café de conocimiento: ejemplos de análisis probabilista de...
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Abril 2015
Café de Conocimiento:
Ejemplos de Análisis Probabilista
de Costo-Beneficio
Use of CBA in DRR
0
5
10
15
20
25
30
35
40
High Income Med Income Low Income
Yes No (not indicated)
• CBA are increasingly being used in DRR investment appraisal but
barriers remain.
• Out of 99 countries who provided
responses to HFA monitoring over
2011-2013, 37 countries (37%) have conducted economic
appraisals on DRR investment. For
LICs, Bangladesh, Burkina Faso,
Ethiopia Malawi and Mozambique
• CBA for DRR investment is seen as
effective ways of evaluating and illustrating the gains that can be
made. (e.g. Fiji, St Lucia, British
Virgin Islands calls for the use of
CBA).
Figure: # of countries that have conducted economic appraisal based on HFA monitor (ODI 2014)
What’s probabilistic CBA?
• CBA that takes probabilistic benefits of risk reduction.
• Non-probabilistic CBA: what is the cost and benefit of sea wall construction given that a 50 year cyclone occurs?
• Probabilistic CBA: what is the cost and benefit of sea wall construction given that cyclones of different sizes occur stochastically with different return periods?
Why should we use probabilistic CBA?
ReturnPeriod EP Losses (A)
Losses (B)
5 0.2 2,000 1,000
10 0.1 6,000 6,000
50 0.02 10,000 50,000
100 0.01 12,000 80,0000
0.05
0.1
0.15
0.2
0.25
0 20,000 40,000 60,000 80,000 100,000
• Gives decision-makers full information about potential
benefits of DRR investment. (e.g. avoids under-funding for
catastrophic risk when we know costs of rare events are high in
advance).
• Possible to construct a portfolio of DRR measures tailored to
specific risks of varying intensity and frequency.
Forward-looking vs. backward-looking assessment
More accurate, but skills, time and
data intensive.
Rougher estimate, but more realistic for
contexts with lower capacity
Do you have hazard, exposure
vulnerability information?
Backward Looking Assessment:
Do you have more than
four credible data points of
past losses?
Non-
ProbabilisticCBA or CEA
Backward CBA
possible
Forward-Looking Assessment
No Yes
YesNo
Forward-looking or backward-looking assessment?
CAVEATS: scope of DRR benefits covered in CBA
CAVEATS: Limitation of Probabilistic CBA
• Due to inherent design of probabilistic CBA
Probabilistic CBA often assumes risk neutrality: it undervalues the benefit in case of ‘extreme events’(intensive risk)
The use of single measure such as B/C ratio, NPV masks inherent value conflicts (e.g. differences in time preference (discount rate) also risk aversion etc).
• Due to misuse of CBA
Probabilistic CBA often lacks incorporation of intangibles and distributional consequences
• Alternatives or complements to CBA include:
Cost Effectiveness Analysis (CEA)
Multi-criteria analysis (MCA)
Robust Decision Making Approach (RDMA)
• Economic assessment such as CBA should be used as part of wider decision-making process involving multiple stakeholders
Probabilistic CBA: Key terms and concepts
• Understanding key risk terms: annual average loss(AAL), exceedance probability(EP), risk layers, etc.
• Understanding key CBA terms: Benefit-Cost (B/C) ratio, Net present value (NPV), discount rate
• Understanding how risk-based information for probabilistic CBA are generated using both forward-looking and backward-looking methods and how different DRR investments reduce different layers of risks
• Understanding how a stream of benefits and costs of DRR investments accruing over-time can be assessed in a single framework (CBA).
• Understanding key strengths and weaknesses of probabilistic CBA.
Forward looking
Probabilistic Approach
• Requires a Probabilistic risk analysis software platform (such as CAPRA, EqCAT, CatSIM , R-Fonden or commercial insurance systems)
• Requires a comprehensive and detailed enough set of data:
Data files used for analysis
Exposure Georeferenced data points of
physical structures in Study area
shape file (shp format)
Hazard Possible hazard intensity (in
Capra is the Ame format)
Vulnerability Containing information on
vulnerability functions
Risk = H x E x V
• Hazard: cyclone intensity
• Exposure: locations of buildings
• Vulnerability: structural robustness
of buildings
-> Vulnerability function:
Relationship between % of damage
and wind-speed
Risk Analysis
General Probabilistic CBA
Process• Basic principle:
A DRR measure is reflected as a change in the vulnerability functions of the assets in questions. Benefits are estimated based on how these DRR measures (example: cyclone retrofit) will shift risk curves, and thus the expected losses.
• Tasks:
i) estimate risk curve and AAL before DRR and
ii) estimate risk curve and AAL after DRR
• Example Scenario:
Earthquake retrofitting of unreinforced masonry residential buildings which
change vulnerability from low design quality to high design quality
(reinforced masonry)
Backward looking CBA:
method and tasks• Method:
i) Risk curves and statistics such as annual average loss (AAL) are calculated using backward methodology
ii) Calculate how AAL will change due to DRR investment usingbackward methodology
iii) Compare costs and benefits of DRR intervention using an appropriate discount rate
iv) Estimate how different discount rate/project duration assumptions affect B/C ratio, NPV, etc/
• Tasks:
i) estimate risk curve and AAL before DRR and
ii) estimate risk curve and AAL after DRR
iii) Calculate B/C ratio, NPV and conduct sensitivity analysis
Calculating Annual Average
Loss in BLCBA• The expected annual loss is estimated using an application
of the Simson rule.
