S tanactsc 372 f11 modern portfolio theory capm p 55

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Unformatted text preview: Additivity property: For a portfolio with RP = ￿N i=1 xi Ri , N Portfolio Beta = βP = Cov(RP , RM ) ￿ = xi βi 2 σM i=1 What is the beta of the market portfolio? hence beta measures the marginal contribution of a security to risk in the market portfolio K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 51 Estimating Beta: E(Ri) − rf = βi [E(RM ) − rf ] Under CAPM, E(Ri ) − rf vs E(RM ) − rf is a straight line with slope βi ⇒ βi can be estimated via linear regression Problem: is not observable Expected returns are not observable True market portfolio In practice, use market index (e.g. S&P 500, TSX) as a proxy for the market portfolio from historical (e.g. monthly) returns, fit a straight line to rit − rf t = αi + βi (rM t − rf t ) + ￿it ⇒ The slope of the best-linear fit is the best estimate of beta or equivalently estimate Cov(Ri , RM ) and Var(RM ) K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 52 Table 11.7: Estimates of Beta Stock Beta High-beta stocks Teck Resources Limited Manulife Financial Average-beta stocks Bank of Nova Scotia Investors Group Talisman Energy Westjet Airlines Low-beta stocks Canadian Utilities Enbridge Dynex Power Inc. 3.02 2.21 1.33 1.27 1.27 1.12 0.37 0.31 0.32 K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 53 Security Market Line (SML) depicts the relationship...
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