cost of capital - A B Freeman School of Business MBA...

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A. B. Freeman School of Business MBA Professor Paul A. Spindt Financial Modeling Spring 2006 A LITTLE ABOUT COST OF CAPITAL 1 Concepts Investors purchase assets with the expectation of earning a return. But, of course, there is no guarantee (with the single exception of a possible risk- free asset) that the actual return earned will equal the return the investor expected when she bought the asset. In fact, the actual return, r s , on some asset s is a random draw from a probablility distribution having a mean of E ( r s ) and a standard deviation of σ s . σ s measures the variability of possible returns, or the riskiness of the asset. That nobody likes risk, at least not for its own sake, is a precept of modern finance theory. Investors who bear risk must be compensated for the burden with increased expected return. On the surface, this logic suggests that to hold assets with higher standard deviations, σ s , investors should demand higher expected returns, E ( r s ). But in a competitive capital market with many risky assets, this surface logic is not always true. As long as asset returns in such a market are not perfectly correlated , meaning loosely that they do not move in perfectly coor- dinated lock-step like a flock of birds wheeling together in the sky, investors can offset some of the risk of one asset by holding it together with another. What is lost on one asset, may be gained on the other. That is, an investor 1
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can reduce the risk she must bear by diversifying her investment across a portfolio of assets. Diversification can only reduce risk so far, however. In the limit, a fully diversified investor holds a value-weighted portfolio of all the risky assets available in her economy. This portfolio is called the market portfolio , and has expected return E ( r M ) and standard deviation (of returns) σ M . σ M is risk that cannot be avoided by diversification. The return on any risky asset s is more or less correlated with the retun on the market portfolio, and this correlation can be expressed as ρ sM , which can range from +1 to - 1. The portion of an asset’s total risk, σ s , that cannot be avoided by diversification is ρ sM σ s . Normalizing this quantity by the unavoidable riskiness of the market portfolio, gives us Beta , which is the standard measure of the non-diversifiable risk of asset s : 1 β s = ρ sM σ s σ M
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