harvey's notes on risk analysis and project evaluation

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Risk Analysis andProject Evaluation

Campbell R. HarveyDuke University

and National Bureau of Economic Research

Project Appraisal and Risk Management (PARM)Duke Center for International Development at the Sanford Institute

May 27-28, 2002



1. Cash Flow versus Discount Rate2. Approaches to Cost of Capital Measurement

3. Recommended Framework4. Comparison of Methods5. Conversion of Cash Flows

6. Project Specific Adjustments7. Conclusions

Risk Analysis and Project Evaluation Plan



Basic Project Evaluation:• Forecast nominal cash flows• Currency choice (assume US$)• Decide what risks will be reflected in cash

flows and those in the discount rate – Beware of double discounting

Risk Analysis and Project Evaluation 1. Cash Flow vs. Discount Rate



Simple example:• Assume a simple project with expected

$100 in perpetual cash flows• If located in the U.S., the discount rate

would be 10% andValue= $100/0.10= $1,000




Simple example:• However, project is not located in the U.S.

but a risky country• If we reflect the country risk in the discount

rate, the rate rises to 20%Value = $100/0.20 = $500




Simple example:• If we reflect the country risk in the cash

flows, the value is identicalValue = $50/0.10 = $500




Our approach• We will propose methods that deliver

discount rates that reflect country risk.• As our example showed, it is a simple

matter of shifting the country risk from thediscount rate to the cash flows.




Our approach• Indeed, we will often do this.

– That is, we will use quantitative methods to get ameasurement of country risk in the discount rate.

– Use the country risk adjustment in the cash flows (andadjust discount rate down accordingly).

– Use Monte Carlo methods on cash flows rather thancash flows and discount rate.




Many different approaches:1. Identical Cost of Capital (all locations)

2. World CAPM or Multifactor Model (Sharpe-Ross)

3. Segmented/Integrated (Bekaert-Harvey)

4. Bayesian (Ibbotson Associates)5. Country Risk Rating (Erb-Harvey-Viskanta)6. CAPM with Skewness (Harvey-Siddique)

Risk Analysis and Project Evaluation 2. International Cost of Capital



Risk Analysis and Project Evaluation

2. International Cost of Capital

7. Goldman-integrated sovereign yield spreadmodel

8. Goldman-segmented9. Goldman-EHV hybrid10. CSFB volatility ratio model

11. CSFB-EHV hybrid12. Damoradan



Identical Cost of Capital

• Ignores the fact that shareholders require differentexpected returns for different risks





Identical Cost of Capital

• Risky investments get evaluated with too low of adiscount rate (and look better than they should)

• Less risky investments get evaluated with too highof a discount rate (and look worse than they are)

• Hence, method destroys valueAvoid





World CAPM• Sharpe s Capital Asset Pricing Model is the

mainstay of economic valuation• Simple formula• Intuition is that required rate of return depends on

how the investment contributes to the volatility ofa well diversified portfolio





World CAPM• Expected discount rate (in U.S. dollars) on

investment that has average in a country = riskfree + b i x world risk premium

• Beta is measured relative to a “world” portfolio

• OK for developed markets if we allow risk tochange through time (Harvey 1991)





World CAPM

• Strong assumptions needed• Perfect market integration• Mean-variance analysis implied by utility

assumptions• Fails in emerging markets





Returns and Beta from 1970

R 2 = 0.013

-0.1

0

0.1

0.2

0.3

0.4

0.5

-0.5 0 0.5 1 1.5 2 2.5 3

Beta

A v e r a g e r e t u r n s

Should be a positive relation, with higher risk associated with higher return!

But perhaps we should look at a more recent sample of data.

Risk Analysis and Project Evaluation2. International Cost of Capital



Returns and Beta from 1990

R 2 = 0.0211

-0.1

0

0.1

0.2

0.3

0.4

0.5

-0.5 0 0.5 1 1.5 2 2.5 3

Beta


Still goes the wrong way - even with data from 1990!




