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estimate the country risk premium.

1. Country bond default spreads: While there are several measures of country risk, one

of the simplest and most easily accessible is the rating assigned to a countryвЂ™s debt by

a ratings agency (S&P, MoodyвЂ™s and IBCA all rate countries). These ratings measure

default risk (rather than equity risk), but they are affected by many of the factors that

drive equity risk вЂ“ the stability of a countryвЂ™s currency, its budget and trade balances

and its political stability, for instance13. The other advantage of ratings is that they

come with default spreads over the US treasury bond. For instance, Brazil was rated

B2 in early 2004 by MoodyвЂ™s and the 10-year Brazilian C-Bond, which is a dollar

denominated bond was priced to yield 10.01%, 6.01% more than the interest rate

13 The process by which country ratings are obtained is explained on the S&P web site at

http://www.ratings.standardpoor.com/criteria/index.htm.

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(4%) on a 10-year treasury bond at the same time.14 Analysts who use default spreads

as measures of country risk typically add them on to both the cost of equity and debt

of every company traded in that country. For instance, the cost of equity for a

Brazilian company, estimated in U.S. dollars, will be 6.01% higher than the cost of

equity of an otherwise similar U.S. company. If we assume that the risk premium for

the United States and other mature equity markets is 4.82%, the cost of equity for a

Brazilian company can be estimated as follows (with a U.S. Treasury bond rate of 4%

and a beta of 1.2).

Cost of equity = Riskfree rate + Beta *(U.S. Risk premium) + Country Bond

Default Spread

= 4% + 1.2 (4.82%) + 6.01% = 15.79%

In some cases, analysts add the default spread to the U.S. risk premium and multiply

it by the beta. This increases the cost of equity for high beta companies and lowers

them for low beta firms.

2. Relative Standard Deviation: There are some analysts who believe that the equity risk

premiums of markets should reflect the differences in equity risk, as measured by the

volatilities of these markets. A conventional measure of equity risk is the standard

deviation in stock prices; higher standard deviations are generally associated with

more risk. If you scale the standard deviation of one market against another, you

obtain a measure of relative risk.

Standard Deviation Country X

Relative Standard Deviation Country X =

Standard Deviation US

This relative standard deviation when multiplied by the premium used for U.S. stocks

should yield a measure of the total risk premium for any market.

Equity risk premium Country X = Risk Premum US * Relative Standard Deviation Country X

Assume, for the moment, that you are using a mature market premium for the United

States of 4.82% and that the annual standard deviation of U.S. stocks is 20%. The

14 These yields were as of January 1, 2004. While this is a market rate and reflects current expectations,

country bond spreads are extremely volatile and can shift significantly from day to day. To counter this

volatility, the default spread can be normalized by averaging the spread over time or by using the average

default spread for all countries with the same rating as Brazil in early 2003.

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annualized standard deviation15 in the Brazilian equity index was 36%, yielding a

total risk premium for Brazil:

36%

Equity Risk Premium = 4.82% * = 8.67%

Brazil 20%

The country risk premium can be isolated as follows:

Country Risk PremiumBrazil = 8.67% - 4.82% = 3.85%

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While this approach has intuitive appeal, there are problems with using standard

deviations computed in markets with widely different market structures and liquidity.

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There are very risky emerging markets that have low standard deviations for their

equity markets because the markets are illiquid. This approach will understate the

equity risk premiums in those markets.

3. Default Spreads + Relative Standard Deviations: The country default spreads that

come with country ratings provide an important first step, but still only measure the

premium for default risk. Intuitively, we would expect the country equity risk

premium to be larger than the country default risk spread. To address the issue of how

much higher, we look at the volatility of the equity market in a country relative to the

volatility of the bond market used to estimate the spread. This yields the following

estimate for the country equity risk premium.

# " Equity &

Country Risk Premium = Country Default Spread * % (

" Country Bond'

$

To illustrate, consider the case of Brazil. As noted earlier, the dollar denominated

bonds issued by the Brazilian government trade with a default spread of 6.01% over

the US treasury bond rate. The annualized standard deviation in the Brazilian equity

index over the previous year was 36%, while the annualized standard deviation in the

Brazilian dollar denominated C-bond was 27%16. The resulting additional country

equity risk premium for Brazil is as follows:

15 Both the US and Brazilian standard deviations were computed using weekly returns for two years from

the beginning of 2002 to the end of 2003. While you could use daily standard deviations to make the same

judgments, they tend to have much more noise in them.

