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:

This is essentially the present value of dividends growing at a constant rate. Three of the four inputs in this model can be obtained externally - the current level of the market (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 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 = (.02*900) /(r - .07)

Solving for r,

r = (18+63)/900 = 9% 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, models. To illustrate this, consider the S&P 500 Index, as of September 23, 2003.

The index was at 1018, and the cash yield (dividends + stock buybacks) on the index over the previous 12 months was roughly 2.93%; the treasury bond rate on that date was 4.05%. In addition, the consensus estimate⁸ of growth in earnings for companies in the index was approximately 9% 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 9% for 5 years, and then lower the growth rate to the treasury bond rate of 4.05% after that⁹. The following table summarizes the expected cash flows for the next 5 years of high growth, and the first year of stable growth thereafter:

If we assume that these are reasonable estimates of the cash flows and that the index is correctly priced, then

Level of the index = 1018 = 32.49/(1+r) + 35.41/(1+r)2+ + 38.60/(1+r)3 + 42.07/(1+r)4 + (45.86+(48.84/(r-.0405))/(1+r)5

Note that the last term in the equation is the terminal value of the index, based upon the stable growth rate of 4.05%, discounted back to the present. Solving for r in this equation yields us the required return on equity of 7.84%. Subtracting the treasury bond rate of 4.05% from this return yields an implied equity premium of 3.79% for the United States in September 2003.

Implied Premiums in Emerging Markets

The advantage of the implied premium approach is that it is market-driven and current, and does not require any historical data. Thus, it can be used to estimate implied equity premiums 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 equity market on September 23, 2003, was estimated from the following inputs.

The index (Bovespa) was at 16889 and the current dividend yield on the index was 4.55%. Earnings in companies in the index are expected to grow 15% (in US dollar terms) over the next 5 years, and 5% thereafter¹⁰. These inputs yield a required return on equity of 12.17%, which when compared to the treasury bond rate of 4.05% on that day results in an implied equity premium of 8.12%. For simplicity, we have used nominal dollar expected growth rates¹¹ and treasury bond rates, but this analysis could have been done entirely in the local currency. While the level of the index and the dividend yield are widely available, earnings growth estimates are more difficult to come by in many markets.

To the extent that firms do not pay out what they can afford to in dividends and expected growth rates cannot be easily estimated, implied risk premiums may be understated. Nevertheless, they offer promise because they offer forward-looking estimates.

Decomposing Implied Equity Risk Premiums

The implied equity risk premium for a market can be very different from the premiums estimated from the three approaches used in the last section. Part of the reason for that is that the implied equity risk premium is an estimate in perpetuity whereas the estimates from the last section are estimated for the immediate future.

The other reason for the difference lies in the assumption that we make when estimating implied equity risk premiums that the market is correctly priced at the time of the estimation. In essence, we are being market neutral, i.e., not taking a view on markets, when we use an implied equity premium. Once we have an estimate of the implied equity risk premium for an emerging market, we can decompose it into a mature market equity risk premium and a countryspecific equity risk premium by comparing it to the implied equity risk premium for a mature equity market (the US, for instance). Applying this approach to Brazil in September 2003, we get the following:

Implied Equity premium for Brazil (see above) = 8.12%

Implied Equity premium for US (see above) = 3.79%

Country Specific Equity Risk Premium for Brazil = 4.33%

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8 We 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.

9 The treasury bond rate is the sum of expected inflation and the expected real rate. If we assume that real growth is equal to the real interest rate, the long term stable growth rate should be equal to the treasury bond rate.

10 We have deviated from our rule of setting the stable growth rate equal to the riskfree rate, because real growth in Brazil is likely to be slightly higher than real growth in mature economy like the United States.

11 The input that is most difficult to estimate for emerging markets is a long term expected growth rate. For Brazilian stocks, I used the average consensus estimate of growth in earnings for the largest Brazilian companies which have ADRs listed on them. This estimate may be biased, as a consequence.

Prof. Aswath Damodaran

Next: Estimating Asset Exposure to Country Risk Premiums

Summary: Index