• It requires three or more loss data points to be accurate
• The expected loss up to a N year event is the cumulative
probability of the N year event minus the cumulative
probability of the M year event multiplied by the average
loss between the M and N year events.
Case of Orosi Project
Loss
Estimated Damage
and Loss (USD)
Reconstruction and rehabilitation for 8
months 431,707
Shortage in drinking water for over
500,000 people and resulting decrease
in revenue from the provision of
drinking water for 18 hours 91,500
Total 523,207
The total economic losses of the 2010 flood are reported to be USD 523,200, and result from both reconstruction and rehabilitation costs, as well losses in revenue from lack of drinking water provision to over 500,000 people for a period of 18 hours (Table 1).
Return period of the disaster (!!?)
• While reports suggest the overall damage from storm
Tomas in 2010 due to widespread flooding and landslides
was very large, (losses at over USD 280 million) (GFDRR,
2010), the reported monthly daily maximum rainfall from
Liberia station suggests the amount of daily maximum
precipitation observed for November 2010 is by no means
extreme (with an estimated return period of less than 1
year (0.6 year)). Using this information, the economic
losses caused by flooding to the Orosi aqueduct resulting
from Storm Tomas was also estimated to have less than 1
year return period.
• CAVEAT: no closer stations were found to provide better
rainfall data.
Return period of the disaster (!!?)
rainfall (< or =)
cumulative
observations
# of
observat
ions frequency
Monthly exc
%
return period
months
return period
years
1
0 34 34 0.110 0.890 1.123 0.094
200 112 78 0.252 0.639 1.566 0.130
500 213 101 0.326 0.313 3.196 0.266
820 268 55 0.177 0.135 7.381 0.615
1000 287 19 0.061 0.074 13.478 1.123
1500 302 15 0.048 0.026 38.750 3.229
2000 307 5 0.016 0.010 103.333 8.611
4000 309 2 0.006 0.003 310.000 25.833
7025 310 1 0.003 50.000
date 2010/10
rainfall 820
return 0.615
Maximum rainfall recorded for November, 2010 (Storm Thomas)
Estimation of curve based on past
losses points
• It is important to keep in mind that risk curve estimation
generally requires more than 3 credible data points of past
disaster events (Mechler 2005), and the use of single data
point with the probability of first loss estimate adopted here
cannot give an accurate loss estimate as recommended.
Despite this data limitation, we have estimated a risk curve
based on estimated exceedance probabilities to perform
illustrative probabilistic CBA.
• CAVEAT: no other (representative) loss data points were
found (DesInventar?)
Estimation of curve based on past
losses points
• “Using this precipitation and loss data, the annual average
loss (AAL) was estimated (Table 2). The expected annual
loss is estimated using an application of the Simpson rule.
For example, based on the return periods identified, the
expected loss up to a 10 year event is the exceedence
probability of the 5 year event (0.2) minus the exceedence
probability of the a 10 year event (0.1) multiplied by the
average loss between the 5 and 10 year events. In
numerical terms:”
EL(5-10 years)= (0.2-.01)*((1,617,974+2,261,959)/2)= 193,997
•
Estimation of curve based on past
losses points
• This process is then repeated for all other intervals. For the
last interval, it is assumed for this CBA that losses
associated with events of more than a 200 year return
period will result in the same losses as the 200 year event.
return period
exceedance
probability Loss expected loss
1 1 699,968 699,968
2 0.5 1,026,400 431,592
5 0.2 1,617,974 396,656
10 0.1 2,261,959 193,997
25 0.04 4,510,318 203,168
50 0.02 8,566,946 130,773
100 0.01 15,729,186 121,481
200 0.005 30,053,666 114,457
>200 114,457
AAL 2,406,549
Estimation of Benefits
• To assess the benefits of the proposed aqueduct project, we
must estimate the amount of economic losses that would be
reduced as a result of the project. There is no clear data on the
expected amount of loss reduction resulting from the aqueduct
project. However, since the proposal was made in response to
the damaging 2010 Tropical Storm Tomas, it is assumed that
the aqueduct would be designed to protect against all
damages caused by a 1-year event. Events with larger return
periods would have damages reduced, but not eliminated
(Table 3). As the actual reduction in damages is not known,
particularly for extreme events, these numbers must be
interpreted with caution and are to serve an illustrative purpose
only.
