Strategy 3 Reserve fund / ex-ante annual budget allocation Figure 8: Probability each instrument is exhausted under each strategy As expected, there is a very high probability that the reserve fund is exhausted under strategy 3 (as this strategy has a particularly low reserve fund), while all three strategies have a similar probability that the emergency budget reallocation will be exhausted. The probability that the insurance is exhausted is lowest under strategy 3 due to the particularly high exhaustion point. 4 CONCLUSION Until now there has been no coherent methodology for governments to assess the opportunity cost of risk financing strategies which combine multiple instruments and budgetary mechanisms. This paper makes a contribution to the literature in this area by suggesting implementable, calculable, simple formulae for capturing the cost of risk financing, allowing governments and their advisors to directly compare the relative costs of different SDRFI instruments when designing and implementing complex SDRFI programs. While the example provided in section 3 focuses only on one particular risk profile, the results are intuitive: financing low layers with risk transfer it is costly, reliance on ex-post credit for low layers is also costly, but funding all losses with a reserve fund will not be feasible for most governments of developing countries. The authors suggest further investigation is required to provide evidence for calibration of the suggested formulae, while further analysis using different risk profiles could also yield more powerful conclusions regarding the relative costs of different instruments for different types of hazards. 17

21 5 REFERENCES 1. Clarke D, Mahul O. Disaster risk financing and contingent credit: a dynamic analysis. World Bank Policy Research Working Paper Series, Paper 5693, Flower, M. et al. Reinsurance pricing: Practical issues and considerations GIRO Reinsurance Matters! Working Party, Hallegatte, S. The indirect cost of natural disasters and an economic definition of macroeconomic resilience. SDRFI Impact Appraisal project,