Earthquake Vulnerability Reduction Program in Colombia A Probabilistic Cost-benefit Analysis

Transcription

1 Publc Dsclosure Authorzed Earthquake Vulnerablty Reducton Program n Colomba A Probablstc Cost-beneft Analyss WPS3939 Publc Dsclosure Authorzed Abstract Francs Ghesquere, World Bank Lus Jamn, Unversty of Los Andes Olver Mahul, World Bank 1 Publc Dsclosure Authorzed Cost-beneft analyss s a standard tool for determnng the effcency of planned projects. However, one of the major dffcultes n rsk mtgaton nvestments s that benefts are by nature uncertan. In ths context, the standard approach relyng on the average value of benefts may provde an ncomplete pcture of the effcency of the rsk mtgaton project under consderaton. Ths paper presents a probablstc cost-beneft analyss relyng on a catastrophe rsk model. It produces rsk metrcs such as the exceedance probablty curve of the beneft-cost rato, thus provdng the decsonmaker wth a more complete rsk analyss of the net benefts of the project. Ths s llustrated wth the earthquake vulnerablty reducton project n Colomba. Key words: Colomba, cost-beneft analyss, dsaster rsk management, earthquake, probablstc rsk models. Publc Dsclosure Authorzed World Bank Polcy Research Workng Paper 3939, June 2006 The Polcy Research Workng Paper Seres dssemnates the fndngs of work n progress to encourage the exchange of deas about development ssues. An objectve of the seres s to get the fndngs out quckly, even f the presentatons are less than fully polshed. The papers carry the names of the authors and should be cted accordngly. The fndngs, nterpretatons, and conclusons expressed n ths paper are entrely those of the authors. They do not necessarly represent the vew of the World Bank, ts Executve Drectors, or the countres they represent. Polcy Research Workng Papers are avalable onlne at 1 Correspondng author: MC 9-904; 1818 H Street, NW; Washngton, D.C Phone: (202) Emal: omahul@worldbank.org.

2 1. Introducton Due to ts locaton, Colomba s hghly prone to natural dsasters. The country strdes the Andean mountan regon and the Pacfc belt of fre, where hgh sesmc potental combnes wth volcanc actvty. In the last 25 years, the country has suffered sx major earthquakes, three volcanc eruptons, major landsldes, avalanches, petroleum and chemcal explosons/leaks, and extensve floodng. Wth major ctes located n areas of elevated rsk, combned wth the hgh rate of urbanzaton, Colomba s extremely vulnerable to adverse natural events. Ths vulnerablty s further aggravated by contnued populaton growth and the ever ncreasng concentraton of settlements and assets. Recent trends n global clmate change followed by rsng clmatc varablty wll lkely exacerbate the country s exposure to floods, eroson, landslde, and drought. The need for a more comprehensve dsaster rsk management approach became clear followng the devastatng earthquake n Popayan n At that tme, the Government of Colomba establshed the Natonal System for Dsaster Response and Preventon, shftng emphass to a broader dsaster rsk management approach and a strategy focused on rsk dentfcaton, rsk reducton, and rsk transfer. In partcular, Parlament passed Law 400 n August 1997, whch establshed sesmc-resstant buldng standards for new constructon and a tmelne for the retrofttng of key publc facltes such as hosptals and fre statons that would be needed to provde crtcal servces durng and after emergences. The World Bank, whch has been actvely supportng ths proactve approach through a seres of projects, s helpng the Captal Dstrct of Bogotá n the fnancng of a comprehensve Dsaster Vulnerablty Reducton Project. Ths project ams at reducng the Dstrct s vulnerablty to adverse natural events by strengthenng natonal capacty to manage dsaster rsk and by reducng vulnerablty n key muncpaltes. Located n a regon of Colomba prone to earthquakes, floods, and landsldes, accommodatng 7 mllon nhabtants and responsble for one-fourth of natonal gross domestc product, Bogotá DC has by far the largest concentraton of rsks n the country. Recent modelng exercses estmate that a 1-n-100-year earthquake n Bogotá DC could generate losses of about US$5 bllon. Earthquakes wth return perods of 200 years and 500 years could result n losses n excess of US$25 bllon and US$47 bllon, respectvely (Cardona 2005). Such a dsaster would have serous socoeconomc repercussons n terms of both human welfare and the overall mpact on the natonal economy. Bogotá DC already has many mportant elements of a dsaster management system. A decree establshed n October 2004 the System for Preventon and Response to Emergences (SDPAE) n Bogotá DC. The system s coordnated by the Drectorate for the Preventon of and Attenton to Emergences (DPAE), whch brngs together dverse publc, prvate, and communty actors nvolved n rsk management under the leadershp of the new mayor. 2

