## H

Country

I □ Stocks - Short term Government Return □ Stocks - Long Term Government Return I

histretSP.xls: This data set has yearly data on treasury bill rates, treasury bond rates and returns and stock returns going back to 1928.

### A Modified Historical Risk Premium

In many emerging markets, there is very little historical data and the data that exists is too volatile to yield a meaningful estimate of the risk premium. To estimate the risk premium in these countries, let us start with the basic proposition that the risk premium in any equity market can be written as:

Equity Risk Premium = Base Premium for Mature Equity Market + Country Premium The country premium could reflect the extra risk in a specific market. This boils down our estimation to answering two questions:

• What should the base premium for a mature equity market be?

• How do we estimate the additional risk premium for individual countries?

To answer the first question, we will make the argument that the US equity market is a mature market and that there is sufficient historical data in the United States to make a reasonable estimate of the risk premium. In fact, reverting back to our discussion of historical premiums in the US market, we will use the geometric average premium earned by stocks over treasury bonds of 4.82% between 1928 and 2003. We chose the long time period to reduce standard error, the treasury bond to be consistent with our choice of a riskfree rate and geometric averages to reflect our desire for a risk premium that we can use for longer term expected returns. There are three approaches that we can use to 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 country's debt by a ratings agency (S&P, Moody'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 - the stability of a country'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 Moody'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.

(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 Co X

Relative Standard Deviation Count 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 PremumUS * 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.

annualized standard deviation15 in the Brazilian equity index was 36%, yielding a total risk premium for Brazil:

The country risk premium can be isolated as follows: Country Risk PremiumBrazil = 8.67%- 4.82% = 3.85%

While this approach has intuitive appeal, there are problems with using standard deviations computed in markets with widely different market structures and liquidity. 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.

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

Equity Risk Premium,

Brazil

Brazils Country Risk Premium = 6.01%

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 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%.

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 - 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 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.

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 - 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 "unknown" 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:

Value =

Expected Dividends Next Period

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

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

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.

Year |
Cash Flow on Index |

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