exposures 5 43 denotes the regression errors let it

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Unformatted text preview: . Theoretically, alpha measures ”. should be zero; however, empirical evidence suggests that alpha exists for various reasons (unidentified risk exposures, mispricing, market friction, etc.) exposures, 5-43 – ε denotes the regression errors, let it be zero now denotes From Sharpe ratio to CAPM (1) Since we have learned the intuition of Sharpe ratio, Since can we use the intuition to learn CAPM? can The answer is: Yes Deriving CAPM from Sharpe ratio: For stock i, it’s Sharpe = [E(ri) - rf ] / σi For market portfolio, it’s Sharpe = [E(rm) - rf ] / σm For Then, in equilibrium and no arbitrage (assuming that vol. is the only risk), these two Sharpe ratios should be equal, i.e., [E(ri) - rf ] = (σi / σm) [E(rm) - rf ], [E(r which is a CAPM model which 5-44 From Sharpe ratio to CAPM (2) Deriving Sharpe ratio from CAPM: The Sharpe ratio equilibrium exists when ri - rf = β [ rm - rf ] then Var(ri - rf) = E[(ri - rf)2] –{E[(ri - rf)]} 2 then = β2 Var(rm - rf) Var(r and β = σi / σm [E(ri) - rf ] = (σi / σm) [E(rm) - rf ] [E(r [E(ri) - rf ]/ σi = [E(rm) - rf ]/ σm [E(r Sharpe of firm i = Sharpe of market Sharpe 5-45 Simple examples Assume E(rm) = 0.11, rf = 0.03, and α = 0 For stock x with βx = 1.25, then For 1.25, E(rx) = 0.03 + 0 + 1.25(0.08) = .130 or 13.0% For stock y with βy = 0.6, then For E(ry) = 0.03 + 0 +0.6(0.08) = .078 or 7.8% 5-46 Tradeoff between market risk exposure (β) and expected return E(r) rx=13% r0=11% ry=7.8% 3% 0.6 1.0 1.25 ßy ß0 ßx ß 5-47 Estimating the CAPM using Real Data Using historical data on T-bill, S&P 500 and Using individual securities individual Regressing individual stock’s excess returns on Regressing the S&P 500’s excess returns the (Risk-free rate source: Risk-free http://www.treasury.gov/offices/domestic-finance/debthttp://www.treasury.gov/offices/domestic-finance/debtmanagement/interest-rate/daily_treas_bill_rates.shtml) Now, data are: “DELL” and “SP500” and “CAPM” Now, in Lecture2_StockPricing in 5-48...
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