3 The World Bank has a long hstory of fnancng dsaster response, emergency recovery projects around the world. The Bank has dsbursed about US$40 bllon n emergency and reconstructon loans (ERLs) over the last 20 years, wth 23 percent of these ERLs provded to Latn Amercan and Carbbean countres. Recently, however, more attenton has been gven to mtgaton programs amed at enhancng governmental capacty to respond to dsasters and reduce ther rsk vulnerablty. Recent Bank-asssted projects n Colomba, Honduras, and Turkey have poneered methodologes for ntegratng rsk analyss nto urban and regonal development plannng, and for evaluatng rsk reducton measures as economc nvestments n urban and regonal nvestment programs. A standard tool for determnng the costs and benefts, and thus the effcency, of planned projects s cost-beneft analyss. It compares the costs of mplementng such projects wth ts benefts and calculates a net present value for the nvestment (or alternatvely, the economc rate of return or the beneft-cost rato). However, one of the major dffcultes n rsk mtgaton nvestments s that benefts are by nature uncertan because they depend on the occurrence of a natural dsaster. In ths context, the standard approach relyng on the average annual value of benefts does not capture the uncertanty related to the occurrence of a catastrophc event. In partcular, ths analyss fals to capture much of the nformaton generated by sophstcated probablstc catastrophe rsk models. To correct ths shortcomng, the methodology proposed by ths paper estmates the dstrbuton functon of the beneft-cost rato of mtgaton nvestments. It uses the statstcal outputs produced by the probablstc rsk models n the cost-beneft analyss, through the development of a mcroeconomc probablstc cost-beneft analyss. In partcular, ths model produces the loss exceedance curve of the beneft-cost rato of the planned mtgaton project. It thus offers decsonmakers addtonal valuable nformaton related to the economc vablty of the rsk mtgaton project under consderaton. Such nformaton provdes the decsonmaker wth, for nstance, the probablty that the project wll be vable over a gven tme perod. As such, the paper proposes expandng the standard cost-beneft analyss, whch focuses only on the expected values produced, by takng nto account the underlyng dstrbuton functon of the techncal varables. The proposed methodology s llustrated wth the earthquake vulnerablty reducton project mplemented by the Government of Colomba, wth the techncal and fnancal assstance of the World Bank. The model shows that ths US$160 mllon earthquake mtgaton project s economcally vable, gven the hgh country exposure to earthquakes, because the average beneft-cost rato s hgher than unty. 2. Probablstc Cost-beneft Analyss Estmatng project costs for the preventon or mtgaton of the effects of a natural dsaster s generally straghtforward. Estmatng projected benefts of preventon nvestments, however, s more complcated. Frst, t s not possble to predct when an actual dsaster event wll occur and wth what ntensty. Second, the effectveness of mtgaton nvestments s estmated through vulnerablty assessments that nclude a degree of uncertanty. Therefore, n dsaster mtgaton projects, whle costs are well 3

4 defned, benefts derved from lkely or avoded losses are not defntve, but are rather probablstc, at best. A macroeconomc approach s pertnent for mtgaton projects when mcro-level data are unavalable or unrelable. Macroeconomc calculatons nclude not only retrofttng nvestments but also emergency preparedness nvestments. Ths approach was adopted n the Istanbul Sesmc Rsk Mtgaton and Emergency Preparedness Project n Turkey fnanced by the World Bank. Under the Bogotá Dsaster Vulnerablty Reducton Program, structural and functonal nvestments n publc buldngs account for about 90 percent of the overall project costs. In addton, the project benefts are assessed through a sophstcated earthquake-rsk-assessment model developed under ths project. In ths context, a probablstc mcroeconomc approach for performng cost-beneft analyss, focusng on key earthquake mtgaton nvestments, s proposed. It reles on a costbeneft analyss combned wth a probablstc earthquake-rsk-assessment model. Probablstc Earthquake Rsk Model The assessment of catastrophe rsk s sgnfcantly dfferent from the evaluaton of rsks of automoble collsons or fres. The severty of the former s hgher because the causatve events are large scale and affect hundreds of square klometers, sometmes mpactng hundreds of thousands of propertes. Snce the frequency of dsaster events s partcularly low, hstorcal data are not adequate to measure potental losses. Therefore, rsk assessments need to be prospectve, antcpatng scentfcally credble events that mght happen n the future. Usng current computer technology and modern earth scence nformaton, models of earthquakes have been developed by specalzed frms for use by nsurers, re-nsurers, and government agences to assess the rsk of loss as a result of a catastrophc event. Snce large uncertantes are nherent n model estmates wth regard to event severty and frequency characterstcs n addton to consequent losses caused by such events, models often are constructed usng probablstc formulatons that ncorporate ths uncertanty nto the rsk assessment. The model, bult upon a sequence of modules, quantfes potental losses arsng from a gven hazard (for example, earthquake), as shown n Fgure 1. Fgure 1. Probablstc Catastrophe Rsk Model Hazard Module Exposure Module Vulnerablty Module Damage Module Loss Module 4

