This statement is incorrect.
The CAPM assumes normally distributed security
returns, but APT does not.
This statement is correct.
Substituting the portfolio returns and betas in the expected return-beta relationship,
we obtain two equations with two unknowns, the risk-free rate (r
) and the factor
risk premium (RP):
12 = r
9 = r
Solving these equations, we obtain:
= 3% and RP = 7.5%
Shorting an equally-weighted portfolio of the ten negative-alpha stocks and
investing the proceeds in an equally-weighted portfolio of the ten positive-
alpha stocks eliminates the market exposure and creates a zero-investment
Denoting the systematic market factor as R
, the expected dollar
return is (noting that the expectation of non-systematic risk,
, is zero):
[0.02 + (1.0
[(–0.02) + (1.0
0.04 = $40,000
The sensitivity of the payoff of this portfolio to the market factor is zero
because the exposures of the positive alpha and negative alpha stocks cancel
(Notice that the terms involving R
sum to zero.)
Thus, the systematic
component of total risk is also zero.
The variance of the analyst’s profit is not
zero, however, since this portfolio is not well diversified.
For n = 20 stocks (i.e., long 10 stocks and short 10 stocks) the investor will
have a $100,000 position (either long or short) in each stock.
exposure is zero, but firm-specific risk has not been fully diversified.
variance of dollar returns from the positions in the 20 stocks is:
] = 18,000,000,000
The standard deviation of dollar returns is $134,164.