Question

Consider the multifactor APT with two factors. Portfolio A has a beta of .5 on factor 1 and a beta of 1.25 on factor 2. The risk premiums on the factor 1 and 2 portfolios are 1% and 7%, respectively. The risk-free rate of return is 7%. The expected return on portfolio A is _ if no arbitrage opportunities exist.
a.13.5%
b.16.25%
c.23%
d.15%

Answer 1

Answer:

(B) 16.25%

Explanation:

Using the multifactor APT,

$E(R_{A} ) = R_{f} + \beta_{1}.RP_{1} + \beta_{2}.RP_{2}$

where $E(R_{A} )$ = expected return on portfolio A,

$R_{f}$ = the risk free rate of return,

$\beta_{i}$ = beta on factor "i"

$RP_{i}$ =  risk premium on factor "i".

Therefore,

return on portfolio A = 7% + (0.5 * 1%) + (1.25 * 7%)

= 0.07 + (0.5 * 0.01) + (1.25 * 0.07)

= 0.07 + 0.005 + 0.0875

= 0.1625

= 16.25%.