5 Hazard module. The hazard module defnes the frequency and severty of a perl, at a specfc locaton. Ths s done by analyzng the hstorcal event frequences and revewng scentfc studes performed on the severty and frequences n the regon of nterest. Once the hazard parameters for each perl are establshed, stochastc event sets are generated that defne the frequency and severty of thousands of stochastc cyclone or floodng events. Ths module can analyze the ntensty at a locaton once an event n the stochastc set has occurred. Ths module models the attenuaton/degradaton of the event from ts locaton to the ste under consderaton and evaluates the propensty of local ste condtons to ether amplfy or reduce the mpact. Exposure module. The exposure values of assets at rsk are estmated ether from avalable secondary data sources or are derved from the dstrbuton of populaton. Ths proxy approach s used when the preferred specfc ste-by-ste data are not avalable. Based on these data, the module then computes the value for all types of exposures as a product of multplcaton of the area of total buldng nventory and the average replacement cost per unt of nventory. Vulnerablty module. The module quantfes the damage caused to each asset class by the ntensty of a gven event at a ste. The development of asset classfcaton s based on a combnaton of constructon materal, constructon type (wall and roof combnaton, for example), buldng usage, number of stores, and age. Estmates of damage are measured n terms of a mean damage rato (MDR). The MDR s defned as the rato of the repar cost dvded by the replacement cost of the structure. The curve that relates the MDR to the earthquake ntensty s called a vulnerablty functon. Each asset class and buldng type wll have dfferent vulnerablty curves for each perl. Damage module. To calculate losses, the damage rato derved n the Vulnerablty module s translated nto dollar loss by multplyng the damage rato by the value at rsk. Ths s done for each asset class at each locaton. Losses are then aggregated as requred. Loss module. Ths module estmates the losses to the nsurer from the damage dstrbuton, based on the nsurance nformaton (for example, deductble, sum nsured). Buldng upon a sequence of the fve modules, the model quantfes potental losses that mght arse as a result of an earthquake. Rsk metrcs produced by the model provde rsk managers and polcymakers wth essental nformaton necessary to manage future rsks. One measure s called the Average Annual Loss and the other s the Loss Exceedance Probablty. Other measures based on these two metrcs are the Pure Rsk Premum and the Probable Maxmum Loss. Average Annual Loss (AAL). AAL s the expected loss per year when averaged over a very long perod (for example, 500 years). Computatonally, AAL s the summaton of products of event losses and event occurrence probabltes for all stochastc events n a loss model. The events are an exhaustve lst affectng the locaton/regon under consderaton, generated by stochastc modelng. In probablstc terms, the AAL s the mathematcal expectaton. 5

6 Pure Rsk Premum (PRP). PRP equals the AAL dvded by the replacement value of the asset, usually expressed as a rate per mll of monetary value. Loss Exceedance Curve (LEC). Ths represents the probablty that a loss of any specfed monetary amount wll be exceeded n a gven year. Ths s the most mportant catastrophe rsk metrc for rsk managers, snce t estmates the amount of funds requred to meet rsk management objectves. The LEC can be calculated for the largest event n one year or for all (cumulatve) events n one year. For rsk management purposes, the latter estmate s preferred, snce t ncludes the possblty of one or more severe events resultng from, for example, earthquakes and/or floods. Probable Maxmum Loss (PML). PML s a subset of the LEC value, whch represents the loss amount for a gven probablty or return perod, per year. Dependng on an organzaton s rsk tolerance, the rsk manager may decde to manage for losses up to a certan return perod (for example, 1 n 300 years). For that organzaton, the PML s the 300-year loss. For others, t may be 150 years, or for others 500 years. It s noteworthy that the general ndustry norm s to set program nsolvency at the 1-n-150-year level to 1-n-200-year level, whch roughly corresponds to the level of solvency requred for BBB+ companes rated by Standard & Poor s. Nature of Cost-beneft Analyss Cost-beneft analyss (CBA) s a systematc procedure for evaluatng decsons that have an mpact on socetes. A CBA s conducted dependng on avalable nformaton. Followng Smyth and others (2003), a smplfed fve-step procedure s descrbed below. Step 1: Specfy the nature of the problem. Optons have to be specfed. One alternatve s the status quo. In the current analyss, the status quo refers to the current vulnerablty of the structure wthout any mtgaton measures. Ths alternatve s usually the reference pont to llustrate how well other alternatves perform. Step 2: Determne the drect costs of mtgaton measures. For each mtgaton alternatve, the drect costs to mplement the mtgaton measure are specfed. If these costs are fnanced through a loan, the cost of captal should also be ncluded. Step 3: Determne the benefts of mtgaton alternatves. Probablstc rsk modelng technques are used to smulate the mpact of catastrophc events (for example, earthquakes). The status quo reflects the expected damage to the buldng wthout mtgaton. Wth respect to each of the mtgaton measures, the expected benefts are estmated as the reducton n damage to the buldng as a result of a catastrophc event (wth varyng magntudes), relatve to the status quo. In addton to reducng physcal damage to key socal nfrastructure, there are addtonal benefts of mtgaton works such as lessenng the number of fataltes or njures caused by the event. Other benefts may nclude costs of busness nterrupton. These costs may be sgnfcant n the case of lfelne nfrastructure lke hosptals. 6

