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Unformatted text preview: A supplement note Kevin Q. Wang MGT 330 INVESTMENTS Multifactor Models and Data Snooping 1 1. The CAPM as a One Factor Model An important issue in f nance is how to quantify the relation between risk and expected return. Common sense suggests that higher expected returns are required for riskier projects. With the development of the CAPM, we were able to go beyond the common sense: to quantify this relation. The CAPM says that E (˜ r i − r f ) = β i E (˜ r M − r f ) . In other words, the expected excess return is the security’s beta (risk of the asset) multiplied by the expected excess return on the market (price of the market risk). The CAPM measure of risk of a security i is β i = cov (˜ r i , ˜ r M ) var (˜ r M ) , which is the asset’s covariance with the market divided by the variance of the market. Empirically, we can obtain beta by running a regression of the excess asset return on the excess market return: ˜ r i,t − r f,t = α i + β i (˜ r M,t − r f,t ) + ˜ ε i,t . In preparation for multifactor models, it is useful to think the return on the market (˜ r M,t ) as a factor . Generally speaking, a factor is something which may track good and bad times of the economy through time and hence may a f ect returns on all securities. In the CAPM world, the factor is the market return. Securities which tend to pay out only when the market does well (i.e. with high beta) are risky, because they pay up in a 1 This note is prepared as a supplement to Class Note 7. 1 good state of the world, just when you don’t need the money. Hence such securities should o f er you high expected returns as compensation. To make it clearer, consider the following example. Suppose that stock i and stock j have the same standard deviation: σ i = σ j = σ . Let’s say that stock i has a higher correlation with the market than stock j : ρ i > ρ j . In the CAPM world, are the two stocks equally risky? If not, which stock is riskier and hence has higher expected return?...
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- Fall '11