16 The standard deviation in C-Bond returns was computed using weekly returns over 2 years as well. Since

there returns are in dollars and the returns on the Brazilian equity index are in real, there is an inconsistency

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" 36% %

Brazils Country Risk Premium = 6.01%$ ' = 8.01%

# 27% &

Note that this country risk premium will increase if the country rating drops or if the

relative volatility of the equity market increases. It is also in addition to the equity

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risk premium for a mature market. Thus, the total equity risk premium for a Brazilian

company using the approach and a 4.82% premium for the United States would b2

12.83%.

Why should equity risk premiums have any relationship to country bond spreads?

A simple explanation is that an investor who can make 11% on a dollar-denominated

Brazilian government bond would not settle for an expected return of 10.5% (in dollar

terms) on Brazilian equity. Both this approach and the previous one use the standard

deviation in equity of a market to make a judgment about country risk premium, but

they measure it relative to different bases. This approach uses the country bond as a

base, whereas the previous one uses the standard deviation in the U.S. market. This

approach assumes that investors are more likely to choose between Brazilian

government bonds and Brazilian equity, whereas the previous one approach assumes

that the choice is across equity markets.

The three approaches to estimating country risk premiums will generally give you

different estimates, with the bond default spread and relative equity standard deviation

approaches yielding lower country risk premiums than the melded approach that uses

both the country bond default spread and the equity and bond standard deviations. In the

case of Brazil, for instance, the country risk premiums range from 3.85% using the

relative equity standard deviation approach to 6.01% for the country bond approach to

We believe that the larger country risk premiums that emerge from the last approach are

the most realistic for the immediate future, but that country risk premiums may decline

over time. Just as companies mature and become less risky over time, countries can

mature and become less risky as well.

In Practice: Should there be a country risk premium?

here. We did estimate the standard deviation on the Brazilian equity index in dollars but it made little

difference to the overall calculation since the dollar standard deviation was close to 36%.

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Is there more risk in investing in a Malaysian or Brazilian stock than there is in

investing in the United States? The answer, to most, seems to be obviously affirmative.

That, however, does not answer the question of whether there should be an additional risk

premium charged when investing in those markets. Note that the only risk that is relevant

for the purpose of estimating a cost of equity is market risk or risk that cannot be

diversified away. The key question then becomes whether the risk in an emerging market

is diversifiable or non-diversifiable risk. If, in fact, the additional risk of investing in

Malaysia or Brazil can be diversified away, then there should be no additional risk

premium charged. If it cannot, then it makes sense to think about estimating a country

risk premium.

For purposes of analyzing country risk, we look at the marginal investor вЂ“ the

investor most likely to be trading on the equity. If that marginal investor is globally

diversified, there is at least the potential for global diversification. If the marginal

investor does not have a global portfolio, the likelihood of diversifying away country risk

declines substantially. Even if the marginal investor is globally diversified, there is a

second test that has to be met for country risk to not matter. All or much of country risk

should be country specific. In other words, there should be low correlation across

markets. Only then will the risk be diversifiable in a globally diversified portfolio. If, on

the other hand, the returns across countries have significant positive correlation, country

risk has a market risk component and is not diversifiable and can command a premium.

Whether returns across countries are positively correlated is an empirical question.

Studies from the 1970s and 1980s suggested that the correlation was low and this was an

impetus for global diversification. Partly because of the success of that sales pitch and

partly because economies around the world have become increasingly intertwined over

the last decade, more recent studies indicate that the correlation across markets has risen.

This is borne out by the speed at which troubles in one market, say Russia, can spread to

a market with which it has little or no obvious relationship, say Brazil.

So where do we stand? We believe that while the barriers to trading across

markets have dropped, investors still have a home bias in their portfolios and that markets

remain partially segmented. While globally diversified investors are playing an

increasing role in the pricing of equities around the world, the resulting increase in

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correlation across markets has resulted in a portion of country risk becoming non-

diversifiable or market risk..