World CAPM

• OK to use in developed markets• May give unreliable results in smaller, less liquid

developed markets





Segmented/Integrated CAPM

• CAPM assumes that markets are perfectlyintegrated – foreign investors can freely invest in the local market

– local investors can freely invest outside the local market• Many markets are not integrated so we need to

modify the CAPM






• Bekaert and Harvey (1995)• If market integrated, world CAPM holds• If market segmented, local CAPM holds

• If going through the process of integration, acombination of two holds





Estimate world beta and expected return= riskfree + b iw x world risk premium

Estimate local beta and expected return= local riskfree + b iL x local risk premium





• Put everything in common currency terms• Add up the two components.

CC= w[world CC] + (1-w)[local CC]

• Weights, w, determined by variables that proxy fordegree of integration, like size of trade sector andequity market capitalization to GDP





• Weights are dynamic, as are the risk loadings andthe risk premiums

• Downside: hard to implement; only appropriate

for countries with equity markets• Recommendation: Wait




Ibbotson Associates(Recognized expert in cost of capital calculation)

• Approach recognizes that the world CAPM is notthe best model

• Ibbotson approach combines the CAPM s prediction with naïve prediction based on past performance.




Ibbotson Associates• STEPS

1 Calculate world risk premium=U.S. risk premiumdivided by the beta versus the MSCI world

2 Estimate country beta versus world index

3 Multiply this beta times world risk premium




Ibbotson Associates

4 Add in 0.5 times the „intercept from the initialregression. “This additional premium representsthe compensation an investor receives for taking

on the considerable risks of the emerging marketsthat is not explained by beta alone.”




Ibbotson Associates

• Gives unreasonable results in some countries• Only useful if equity markets exist• Ibbotson Associates does not even use it

Recommendation: Do not use this version.Ibbotson has alternative methods available.




CAPM with Skewness

• For years, economists did not understand why people spend money on lottery tickets and horse betting

• The expected return is negative and the volatilityis high• Behavioral explanations focused on “risk loving”




CAPM with Skewness

• But this is just preference for positive skewness(big positive outcomes)

• People like positive skewness and dislike negative

skewness (downside)




CAPM with Skewness

• Most are willing to pay extra for an investmentthat adds positive skewness (lower hurdle rate),e.g. investing in a startup with unproventechnology




CAPM with Skewness

• Harvey and Siddique (2000) tests of a model thatincludes time-varying skewness risk

• Bekaert, Erb, Harvey and Viskanta detail the

implications of skewness and kurtosis in emergingmarket stock selection




CAPM with Skewness

• Model still being developed• Skewness similar to many “real options” that are

important in project evaluation

Recommendation: Wait




Goldman-Integrated*

• This model is widely used by McKinsey, Salomonand many others.

• Addresses the problem that the CAPM gives a

discount rate too low.• Solution: Add the sovereign yield spread


*J.O. Mariscal and R. M. Lee, The valuation of Mexican Stocks: An extension of the capitalasset pricing model to emerging markets, Goldman Sachs, June 18, 1993.



Goldman-Integrated

• The sovereign yield spread is the yield on a U.S.dollar bond that a country offers versus a U.S.Treasury bond of the same maturity

• The spread is said to reflect “country risk”




Goldman-Integrated

STEPS• Estimate market beta on the S&P 500• Beta times historical US premium

• Add sovereign yield spread plus the risk free




Goldman-Integrated-EHV Hybrid

• Goldman model only useful if you have sovereignyield spread

• Use Erb, Harvey and Viskanta model to fit ratings

on yield spread




Real Yields and Institutional Investor CountryCredit Ratings from 1990 through 1998:03

R 2 = 0.8784

0.00%2.00%4.00%6.00%8.00%

10.00%12.00%

14.00%

0 20 40 60 80 100

Rating

R e a l

Y i e l d s






• You just need a credit rating (available for 136countries now) and the EHV model will deliverthe sovereign yield





• Even adding this yield spread delivers a cost ofcapital that is unreasonably low in many countries

