Week 4. Capital Asset Pricing and Arbitrage Pricing Theory. Capital Asset Pricing Model (CAPM). CAPM: A model that relates the required rate of return for a security to its risk measured by beta. CAPM predicts the relationship between the risk and equilibrium expected returns on risky assets.
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Capital Asset Pricing and Arbitrage Pricing Theory
[E(rM) – rf] / bM = [E(ri) – rf] / bi, where bM = 1.0
E(ri) = rf + bi [E(rM) – rf], bi = [COV(ri,rM)] / sM2
bM = 1.0
E(rM) - rf = .08 rf = .03
bx = 1.25
E(rx) = .03 + 1.25(.08) = .13 or 13%
by = .6
E(ry) = .03 + .6(.08) = .078 or 7.8%
ri – rf = ai + bi (rM – rf) + ei
E(ri) – rf = ai + bi [E(rM)– rf]
(rGM - rf) =ai+ bGM(rm - rf)
Std error of estimate
Variance of residuals = 12.601
Std dev of residuals = 3.550
R-square = 0.575
Stock Price$Return%Dev. %
A 10 25.0 29.58
B 10 20.0 33.91
C 10 32.5 48.15
D 10 22.5 8.58
Portfolio P(A,B,C) 25.83 6.40 0.94
D 22.25 8.58
Short 3 shares of D and Buy 1 of A, B & C to form P (Arbitrage Portfolio: Zero-investment Portfolio).
You earn a higher rate on the investment than you pay on the short sale.
Ri = ai + biRM + e, where Ri = (ri – rf)
Rp = ap + bpRM
Beta(V+U) = bv[-bu/(bv-bu)] + bu[bv/(bv-bu)] = 0
R(V+U) = av[-bu/(bv-bu)] + au[bv/(bv-bu)] 0
rf + bp1 [E(rM1) – rf] + bp2 [E(rM2) – rf]