STANDARD APPROACH. The conventional approach for estimating the beta of an in-
vestment is a regression of the historical returns on the investment against the his-
torical returns on a market index. For firms that have been publicly traded for a length
of time, it is relatively straightforward to estimate returns that an investor would have
made on investing in stock in intervals (such as a week or a month) over that period.
In theory, these stock returns on the assets should be related to returns on a market
portfolio (i.e., a portfolio that includes all traded assets, to estimate the betas of the
assets). In practice, we tend to use a stock index, such as the S&P 500, as a proxy for
the market portfolio, and we estimate betas for stocks against the index. When we
regress stock returns (Rj) against market returns (Rm):
where
Theslopeof the regression corresponds to the beta of the stock and measures the
riskiness of the stock.
HISTORICAL BETA ESTIMATE FOR COMPANIES IN SMALLER OR EMERGING MARKETS. The process
for estimating betas in markets with fewer stocks listed on them is no different from
the process described above, but the estimation choices on return intervals, the mar-
ket index and the return period can make a much bigger difference in the estimate.
The historical beta is likely to be flawed for the following reasons:
- When liquidity is limited, as it often is in many stocks in emerging markets, the
betas estimated using short return intervals tend to be much more biased. In fact,
using daily or even weekly returns in these markets will tend to yield betas that
are not good measures of the true market risk of the company. - In many emerging markets, both the companies being analyzed and the market
itself change significantly over short periods of time. Using five years of returns,
as we did for Boeing, for a regression may yield a beta for a company (and mar-
ket) that bears little resemblance to the company (and market) as it exists today. - Finally, the indices that measure market returns in many smaller markets tend to
be dominated by a few large companies. For instance, the Bovespa (the Brazil-
ian index) was dominated for several years by Telebras, which represented al-
most half the index. Nor is this just a problem with emerging markets. When an
index is dominated by one or a few companies, the betas estimated against that
index are unlikely to be true measures of market risk. In fact, the betas are likely
to be close to one for the large companies that dominate the index and wildly
variable for all other companies.
ILLUSTRATION1:BETA ESTIMATES FOR TITAN CEMENTS.
Consider, for instance, the beta estimated for Titan Cements, a cement and construc-
tion company in Greece. Exhibit 9.4 is the beta estimate for Titan obtained from a
beta service (Bloomberg) from January 1996 to December 2000. Note that the index
bSlope of the regressionCov 1 Rj,Rm 2s^2 maIntercept from the regressionRjabRm9.2 ESTIMATING DISCOUNT RATES 9 • 17