• While you can get the yield spread in 136

countries with the EHV method, you can only getrisk premiums for those countries with equitymarkets




Goldman-Segmented

• Main problem is the beta• It is too low for many risky markets• Solution: Increase the beta




Goldman-Segmented

• Modified beta=standard deviation of local marketreturn in US dollars divided by standard deviationof the US market return

• Beta times historical US premium• Add sovereign yield spread




Goldman-Segmented

• No economic foundation for modification• No clear economic foundation for method in

general

Recommendation: Not recommended




CSFBE[r i]=SY i + b i{E[r us-RF us] x A i} x K i

• SYi = brady yield (use fitted from EHV)• b i = the beta of a stock against a local index


L. Hauptman and S. Natella, The cost of equity in Latin American, Credit Swisse First Boston, May 20, 1997.



CSFBE[r i]=SY i + b i{E[r us-RF us] x A i} x K i

• Ai =the coefficient of variation (CV) in the localmarket divided by the CV of the U.S. market)where CV = s /mean.

• K i =“constant term to adjust for theinterdependence between the risk-free rate and theequity risk premium”




CSFB

• No economic foundation• Complicated, nonintuitive and ad hoc

Recommendation: Avoid




Damodaran

• Idea is to adjust the sovereign spread tomake it more like an equity premium ratherthan a bond premium


A. Damodaran, Estimating equity risk premiums, working paper, NYU, undated.



Damodaran

Country Sovereign Equity std. dev.equity = yield x ------------------

premium spread Bond std. dev.




Damodaran• Advantage: Recognizes that you just can t

use the bond yield spread as a plug numberin the CAPM

• Disadvantage: Assumes that Sharpe ratios

for stocks and bonds must be the same inany particular country.




Country Risk Rating Model

• Erb, Harvey and Viskanta (1995)• Credit rating a good ex ante measure of risk• Impressive fit to data

Risk Analysis and Project Evaluation3. Recommended Framework

C.B. Erb, C. R. Harvey and T. E. Viskanta, Expected returns and volatility in 135 countries,

Journal of Portfolio Management, 1995.



Country Risk Rating Model

• Erb, Harvey and Viskanta (1995)• Explore risk surrogates:

– Political Risk,

– Economic Risk, – Financial Risk and – Country Credit Ratings




Country Risk Rating ModelSources • Political Risk Services International Country Risk Guide • Institutional Investor s Country Credit Rating • Euromoney s Country Credit Rating • Moody s • S&P




Political risk. International Country Risk Guide % of

Individual % of Political Points Index CompositeEconomic expectations vs. reality 12 12% 6%Economic planning failures 12 12% 6%Political leadership 12 12% 6%External conflict 10 10% 5%Corruption in government 6 6% 3%Military in politics 6 6% 3%Organized religion in politics 6 6% 3%Law and order tradition 6 6% 3%

Racial and nationality tensions 6 6% 3%Political terrorism 6 6% 3%Civil war 6 6% 3%Political party development 6 6% 3%Quality of the Bureaucracy 6 6% 3%

Total Political Points 100 100% 50%




Financial risk. International Country Risk Guide

FinancialLoan Default or unfavorable loan restructuring 10 20% 5%Delayed payment of suppliers credits 10 20% 5%Repudiation of contracts by governments 10 20% 5%Losses from exchange controls 10 20% 5%Expropriation of private investments 10 20% 5%

Total Financial Points 50 100% 25%




International Country Risk Guide Risk Categories

Risk Category Composite Score RangeVery High Risk 0.0-49.5High Risk 50.0-59.5Moderate Risk 60.0-69.5Low Risk 70.0-84.5Very Low Risk 85.0-100.0




Institutional Investor’s Country Credit Ratings

OECD Emerging Rest of World1979 1994 1979 1994 1979 1994

Economic Outlook 1 1 2 3 3 4Debt Service 5 2 1 1 1 1Financial Reserves/CurrentAccount

