The very real possibility that the risk premium is low because investors had over priced equity

Choosing between the approaches

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

One way to adjust country risk premiums over time is to begin with the premium that emerges from the melded approach and to adjust this premium down towards either the country bond default spread or the country premium estimated from equity standard deviations. Another way of presenting this argument is to note that the differences between standard deviations in equity and bond prices narrow over longer periods and the resulting relative volatility will generally be smaller 13. Thus, the equity risk premium will converge to the country bond spread as we look at longer term expected returns. As an illustration, the country risk premium for Brazil would be 9.69% for the next year but decline over time to either the 4.83% (country default spread) or 4.13% (relative standard deviation).

Estimating Asset Exposure to Country Risk Premiums

Once country risk premiums have been estimated, the final question that we have to address relates to the exposure of individual companies within that country to country risk. There are three alternative views of country risk.

* Assume that all companies in a country are equally exposed to country risk. Thus, for

Brazil, where we have estimated a country risk premium of 9.69%, each company in the market will have an additional country risk premium of 9.69% added to its expected returns. For instance, the cost of equity for Aracruz Celulose, a paper and pulp manufacturer listed in Brazil, with a beta of 0.72, in US dollar terms would be (assuming a US treasury bond rate of 5% and a mature market (US) risk premium of 5.59%):

Expected Cost of Equity = 5.00% + 0.72 (5.51%) + 9.69% = 18.66% Note that the riskfree rate that we use is the US treasury bond rate, and that the 5.51% is the equity risk premium for a mature equity market (estimated from historical data in the US market). To convert this dollar cost of equity into a cost of equity in the local currency, all that we need to do is to scale the estimate by relative inflation. To illustrate, if the BR inflation rate is 10% and the U.S. inflation rate is 3%, the cost of equity for Aracruz in BR terms can be written as

This will ensure consistency across estimates and valuations in different currencies. The biggest limitation of this approach is that it assumes that all firms in a country, no matter what their business or size, are equally exposed to country risk.

* Assume that a companys exposure to country risk is proportional to its exposure to

all other market risk, which is measured by the beta. For Aracruz, this would lead to a cost of equity estimate of:

Expected Cost of Equity = 5.00% + 0.72 (5.51% + 9.69%) = 15.94% This approach does differentiate between firms, but it assumes that betas which measure exposure to market risk also measure exposure to country risk as well. Thus, low beta companies are less exposed to country risk than high beta companies.

* The most general, and our preferred approach, is to allow for each company to have

an exposure to country risk that is different from its exposure to all other market risk. We will measure this exposure with ?and estimate the cost of equity for any firm as follows:

Expected Return = Rf + Beta (Mature Equity Risk Premium) + ?(County Risk Premium) How can we best estimate ?? I consider this question in far more detail in the next chapter on beta estimation but I would argue that commodity companies which get most of their revenues in US dollars14 by selling into a global market should be less exposed than manufacturing companies that service the local market. Using this rationale, Aracruz, which derives 80% or more of its revenues in the global paper market in US dollars, should be less exposed15 than the typical Brazilian firm to of 0.25, for instance, we get a cost of equity in US dollar terms for Aracruz of:

Expected Return = 5% + 0.72 (5.51%) + 0.25 (9.69%) =11.39%

Note that the third approach essentially converts our expected return model to a two factor model, with the second factor being country risk as measured by the parameter ??and the country risk premium. This approach also seems to offer the most promise in analyzing companies with exposures in multiple countries like Coca Cola and Nestle. While these firms are ostensibly developed market companies, they have substantial exposure to risk in emerging markets and their costs of equity should reflect this exposure. We could estimate the country risk premiums for each country in which they operate and a ?relative to each country and use these to estimate a cost of equity for either company.

There is a data set on the website that contains the updated ratings for countries and the risk premiums associated with each.

An Alternative Approach: 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 market overall is correctly priced. Consider, for instance, a very simple valuation model for stocks.

Expected Dividends Next Period

(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 - 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:

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, as of December 31, 1999. The index was at 1469, and the dividend yield on the index was roughly 1.68%. In addition, the consensus estimate16 of growth in earnings for companies in the index was approximately 10% for the next 5 years. Since this is not a growth rate that can be sustained forever, we employ a two-stage valuation model, where we allow growth to continue at 10% for 5 years and then lower the growth rate to the treasury bond rate of 6.50% after the 5 year period.17 The following table summarizes the expected cash flows for the next 5 years of high growth and the first year of stable growth thereafter.

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 Argentine market on September 30, 1998 was estimated from the following inputs. The index (Merval) was at 687.50 and the current dividend yield on the index was 5.60%. Earnings in companies in the index are expected to grow 11% (in US dollar terms) over the next 5 years and 6% thereafter. These inputs yield a required return on equity of 10.59%, which when compared to the treasury bond rate of 5.14% on that day results in an implied equity premium of 5.45%. For simplicity, we have used nominal dollar expected growth rates18 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 7.1.

In terms of mechanics, we used smoothed historical growth rates in earnings and dividends as our projected growth rates and a two-stage dividend discount model. Looking at these numbers, we would draw the following conclusions. * The implied equity premium has seldom been as high as the historical risk premium.

Even in 1978, when the implied equity premium peaked, the estimate of 6.50% is well below what many practitioners use as the risk premium in their risk and return models. In fact, the average implied equity risk premium has been between about 4% over the last 40 years. We would argue that this is because of the survivor bias that pushes up historical risk premiums.

* The implied equity premium did increase during the seventies, as inflation increased. This does have interesting implications for risk premium estimation. Instead of assuming that the risk premium is a constant and unaffected by the level of inflation and interest rates, which is what we do with historical risk premiums, it may be more realistic to increase the risk premium as expected inflation and interest rates increase.

In fact, an interesting avenue of research would be to estimate the fundamentals that determine risk premiums.

* Finally, the risk premium has been on a downward trend since the early eighties and

the risk premium at the end of 1999 was a historical low. Part of the decline can be attributed to a decline in inflation uncertainty and lower interest rates and part of it, arguably, may reflect other changes in investor risk aversion and characteristics over the period. There is, however, the very real possibility that the risk premium is low because investors had over priced equity. In fact, the market correction in 2000 pushed the implied equity risk premium up to 2.87% by the end of 2000.

As a final point, there is a strong tendency towards mean reversion in financial markets. Given this tendency, it is possible that we can end up with a far better estimate of the implied equity premium by looking at not just the current premium, but also at historical data. There are two ways in which we can do this.

* We can use the average implied equity premium over longer periods, say ten to

fifteen years. Note that we do not need as many years of data here as we did with the traditional estimate because the standard errors tend to be smaller.

* A more rigorous approach would require relating implied equity risk premiums to

fundamental macroeconomic data over the period. For instance, given that implied equity premiums tend to be higher during periods with higher inflation rates (and interest rates), we ran a regression of implied equity premiums against treasury bond rates and a term structure variable between 1960 and 2000:

Implied Equity Premium = 1.87% + 0.2903 (T.Bond Rate) - 0.1162 (T.Bond - T.Bill)

The regression has significant explanatory power with an R-squared of 49% and the t statistics (in brackets under the coefficients) indicating the statistical significance of the independent variables used. Substituting the current treasury bond rate and bond-bill spread into this equation should yield an updated estimate19 of the implied equity premium.

histimpl.xls: This data set on the web shows the inputs used to calculate the premium in each year for the U.S. market.

implprem.xls: This spreadsheet allows you to estimate the implied equity premium in a market.

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Previous Issues

200705-24

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200705-19

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200705-18

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