Estimation of Benefits
Before Aqueduct After Aqueduct
return
period
exceedance
probability loss expected loss Loss reduction expected loss
1 1 699,968 699,968 1 0
2 0.5 1,026,400 431,592 0.50 215,796
5 0.2 1,617,974 396,656 0.20 297,492
10 0.1 2,261,959 193,997 0.10 174,597
25 0.04 4,510,318 203,168 0.04 195,042
50 0.02 8,566,946 130,773 0.02 128,157
100 0.01 15,729,186 121,481 0.01 120,266
200 0.005 30,053,666 114,457 0.005 113,885
>200 114,457 0.000 114,457
AAL Before
DRR 2,406,549 AAL After DRR 1,359,692
Benefit in
terms of AAL
Reduction 1,046,857
Estimation of Benefits
0
500000
1000000
1500000
2000000
2500000
3000000
0 1 2 3 4 5 6 7 8 9 10
Eco
no
mic
Lo
ss (
US
D)
Return Period (years)
Loss Return Period Curve: Orosi Aqueduct
Orosi Aqueduct
Baseline, No DRR
Costs
The cost of the Orosi Aqueduct is USD 5.56 million, plus maintenance costs. The maintenance costs are separated between annual maintenance (USD 1,835) and, maintenance that is required on a five-year basis (USD 64,220). The breakdown of the costs, which come directly from the project report, are seen in Table 4 below.
Table 4: Costs of the proposed project
Time Factors
VI.1 Discount rate. There has been no official social discount rate in Costa Rica. However, literature suggests a social discount rate in Costa Rica to be between 9-10% (Aylward, Porras, 1998). Therefore, we start with initial assumption of 10%, but apply different rates as a means of sensitivity analysis.
VI.2 Increase in Exposed AssetsAs the project is assumed to last and protect against flooding for a period of 50 years, it is assumed that the amount of exposed assets in the region, as well as the number of people who will be provided with drinking water from the aqueduct, will increase in a yearly basis. The GNP per capita has increased by an average of 8% annually of the last decade, and the population has grown at an average of 1.5% per year over the same period (World bank development indicators 2014). For a baseline level, an increase of 1.5% of exposed assets per year will be applied to the analysis. This will be represented as an annual increase of 1.5% to the annual benefits.
Cost Benefit results
Using the data, provided information, and assumptions described to this
point, we are able to conduct an illustrative cost-benefit analysis for the
project. Table 5 below shows the net present value of the project with a 50-
year lifespan, a 10% discount rate, and an annual increase in exposed
assets of 1.5%.
In this scenario, the results of the CBA suggest the project to be cost-
efficient with a net present value (NPV) of USD 6,328,984, and a Benefit –
Cost ratio (B/C) of 2.1.
Tables 6 and 7 below show sensitivity analysis with regards to the discount
rate and the increase in exposed assets.
Cost Benefit results
YearCalendar
YearCosts USD Benefits
Net benefits:
benefits-costsDiscounted costs
Discounted
benefits
Discounted net
benefits
1 2013 5,563,396 0 -5,563,396 5,563,396 0 -5,563,396
2 2014 1,835 1,046,857 1,045,022 1,668 951,688 950,020
3 2015 1,835 1,062,560 1,060,725 1,517 878,149 876,632
4 2016 1,835 1,078,498 1,076,663 1,379 810,292 808,913
5 2017 1,835 1,094,676 1,092,841 1,253 747,678 746,425
6 2018 64,220 1,111,096 1,046,876 39,876 689,903 650,027
7 2019 1,835 1,127,762 1,125,927 1,036 636,592 635,557
8 2020 1,835 1,144,679 1,142,844 942 587,401 586,459
9 2021 1,835 1,161,849 1,160,014 856 542,011 541,155
10 2022 1,835 1,179,277 1,177,442 778 500,128 499,350
11 2023 64,220 1,196,966 1,132,746 24,760 461,482 436,722
12 2024 1,835 1,214,920 1,213,085 643 425,822 425,179
13 2025 1,835 1,233,144 1,231,309 585 392,918 392,333
14 2026 1,835 1,251,641 1,249,806 532 362,556 362,024
15 2027 1,835 1,270,416 1,268,581 483 334,540 334,057
16 2028 64,220 1,289,472 1,225,252 15,374 308,689 293,316
17 2029 1,835 1,308,814 1,306,979 399 284,836 284,437
18 2030 1,835 1,328,446 1,326,611 363 262,826 262,463
19 2031 1,835 1,348,373 1,346,538 330 242,517 242,187
20 2032 1,835 1,368,599 1,366,764 300 223,777 223,477
21 2033 64,220 1,389,128 1,324,908 9,546 206,485 196,939
22 2034 1,835 1,409,964 1,408,129 248 190,529 190,281
23 2035 1,835 1,431,114 1,429,279 225 175,807 175,581
24 2036 1,835 1,452,581 1,450,746 205 162,222 162,017
25 2037 1,835 1,474,369 1,472,534 186 149,686 149,500
26 2038 64,220 1,496,485 1,432,265 5,927 138,120 132,192
27 2039 1,835 1,518,932 1,517,097 154 127,447 127,293
28 2040 1,835 1,541,716 1,539,881 140 117,599 117,459
29 2041 1,835 1,564,842 1,563,007 127 108,511 108,384
30 2042 1,835 1,588,314 1,586,479 116 100,126 100,011
31 2043 64,220 1,612,139 1,547,919 3,680 92,389 88,709
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