Beta: general description of the theory, current examples and the way in which the theory impacts the business decisions of either the domestic or global financial manager.

Solution Preview

Introduction
For over two decades, it has been understood that a key measure of risk is the beta coefficient, which measures the relationship between an asset's returns and the returns on an index. The Capital Asset Pricing Model is based entirely on beta. Without a reliable beta you can't have CAPM any more than a value investor can buy stocks without knowing anything about assets or earnings. The appropriate use for a beta coefficient is determined by its method of calculation and the assumptions of the underlying estimation process. The first meaning of β arose in early attempts to use mean-variance analysis to aid in the management of actual portfolios—that is, in "normative portfolio analysis." The second meaning of beta arose in the assumption in the theory of capital markets that investors in fact use mean-variance analysis that is, in positive mean-variance theory. In other words, one type of beta estimate is a statistic used to reduce the computational effort required to put together a diversified portfolio of financial assets, be they individual stocks or mutual funds. Classical portfolio analysis requires the analyst to compute all possible relationships among portfolio components; a 100-security portfolio would contain 5,050 of these. Given that classical portfolio analysis was developed in the 1950s and early 1960s, this was beyond the computing capability of most portfolio managers
Calculation of Beta
Let's give an example of Morningstar's beta estimation process. Morningstar Inc. routinely provides two betas for the open-end equity funds that appear in its publications. Both betas are slope coefficient estimates from the following linear regression equation:
Rjt - Rft = aj + bj (It - Rft) + ejt
Rjt is the monthly return for fund j over the most recent consecutive 36 months; Rft is the U.S. Treasury rate for each month; aj and bj are the intercept and slope coefficient estimates; It is the monthly return on an index in month t; and ejt is a random error term. The gist of the model is that monthly returns in excess of the risk-free rate (that is, Rjt - Rft) for each fund are compared with the analogous values for an index, and the estimated slope coefficient, bj (or "beta") describes the relationship between the fund's excess returns and those of the index. The index takes a number of different values: the Standard & Poor's (S&P) 500 index is a proxy for the overall market, while narrower indices are proxies for specific sectors.
To estimate the reported beta coefficients for each stock fund, Morningstar follows a two-step process. First, the monthly excess returns of a given fund are regressed against those of the S&P 500 index. This results in the reported "Standard Index" beta values. Next, Morningstar identifies the "Best Fit" index by regressing the fund's monthly returns against the following sector indexes:
• JSE Gold
• MSCI Pacific
• MSCI Pacific ex Japan
• MSCI World ex U.S.
• MSCI EASEA
• MSCI Europe
• MSCI All Country
• Russell 2000
• S&P Midcap 400
• Wilshire 4500
• Wilshire REIT
• S&P 500
• LB Long-Term Treasury
• LB High-Yield

The Best Fit index is that which is most highly correlated with the fund—that is, the index that yields ...