2 3 4 4 4 3

Fiscal Policy 9 4 9 7 6 6

Political Outlook 3 5 3 2 2 2Access to Capital Markets 6 6 7 9 8 9Trade Balance 4 7 5 5 5 5Inflow of Portfolio Investment 7 8 8 8 7 8Foreign Direct Investment 8 9 6 6 9 7




Ratings are correlated:

0102030405060708090

100

I n s t i t u

t i o n a

l I n v e s t o r

C C R

A A +

A A

A A -

A + A A

-

B B B +

B B B

B B B -

B B +

B B

B B -

B + B

N R

S&P Sovereign Ratings





0102030405060708090

100

E

u r o m o n e y

C C R

A A +

A A

A A -

A + A A

-

B B B +

B B B

B B B -

B B +

B B

B B -

B + B

N R






0102030405060708090

100

I C R G C o m p o s i t e

A A +

A A

A A -

A + A A

-

B B B +

B B B

B B B -

B B +

B B

B B -

B + B

N R






Risk Measure ChangesII CCR ICRGC ICRGP ICRGF ICRGEII CCR -0.03 0.01 0.03 -0.09ICRGC 0.35 0.79 0.54 0.43ICRGP 0.30 0.83 0.25 0.06ICRGF 0.26 0.60 0.35 0.05ICRGE 0.10 0.52 0.24 0.25

Risk Measure Levels




ICRG ratings predict changes in II ratings:

Attribute Coefficient T-Stat R-SquareICRGC 0.2120 7.59 5.0%

ICRGP 0.1244 5.67 2.8%

ICRGF 0.0956 5.69 2.8%

ICRGE 0.0833 4.65 1.9%




Ratings predict inflation:

00.10.20.30.40.50.60.70.8

0.91

0 20 40 60 80 100

II Rating September 1996

I n f l a t i o n e x p e c t a

t i o n s

f o r 1 9 9 7




Ratings correlated with wealth:

$0

$5,000

$10,000

$15,000

$20,000

$25,000

0 20 40 60 80 100

II ratings for 74 countries

P e r c a p

i t a r e a

l G D P




Time-series of ratings:

01020

304050607080

90100

1 9 7 9

1 9 8 0

1 9 8 1

1 9 8 2

1 9 8 3

1 9 8 4

1 9 8 5

1 9 8 6

1 9 8 7

1 9 8 8

1 9 8 9

1 9 9 0

1 9 9 1

1 9 9 2

1 9 9 3

1 9 9 4

1 9 9 5

1 9 9 6

1 9 9 7

1 9 9 8

Switzerland Italy Kuwait Argentina




Returns and Institutional Investor Country CreditRatings from 1990

R 2 = 0.2976

-0.1

0

0.1

0.2

0.30.4

0.5

0 20 40 60 80 100

Rating


Fit is as good as it gets - lower rating (higher risk) commands higherexpected returns. Even in among US firms, our best model gets about30% explanatory power.


3. Recommended Framework



Credit Rating Model

• Intuitive• Can be used in 136 countries, that is, in countries

without equity markets

• Fits developed and emerging markets




Country Risk Rating ModelSTEPS:

EVR = risk free + intercept - slope x Log(IICCR)• Where Log(IICCR) is the natural logarithm of the

Institutional Investor Country Credit Rating




Easy to use:

0%

10%

20%

30%

40%

50%

60%

70%

0 1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

Rating

H u r d

l e r a

t e

ICRGC IICCR:84 IICCR:79




Also predicts volatility:

R 2 = 0.5033

0%

10%

20%

30%

40%

50%

60%

70%

0 20 40 60 80 100

Institutional Investor Country Credit Rating

A n n u a l i z e d V o l a t i l i t y




Fitted volatility:

0%

10%20%30%40%50%60%

70%80%

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

Rating

E x p e c t e d v o

l a t i l i t y

IICCR:84 IICCR:79




And correlation.