There is a data set on the website that contains the updated ratings for countries

and the risk premiums associated with each.

3. Implied Equity Premiums

There is an alternative to estimating risk premiums that does not require historical

data or corrections for country risk, but does assume that the overall stock market is

correctly priced. Consider, for instance, a very simple valuation model for stocks.

Expected Dividends Next Period

Value =

(Required Return on Equity - Expected Growth Rate in Dividends)

This is essentially the present value of dividends growing at a constant rate. Three of the

four variables in this model can be obtained externally вЂ“ the current level of the market

(i.e., value), the expected dividends next period and the expected growth rate in earnings

and dividends in the long term. The only вЂњunknownвЂќ is then the required return on equity;

when we solve for it, we get an implied expected return on stocks. Subtracting out the

riskfree rate will yield an implied equity risk premium.

To illustrate, assume that the current level of the S&P 500 Index is 900, the

expected dividend yield on the index for the next period is 2% and the expected growth

rate in earnings and dividends in the long term is 7%. Solving for the required return on

equity yields the following:

900(0.02)

900 =

r - 0.07

Solving for r,

r ! 0.07 = 0.02

r = 0.09 = 9%

If the current riskfree rate is 6%, this will yield a premium of 3%.

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This approach can be generalized to allow for high growth for a period and

extended to cover cash flow based, rather than dividend based, models. To illustrate this,

consider the S&P 500 Index on January 1, 2004. The index was at 1111.91 and the

dividend yield on the index in 2003 was roughly 2.81%.17 In addition, the consensus

estimate18 of growth in earnings for companies in the index was approximately 9.5% for

the next 5 years and the 10-year treasury bond rate on that day was 4.25%. Since a

growth rate of 9.5% cannot be sustained forever, we employ a two-stage valuation model,

where we allow dividends to grow at 9.5% for 5 years and then lower the growth rate to

the treasury bond rate of 4.25% after the 5 year period.19 Table 4.3 summarizes the

expected cash flows for the next 5 years of high growth and the first year of stable growth

thereafter.

Table 4.3: Expected Cashflows on S&P 500

Year Cash Flow on Index

1 34.26

2 37.52

3 41.08

4 44.98

5 49.26

6 51.35

a

Cash flow in the first year = 2.81% of 1111.91 (1.095)

If we assume that these are reasonable estimates of the cash flows and that the index is

correctly priced, then

34.26 37.52 41.08 44.98 49.26 49.26(1.0425)

Index level = 1111.91 = + + + + +

(1+ r) (1+ r) 2 (1+ r) 3 (1+ r) 4 (1+ r) 5 (r " .0425)(1+ r) 5

Note that the last term of the equation is the terminal value of the index, based upon the

stable growth rate of 4.25%, discounted back to the present. Solving for r in this equation

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yields us the required return on equity of 7.94%. Subtracting out the treasury bond rate of

4.25% yields an implied equity premium of 3.69%.

The advantage of this approach is that it is market-driven and current and it does

not require any historical data. Thus, it can be used to estimate implied equity premiums

17 Stockbuybacks during the year were added to the dividends to obtain a consolidated yield.

18We used the average of the analyst estimates for individual firms (bottom-up). Alternatively, we could

have used the top-down estimate for the S&P 500 earnings.

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in any market. It is, however, bounded by whether the model used for the valuation is the

right one and the availability and reliability of the inputs to that model. For instance, the

equity risk premium for the Brazilian market in January 2004 was estimated from the

following inputs. The index (Bovespa) was at 21050 and the current dividend yield on the

index was 4%. Earnings in companies in the index are expected to grow 14% (in US

dollar terms) over the next 5 years and 4.5% thereafter. These inputs yield a required

return on equity of 10.70%, which when compared to the treasury bond rate of 4% on that

day results in an implied equity premium of 6.70%. For simplicity, we have used nominal

dollar expected growth rates20 and treasury bond rates, but this analysis could have been

done entirely in the local currency.

The implied equity premiums change over time much more than historical risk

premiums. In fact, the contrast between these premiums and the historical premiums is

best illustrated by graphing out the implied premiums in the S&P 500 going back to 1960

in Figure 4.2.

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