7 Step 4: Calculate attractveness of mtgaton alternatves. The attractveness of mtgaton s calculated as the dfference between the benefts to each nterested party and the upfront costs of mtgaton. Wth respect to lfelnes, the alternatves nvolve a degree of outage or servceablty over a defned tme horzon. The socal dscount rate s then used to convert future benefts and costs nto a net present value (NPV) or beneft-cost (B/C) rato. A mtgaton measure s consdered attractve f the NPV s postve or, equvalently, f the B/C rato s hgher than unty. Step 5: Choose the best mtgaton alternatve. The best alternatve among mutually exclusve mtgaton alternatves s the one wth the hghest NPV or, equvalently, the hghest B/C rato. 3. Applcaton to the Bogotá Dsaster Vulnerablty Reducton Program The World Bank-fnanced Bogotá Dsaster Vulnerablty Reducton Project s a fve-year project wth a World Bank loan of US$80 mllon, and a contrbuton of US$80 mllon from the Dstrct of Bogotá. The purpose of ths project s to reduce the cty s exposure to adverse natural events by strengthenng local capacty to manage dsaster rsk and reduce vulnerablty of key nfrastructure. By the tme of program completon both physcal and fnancal vulnerablty to adverse natural events should be measurably reduced. Ths project addresses fve lnes of acton outlned n the cty s 10-year plan: (a) rsk dentfcaton, (b) rsk reducton, (c) nsttutonal strengthenng, (d) rsk preventon and awareness, and (e) fnancal coverage. The objectve of the Rsk Identfcaton component s to enhance the capacty of the Dstrct of Bogotá to dentfy and montor rsks. The component wll help the Dstrct better target ts nvestments and dentfy potental calamtes before they occur. Actvtes nclude studes for hazard dentfcaton (for example, floods, geotechncal and sesmc rsks), vulnerablty assessments (for example, assessment of substandard housng and publc buldngs), and rsk management (for example, probablty of loss of lfe when vulnerablty s not addressed), and studes for hazard mappng, whch nvolve equpment dentfcaton to gather nformaton on earthquakes, floods, and landsldes. The Rsk Reducton component ams to complement the cty s exstng rsk reducton efforts to reduce the vulnerablty of crtcal facltes and lfelne nfrastructure. The purpose of ths component s to save lves by ensurng the contnued functonng of such facltes n the event of adverse natural or technologcal catastrophe. The component also supports the mplementaton of nonstructural and functonal mtgaton measures for the contnuty of servce durng and after emergences. Actvtes under ths component nclude sesmc mtgaton through the development of engneerng desgns and retrofttng or constructon works for publc buldngs to meet the latest sesmc standards as defned n Law 400, ncludng hosptals, schools, and fre statons. 7

8 The purpose of the Insttutonal Strengthenng component s to enhance the effectveness and capacty of the Dstrct Admnstraton to prepare for, respond to, and recover from sgnfcant emergences. In ths context, the component also supports the strengthenng of the Dstrct s capacty to mplement the project. The Rsk Preventon and Awarenes component ams to ncrease awareness at all levels of socety, and n partcular, at the communty level n order to convey the mportance of rsk mtgaton and dsaster preparedness. The objectve of the Fnancal Coverage component s to develop a rsk fnancng strategy for losses arsng from natural dsasters. It ams to provde the Muncpalty of Bogotá DC wth a fnancal strategy to ensure the avalablty of resources for relef, early recovery, rehabltaton, and reconstructon, should a major dsaster occur. It also ams to facltate the development of a prvate catastrophe nsurance market, based on recent experences n Colomba. Earthquake Rsk Model A probablstc earthquake rsk assessment model for the cty of Bogotá DC was developed to assess the earthquake rsk exposure of a portfolo of publc buldngs n Bogotá Dstrct. Ths model reles on a mcro-zonaton of Bogotá DC and apples the most advanced smulaton technques on ground moton descrpton, structural modelng, and computaton of structural response. 2 A sample of 388 buldngs was randomly chosen (ncludng 63 fre statons, 65 hosptals, 9 schools, and 251 admnstratve buldngs; see Fgure 2) for further analyss. The value at rsk of these buldngs s estmated at US$1,383 mllon. 2 The descrpton of the probablstc sesmc loss estmaton methodology s beyond the scope of ths paper. It can be found n Jamn (2005). 8