R 2 = 0.6809

-20%

0%

20%

40%

60%

80%

100%

0 20 40 60 80 100

Institutional Investor Countyr Credit Rating

C o r r e l a t i o n w

i t h M S C I A C W o r l d




Fitted correlation.

-100%

-80%

-60%

-40%

-20%

0%

20%40%

60%

80%

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

Rating

E x p e c

t e d c o r r e l a

t i o n w i t

h w o r l d

IICCR:84 IICCR:79




Asian Crisis.

0

102030405060708090

100

J a n - 9 7

M a r - 9 7

M a y - 9

7 J u l -

9 7 S e p

- 9 7 N o

v - 9 7

J a n - 9 8

M a r - 9 8

M a y - 9

8 J u l -

9 8

I C R G r a

t i n g

China Hong Kong India IndonesiaKorea Malaysia Pakistan PhilippinesSingapore Taiwan Thailand Russia




Asian Crisis.

60

65

70

75

80

85

90

J a n - 9 7

M a r - 9 7

M a y - 9

7 J u l -

9 7 S e p

- 9 7 N o

v - 9 7

J a n - 9 8

M a r - 9 8

M a y - 9

8 J u l -

9 8 S e p

- 9 8

I C R G r a

t i n g

Korea Malaysia Russia

Beginning ofcrisis




Value of local currency(indexed at 100)

0

20

40

60

80

100

120

J a n - 9 7

M a r - 9 7

M a y - 9

7 J u l -

9 7 S e p

- 9 7 N o

v - 9 7

J a n - 9 8

M a r - 9 8

M a y - 9

8 J u l -

9 8 S e p

- 9 8

V a

l u e o

f $ 1 0 0

Korea Malaysia Russia

Beginning ofcrisis





• September 11 impacted the way that business is conducted all over the world(cannot be diversified away)

• It is reasonable to expect that investorsdemand a premium to compensate themfor new investment in ventures that arenow deemed riskier.




950

970990

1010

1030

1050

1070

1090

1110

1130

1150

9 / 1 / 0 1

9 / 2 / 0 1

9 / 3 / 0 1

9 / 4 / 0 1

9 / 5 / 0 1

9 / 6 / 0 1

9 / 7 / 0 1

9 / 8 / 0 1

9 / 9 / 0 1

9 / 1 0

/ 0 1

9 / 1 1

/ 0 1

9 / 1 2

/ 0 1

9 / 1 3

/ 0 1

9 / 1 4

/ 0 1

9 / 1 5

/ 0 1

9 / 1 6

/ 0 1

9 / 1 7

/ 0 1

9 / 1 8

/ 0 1

9 / 1 9

/ 0 1

9 / 2 0

/ 0 1

9 / 2 1

/ 0 1

S&P 500 September 2001

September 11




950

1000

1050

1100

1150

1200

1250

1300

1350

1400

1 / 2 / 0 1

2 / 2 / 0 1

3 / 2 / 0 1

4 / 2 / 0 1

5 / 2 / 0 1

6 / 2 / 0 1

7 / 2 / 0 1

8 / 2 / 0 1

9 / 2 / 0 1

1 0 / 2 /

0 1

1 1 / 2 /

0 1

1 2 / 2 /

0 1

September 2001

S&P 500 2001




80

280

480

680

880

1080

1280

1480

1680

1 / 3 1 / 8 0

1 / 3 1 / 8 2

1 / 3 1 / 8 4

1 / 3 1 / 8 6

1 / 3 1 / 8 8

1 / 3 1 / 9 0

1 / 3 1 / 9 2

1 / 3 1 / 9 4

1 / 3 1 / 9 6

1 / 3 1 / 9 8

1 / 3 1 / 0 0

1 / 3 1 / 0 2

September 2001

S&P 500 1980-2002




• Impact not as substantial as one might thinkin advance.

• Nevertheless, risk increased.• Initially, people thought more terror would

be soon to come.

• As time elapsed, the probability ofadditional terror decreased.




