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Asset
Actual
Return
CAPM
Return
Over- or
Underperformed
CAPM
A 8.00% 8.80% Under
B 6.86% 9.70% Under
C 15.00% 13.00% Over
D 12.50% 11.50% Over
Security analysts typically use statistical techniques to estimate an asset’s beta by obtaining a
line of best fit through historical asset and market returns. The slope of this line is beta. Data
points—that is, actual returns on the asset and market for a given period—will be randomly
scattered around the line no matter how well it “fits” the data. The point here is asset betas are
estimates. The CAPM return is, in a sense, a forecast and even good forecasts are subject to
random error. Another possibility is beta does not fully capture all nondiversifiable or systemic
factors that affect expected returns. Still another possibility is the firm behind the asset has
changed, so the beta estimated with historical data does not reflect the asset’s current beta.
P8-28 Security market line—SML (LG 6; Intermediate)
a, b, d.
c. Using the CAPM equation: rj RF [(rm RF)], where rj is the required return on asset j,
RF the risk-free rate, the beta on asset j and rm the return on the market portfolio:
Asset A: rj 0.09 [0.80(0.13 0.09)] = 0.122 or 12.2%
Asset B: rj 0.09 [1.30(0.13 0.09)] = 0.142 or 14.2%
d. Asset A has the smaller beta, hence the smaller risk premium and required return. Specifically,
the risk premium is 3.2% (12.2% 9%)—compared with 5.2% for Asset B’s (14.2% 9%).
P8-29 Shifts in the security market line (LG 6; Challenge)
a, b, c, d.
b. Using the CAPM equation: rA RF [(rm RF)], where RF is the risk-free rate (here 8%),
the beta on asset A (here 1.1) and rm the return on the market portfolio (here 12%), solve for rA
is the required return on asset A: rA 8% [1.1(12% 8%)] = 8% 4.4% = 12.4%.
c. Using the CAPM equation, rA = RF [(rm RF)], with RF = 6%, = 1.1 and rm = 10%, solve
