Required Rate of Return?

Question

Your portfolio consists of $100,000 invested in a stock which has a beta=0.8, $150,000 invested in a stock which has a beta=1.2, & $50,000 invested in a stock which has a beta=1.8. The risk free rate is 7%. Last year this portfolio had a required rate of return of 13%. This year nothing changed except for the fact that the mareket risk premium has increased by 2 percent(two percentage points). What is the portfolio's current required rate of return?

Answer 1

According to CAPM:

Ri = Rf + Bi*Rm

Where Rm is market risk premium

For a portfolio, Rp = w1R1 + w2R2 + w3R3

We know that last year, Rp = 13%.

This year, Rm increased by 2%. Therefore Ri increases by 0.02*Bi so that Ri(this year) = Ri(last year) + 0.02*Bi

You replace Ri for each stock in the Rp(this year) formula and you have:

Rp = w1R1(this year) + w2R2(this year) + w3R3(this year)

      = w1[R1(last year) + 0.02*B1] + w2[R2(last year) + 0.02*B2] + w3[R3(last year) + 0.02*B3]

     = w1R1(last year) + w2R2(last year) + w3R3(last year) + 0.02*w1B1 + 0.02*w1B2 + 0.02*w1B3

     = Rp(last year) + 2%(w1B1+w1B2+w1B3)

And we know that w1 = 100/(100+150+50) = 100/300=1/3 and w2 = 150/300 = 1/2 and w3 = 50/300 = 1/6 therefore

Rp(this year) = 13% + 2%(1/3*0.8 + 1/2*1.2 + 1/6*1.8)

                       = 13% + 2%[(1.6+3.6+1.8)/6] = 15.33%