9 Fgure 2. Selected Publc Buldngs n Bogotá DC Source: Jamn (2005). The project fnances hazard rsk mtgaton measures. These nterventons are structural, nonstructural, and functonal. Structural mtgatons encompass basc renforcements to exstng buldngs, whle nonstructural nterventons consst of the resettlement of vulnerable populatons n hgh-rsk areas. Fnally, functonal mtgaton nvolves the protecton of people and assets, so that they reman functonal durng and mmedately after an emergency (ths nvolves such tasks as contngency plannng, busness contnuty plannng, emergency access, safeguardng of equpment, and so forth). Specfcally, these measures am to ensure that any damage resultng from an adverse event s lmted enough to preclude evacuaton of vtal buldngs such as hosptals, whle understandng that the dsrupton of some noncrucal functons may be unavodable. The analyss shows that structural nvestments have a sgnfcant mpact on the nfrastructure reslence to earthquakes. On the portfolo of selected publc assets, the pure premum s estmated to declne from 7.4 per mll to 1.5 per mll once the buldngs are retroftted. Fgure 3 shows the benefts of structural nvestments for the selected publc buldngs. 9

10 Fgure 3. Pure Rsk Premums, before and after Structural Investments Unretroftted Retroftted Per mll Schools Fre statons Hosptals Other publc buldngs The benefts of the structural nvestments can also be captured through the reducton n PML of an earthquake event wth a 1-n-1000 year return perod on the portfolo of selected publc buldngs (see Fgure 4). If such an earthquake were to ht the cty, the resultng losses to school buldngs would decrease from 30 percent to 4 percent of ther asset value f they were retroftted. Fgure 4. PML of 1-n-1000 year Earthquake Event, before and after Structural Investments PML (percent) Unretroftted Retroftted Schools Fre statons Hosptals Other publc buldngs The loss exceedance curves of the portfolo of publc assets before and after structural nvestments are depcted n Fgure 5. Ths program would sgnfcantly reduce the potental losses caused by earthquakes. For example, a 1-n-500-year earthquake s estmated to cause losses of up to 9.2 percent of the value of unretroftted buldngs, whle the structural program would reduce these losses to 3.8 percent. It s noteworthy that the benefts of these structural nvestments are also sgnfcant for more frequent events: the probable maxmum loss (PML) of a 1-n-100-year earthquake decreases from 6.1 percent to 2.2 percent. 10

11 Fgure 5. Loss Exceedance Curves of Portfolo of Selected Publc Buldngs, before and after Structural Investments Exceedance probablty (percent) ,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 Return perod (years) Unretroftted Retrof tted Probablstc Cost-beneft Analyss of the Rsk Mtgaton Project Approxmately US$160 mllon has been earmarked for the structural and functonal strengthenng of 134 schools (ncludng kndergartens), 32 hosptals, and 2 fre statons. Rsk mtgaton measures under ths project are planned to be mplemented wthn a fouryear perod. The tme horzon of ths project s 30 years, whch s less than the average lfetme of a standard buldng. The average annual return on mtgaton nvestment s defned by R = L w / o I L w where s the type of mtgaton nvestment (structural, structural and functonal), and L / ( L ) s the annual average earthquake loss before (after) mtgaton nvestment and w o w I s the nvestment amount. Smulatons from the probablstc earthquake rsk assessment model show that structural nvestments generate an average annual return equal to 14.5 percent for retroftted schools and 19.1 percent for retroftted hosptals and fre statons (see Table 1). Ths means that a US$100 nvestment wll reduce the average annual property loss caused by an earthquake by US$14.5 for schools and by US$19.1 for hosptals and fre statons. Structural and functonal nvestments not only provde for reducton n property losses, but may also save lves and reduce the number of njures. 3 In the case of an earthquake 3 Most conventonal cost-beneft models assgn a monetary value to human lfe, whch commands a much greater monetary amount than property. Based on recent studes, the value of a statstcal lfe n Colomba 11