ICRG Political Risk Rating

60.0

65.0

70.0

75.0

80.0

85.0

90.0

95.0

A p r - 0 1

M a y - 0

1

J u n - 0

1

J u l - 0 1

A u g - 0

1

S e p - 0

1

O c t - 0 1

N o v - 0

1

D e c - 0

1

J a n - 0

2

F e b - 0

2

M a r - 0 2

United States

World




• More impact on U.S. than average of othercountries.

• Implies a small increase in the risk premiumin the U.S. (10bp) and a smaller increase inworld premium (2bp).




• Graham-Harvey survey of the risk premiumduring September 11 crisis.




Pre-Sept. 11 Post-Sept. 1110-year premium

Mean premium 3.63 4.82Disagreement volatility 2.36 3.03



0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

Argentina Mexico Thailand

CAPMIbbotsonEHVGS-EHVGS-SegCSFB-EHV

68%

Risk Analysis and Project Evaluation4. Comparison of Methods



-20.00%-15.00%-10.00%

-5.00%0.00%5.00%

10.00%15.00%

20.00%25.00%30.00%

Slovakia Pakistan United States

CAPMIbbotsonEHVGS-EHVGS-SegCSFB-EHV

537%

Risk Analysis and Project Evaluation4. Comparison of Methods




Excel version 4. Comparison of Methods




5. Conversion of Cash Flows

Forward Rate• Intuitive (expected exchange rate levels)

• Works fine for developed countries• In emerging markets, there are two problems

– Data not readily available

– Will reflect a risk premium





Forward Rate• Risk premium in forward rate will lead to “double

discounting” • Think of the forward rate as the difference

between two interest rates (local and U.S.). – This difference will tell us something about

inflation expectations – But the local interest rate also reflects a default

probability (sovereign risk)





Purchasing Power Parity• Simple theory: The exchange rate will depreciate

by the difference in the local inflation rate and theU.S. inflation rate.• Empirical evidence shows this assumption works

well in emerging markets (but not that well indeveloped markets)





Purchasing Power Parity• To operationalize, we need multiyear forecasts of

inflation in the particular country as well as theU.S.• The difference in these rates is used to map out the

expected exchange rates• The expected exchange rates are used to convert

cash flows into US$• We then apply the US$ discount rate to US$ cash

flows

Risk Analysis and Project Evaluationf d



6. Project Specific Adjustments

Project Risk Analysis• Operating Risk

– Pre-completion – Post-completion – Sovereign

• Financial Risk

Risk Analysis and Project Evaluation6 P j S ifi Adj




Operating Risk• Precompletion

– Resources available (quality/quantity) – Technological risk (proven technology?) – Timing risks (failure to meet milestones)

– Completion riskHandle in cash flows





Operating Risk• Post-completion

– Market risks (prices of outputs) – Supply/input risk (availability) – Throughput risk (material put through plus

efficacy of systems operations) – Operating cost

Handle in cash flows





Operating Risk• Sovereign Risk (Macroeconomic)

– Exchange rate changes – Currency convertibility and transferability – Inflation

Handle through discount rate

Risk Analysis and Project Evaluation6 P j t S ifi Adj t t




Operating Risk• Sovereign Risk (Political/Legal)

– Expropriation• Direct (seize assets)• Diversion (seize project cash flows)• Creeping (change taxation or royalty)

– Legal system• May not be able to enforce property rights






Operating Risk• Sovereign Risk (Force Majeure)

– Political events• Wars• Labor strikes• Terrorism• Changes in laws

– Natural catastrophes• Hurricanes/earthquakes/floods






Financial Risks• Probability of default

– Look at debt service coverage ratios andleverage through life of project

• Check to see if internal rate of return isconsistent with (at least) the financial risks


Risk Analysis and Project Evaluation6 Project Specific Adj stments




Conclusions• Project evaluation in developing countries is

much more complex than in developedcountries

• Critical to: accurately identify risks and tomeasure the degree of mitigation – if any.

• Each risks need to be handle consistently – either in the cash flows or the discount rate,

harvey's notes on risk analysis and project evaluation

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