Assume that both portfolios A and Bare well diversified that

Assume that both portfolios A and Bare well diversified, that Eva-21%, and EVs) = 16%. If the economy has only one factor, and ßA- 1.4, whereas Bg 1.0, what must be the risk-free rate? (Do not round intermediate calculations.) Risk-free rate

Solution

Expected return=risk-free rate +Beta*(MArket rate- risk-free rate )

A:

21=Rf+1.4*(Rm-Rf)

21=1.4Rm-0.4Rf

B:

16=Rf+1*(Rm-Rf)

Hence Rm=16%

Putting the value in equation for A:

21=1.4Rm-0.4Rf

21=(1.4*16)-0.4Rf

Hence Rf=(22.4-21)/0.4

=3.5%=risk free rate.