12 wth a return perod of 50 years, these rsk mtgaton nvestments are assumed to save about 5,000 lves (1,000 lves n schools and 4,000 lves n hosptals) and avod about 50,000 njures. Lves saved n hosptals and fre statons nclude not only drect-saved lves (that s, people stayng at the hosptal at that tme), but also ndrect saved lves (that s, lves saved because hosptals and fre statons are able to provde emergency servce to the affected populaton n the aftermath of the earthquake). Under these assumptons, the average annual return of structural and functonal nvestments s estmated at 7.7 percent for schools and 32.8 percent for hosptals and fre statons (see Table 1). These hgh returns hghlght the hgh (average) monetary benefts generated by these mtgaton nvestments. Table 1. Average Annual Returns on Mtgaton Investments Structural Investments Structural and Functonal Investments Schools 14.5% 7.7% Hosptals and Fre Statons 19.1% 32.8% Mtgaton Measures Outwegh Costs A model was developed to carry out the probablstc cost-beneft analyss. It computes the net present value, the economc rate of return, and the beneft-cost rato (that s, NPV of benefts / NPV of costs) of the rsk mtgaton nvestments (see annexes). It reles on the followng expressons: NPV NPV t ( Benefts ) [ L L ] (1 + d = w o w 2 3 4(1 + d) 2(1 + d) 4(1 + d) t= 4 / ) I ( Cost ) = (1 + d) (1 + d) (1 + d) where s the type of mtgaton nvestment, L / ( L ) s the average annual earthquake loss before (after) the mtgaton nvestment, I s the amount of the mtgaton nvestment, and d s the dscount factor. Fgure 6 shows the average economc rate of return (ERR) of structural nvestments and the ERR of structural and functonal (S&F) nvestments. Under the above assumptons (scalng factor s 1), the ERR of the structural nvestment s estmated as 16.6 percent, whle the ERR of the S&F nvestments s estmated at 20.2 percent. They are well above the dscount factor of 12 percent suggested as a reference n the World Bank projects, meanng that ths project s economcally vable. w o w s assumed to be US$500,000. Ths approach s conservatve. A hgher value would of course ncrease the monetary benefts of the project. 12

13 A basc senstvty analyss s also performed because the potental benefts of such nvestments are hghly uncertan. A scalng factor s appled to the avoded average annual losses (that s, benefts). The scalng factor ranges from 1.0 to 0.6, that s, the benefts of ths project are reduced by 10 percent to 40 percent. For example, a scalng factor of 0.8 means that average annual benefts are reduced by 20 percent. Fgure 6 shows that the ERR of the S&F nvestments s always hgher than the ERR of the structural nvestments, whatever the scalng factor. It decreases from 20.2 percent to 10.8 percent f the average annual benefts are reduced by 40 percent. Therefore, wth a dscount factor of 12 percent, the earthquake rsk mtgaton project s economcally vable (that s, the ERR s hgher than 12 percent), even when the average benefts are reduced by up to 30 percent. Fgure 6. Economc Rate of Return (ERR) of Structural Investments and Structural and Functonal Investments ERR (percent) Structural Structural + functonal Scalng factor Note: The scalng factor s a multpler coeffcent appled to the average annual benefts of the rsk mtgaton project to take nto account the uncertanty around these potental benefts. Beneft-cost Ratos wth Fnancng Structure The above analyss takes nto account only the costs and average annual benefts generated by the project. Other costs and benefts come from the fnancng structure of ths project. Ths project s fnanced wth a US$80 mllon loan fnanced by the World Bank and US$80 mllon n bonds ssued by the Dstrct of Bogotá on the fnancal markets. 13

14 Table 2 descrbes the cost of fnancng used n ths analyss. Table 2. Fnancal Assumptons WB Loan Other Loan Front-end Fees 0.5% no Commtment Fees 0.35% no Grace Perod 5 years no Maturty 17 years 11 years Average Interest Rate 3% 8% The net present value of the cost of the project becomes NPV ( Cost ) = I WB + I 3 1 FEF + CF + 4(1 + d) 2(1 + d) ˆ I 11 OB t= 1 OB (1 + d) t (1 + d) t= 6 Iˆ WB (1 + d) t where FEF s the front-end fees pad on the total amount, CF s the commtment fees pad on the undsbursed amount, I WB s the loan amount borrowed from the World Bank, and I OB s the loan amount borrowed from another credt nsttuton, wth I WB + I OB = I. Î WB satsfes 17 WB t= 6 I ˆ (1 + ) t WB = I 4 WB [ 1+ (1 + ) + (1 + ) + (1 + ) ] WB WB WB where WB s the annual average nterest rate charged by the World Bank. Î OB satsfes 11 WB t= 1 I ˆ (1 + ) t OB = I 4 OB [ 1+ (1 + ) + (1 + ) + (1 + ) ] OB OB OB where OB s the annual nterest rate charged by the other credt nsttuton. The beneft-cost (B/C) rato of the structural and functonal nvestments s estmated wth a dscount factor of 12 percent. 4 The analyss shows a postve rate of return for the project even wthout the favorable terms offered by the World Bank. Indeed, Fgure 7 4 Ths dscount factor s used to evaluate the economc and fnancal vablty of all World Bank projects. However, some economsts suggest usng declnng dscount rates for mpacts that occur further n the future n order to reflect the concern wth future generatons (Cropper, Aydede, and Portney 1992). 14

15 shows an ncrease of the B/C rato for the project from 1.6 to 2.5 f the favorable terms offered by the World Bank are taken nto account. A sensblty analyss shows that the project would stll be economcally vable f the average benefts are reduced by 40 percent. In other words, the proposed nvestments would stll have an economc rate of return hgher than 12 percent even f the average benefts of the project were reduced by 40 percent, thanks to the frendly fnancng condtons offered by the World Bank. Fgure 7. Beneft-cost Rato of Structural and Functonal Investments wth and wthout Loan Fnancng w /o loan fnancng w th loan fnancng B/C rato Scalng factor Note: The scalng factor s a multpler coeffcent appled to the average benefts of the rsk mtgaton project to take nto account the uncertanty around these potental benefts. The net benefts of the structural nvestments and structural and functons nvestments are lsted n Annex 3. Negatve values ndcate economcally unvable nvestments for the gven tme horzon, whle postve values ndcate an economcally vable nvestment. The projects are economcally vable after two years of earthquake exposure wth the loan fnancng program, and after four years wthout the loan fnancng program. Whle the analyss shows a postve economc rate of return, t should be recalled that muncpal nvestment budgets are lmted and that the decson to nvest n preparedness and rsk reducton actvtes represents a choce made n an envronment of lmted resources. The decson to channel funds to dsaster mtgaton or management should respond to an objectve analyss, quanttatve at best. Probablstc Beneft-cost Rato of Structural Investments The benefts generated by the structural nvestments are exposed to a hgh level of uncertanty related to the (very low) frequency and the (potentally very hgh) severty of an earthquake that would strke Bogotá DC. Unfortunately, the standard cost-beneft analyss, as performed above, reles on average economc values, such as the B/C rato defned as the NPV of the average annual benefts over the NPV of the costs. Therefore, t cannot capture the varablty related to the occurrence of a catastrophc event. In partcular, these analyses fal to capture much of the nformaton generated by sophstcated earthquake-rsk models. 15

16 Such an approach based on average values mplctly assumes that decsonmaker s rsk neutral. Ths assumpton s realstc f the government has a large tax base to spread ts rsk effcently among the ctzens (Arrow and Lnd 1970). However, the rsk-neutralty assumpton clamed by Arrow and Lnd may not hold for ctes lke Bogotá DC, whch are hghly exposed to large natural dsasters. Ther tax base may not be large enough to spread catastrophc losses among the taxpayers, and ther level of ndebtedness may lmt ther capacty to borrow ex post, thus generatng a macroeconomc rsk. In ths context, the dstrct of Bogotá may act as a rsk-averse decsonmaker, where the nvestment decsons are based not only on the expected values but also on ther volatlty and the potental extreme values. The polcymaker s nvestment decson s thus based on the dstrbuton of the B/C rato, and not only on ts average value. A probablstc cost-beneft rato of the structural nvestment s derved from the outputs of the earthquake rsk model. The earthquake losses, denoted by the random varable L ~, are defned by the yearly occurrence of an earthquake, denoted by the random varable P ~ and ts severty, denoted by the random varable l ~ : L ~ ~~ = Pl, where P ~ follows a Posson dstrbuton and l ~ follows a Normal dstrbuton. The average number of earthquakes every year s specfed by the Posson parameter p, where p s 2 percent, that s, an earthquake occurs every 50 years, on average. The random annual earthquake losses (before and after structural nvestment), condtonal on the occurrence of an earthquake, are assumed to follow a normal dstrbuton, wth an expected value equal to AAL/p. The varance of the annual earthquake losses (before and after the mtgaton nvestment) s estmated from the emprcal loss exceedance curves generated by the probablstc earthquake model. The random earthquake losses (before and after structural nvestments) are assumed to be stochastcally ndependent over tme. Ths means that the occurrence of an earthquake n a gven year does not affect the potental benefts of these nvestments the followng years. Ths assumpton s n fact conservatve snce the structure of an unretroftted buldng after a dsaster would be more vulnerable to a new dsaster, thus ncreasng the benefts of structural nvestments. On the other hand, the correlaton between these earthquake losses s assumed perfect. Ths means that when an earthquake hts the cty of Bogotá, potental benefts on (retroftted or unretroftted) schools and on (retroftted or unretroftted) hosptals and fre statons are perfectly correlated. The random structural benefts are defned as the dfference between the random earthquake losses before structural nvestment and random earthquake losses after structural nvestments: 16

17 ~ B ~ ~ = L w L. / o w The probablstc B/C rato s defned as the NPV of the random benefts (that s, the earthquake losses avoded thanks to the mtgaton nvestment) B ~ dvded by the NPV of the structural nvestments. The coeffcent of varaton of the random annual benefts s estmated from the earthquake rsk model at 2.5 for structural nvestments on hosptal and fre statons and 2.7 for structural nvestments on schools. Fgure 8 shows the exceedance probablty curve of the probablstc B/C rato for structural nvestments on the portfolo of publc assets, wth a dscount factor of 12 percent and the World Bank fnancng faclty. 5 The probablstc B/C rato s hgher than unty wth a probablty of 32 percent, that s, ths nvestment generates an economc rate of return hgher than 12 percent wth probablty 32 percent. There s stll a 22 percent probablty that the benefts wll be three tmes larger than the structural costs, and the probablstc B/C rato wll exceed 17 wth a 1 percent probablty. Ths means that the more severe the earthquake, the more proftable the structural nvestments. Ths also means that ths structural nvestment turns out to be economcally unvable wth a 68 percent probablty. The assessment of the probablstc dstrbuton functon of the B/C rato, captured through the loss exceedance curve, hghlghts the hgh volatlty of ths rato. Ths also llustrates that, although the rsk mtgaton nvestment s fnancally vable on average (that s, the average value of B/C rato s hgher than unty), such an nvestment s n fact non-vable n the most frequent cases where no or low-magntude earthquakes occur (that s, B/C rato less than unty), whle t becomes hghly valuable (that s, B/C much hgher than unty) when hgh-magntude earthquakes ht the cty. 5 Under these assumptons, the B/C rato follows a Normal dstrbuton, wth expectaton equal to 1.60 and standard devaton equal to

18 Fgure 8. Probablstc Beneft-cost Rato of Structural Investment, Exceedance Probablty Curve 35 Exceedance probablty (percent) B/C rato 4. Concluson The World Bank s becomng ncreasngly nvolved n mtgaton nvestments related to natural dsasters, ncludng those resultng from earthquakes and hurrcanes. The World Bank requres from ts Borrowers that they conduct a sophstcated cost-beneft analyss to assess whether the proposed nvestments yeld a suffcently hgh rate of return. The cost-beneft analyss of projects exposed to varable benefts has usually been performed usng average values. However, such a methodology fals to capture much of the nformaton avalable and may lead to napproprate decsons. Ths paper has presented a probablstc cost-beneft analyss where economc ndcators, such as beneft-cost ratos, are analyzed usng rsk metrcs, ncludng exceedance probablty curves. The analyss reles on sophstcated catastrophc rsk models that smulate the loss mpact of natural dsasters on (retroftted and unretroftted) buldngs. Ths analyss has been llustrated usng the earthquake vulnerablty reducton project of Bogotá Dstrct, mplemented wth the techncal and fnancal assstance of the World Bank. The model has shown that the proposed nvestments are economcally vable, gven the country s exposure to earthquakes. Whle ths methodology reles heavly on the avalablty of probablstc catastrophe rsk models, t offers a new framework that could be used n a varety of rsk mtgaton projects fnanced by the World Bank and other multlateral fnance nsttutons. 18

19 Annex 1. Rsk Mtgaton Costs (US$ mllons) World Bank Loan Other Loan Loan Fnancng No Loan Fnancng TOTAL Year FEF CF Dsburs. Repay. Dsburs. Repay. COST TOTAL COST NPV FEF = Front-end fees. CF = Commtment fees. 19

20 Annex 2. Annual Average Benefts (US$ mllons) Health Educaton Year S S+F S S+F NPV S = Structural nvestments. SF = Structural and functonal nvestments. 20

21 Annex 3. Annual Average Net Benefts (US$ mllons) Wth Loan Fnancng Wthout Loan Fnancng Year S S+F S S+F NPV S = Structural nvestments. SF = Structural and functonal nvestments. Net benefts = Benefts costs. 21

22 References Arrow, K., and R. Lnd Uncertanty and the Evaluaton of Publc Investment Decsons. Amercan Economc Revew 60(3): Boardman, A., D. Greenberg, A. Vnng, and D. Wemer Cost-Beneft Analyss: Concepts and Practce. Englewood Clffs, NJ: Prentce Hall. Cardonna, O. D Defncón de la Responsabldad del Estado, su Exposcón ante Desastres Naturales y Dseño de Mecansmo para la Cobertura de los Resgo Resduales del Estado. Report prepared for the World Bank. Cropper, M., A. S. Aydede, and P. Portney Rates of Tme Preference for Savng Lves. Amercan Economc Revew (May): Jamn, L Estratega para la Transferenca, Retencón y Mtgacón des Resgo Sísmco en Edfcacones Indspensables y de Atencón a la Comundad del Dstrto Captal. Report prepared for the World Bank. Klendorfer, P., and H. Kunreuther The Complementary Role of Mtgaton and Insurance n Managng Catastrophc Rsks. Rsk Analyss 19: Mechler, R Cost-Beneft Analyss of Natural Dsaster Rsk Management n Developng Countres. Deutsche Gesellschaft fur Technsche Zusammenarbet (GTZ)-funded Workng Paper. Schulze, W., D. Brookshre, R. Hageman, and J. Tscrhart Benefts and Costs of Earthquake Resstant Buldngs. Southern Economc Journal 53: Smyth, A. W., G. Altay, G. Deodats, M. Erdck, G. Franco, P. Gulkan, H. Kunreuther, H. Lus, E. Mete, N. Seeber, and O. Yuzugullu Probablstc Beneft-Cost Analyss for Earthquake Damage Mtgaton: Evaluatng Measures for Apartment Houses n Turkey. EERI Earthquake Spectra. 22