Question

5. Suppose the current risk-free rate is 7.7 percent. Potpourri Inc. stock has a beta of 1.5 and an expected return of 16.7 percent. (Assume the CAPM is true.) (A) Calculate the risk premium on the market. has a beta of 0.8. on the Magnolia (B) Magnolia Industries stock Calculate the expected stock. return Suppose you have invested. $10,000 in Potpourri and Magnolia, and the beta of the portfolio is 1.255. invest in each stock? a combined total of (C) How much money did you (D) Calculate the expected return on the portfol io in part c.

Answer 1

5.(A)

The risk premium on the market can be calculated as,

The expected rate of return of Potpourri is 16.7%,so according to the CAPM model,

Re = Rf + beta (Rm - Rf) where, Re = expected return on stock

16.7 % = 7.7% + 1.5 ( Rm - Rf)

So, the risk premium on the market is 6% .

(B ) As the market risk premium is same for all stocks, Magnolia also has a market risk premium of 6%,

So, the expected rate of return of this stock is ,

Re = Rf + beta (Rm - Rf)

= 7.7% + 0.8 * 6

= 12.5%

So, the expected rate of return of Magnolia 12.5%

(C ) Let the amount invested in Potpourri be X and the amount invested in Magnolia is ($10,000 - X)

So, the beta of portfolio can be calculated as:

weight of potpourri * beta of potpourri + Weight of magnolia * beta of magnolia = beta of portfolio

X/10,000 * 1.5 + ( 10,000 - x) /10,000 * 0.8 = 1.255

1.5 x + (10,000 - x) 0.8 = 1.255* 10,000

1.5 X + 8,000 - 0.8X = 12,550

0.7x =4,550

X = $6,500

So, the amount invested in $6,500 in Potpourri and the amount invested in Magnolia is ( $10,000 - $6,500 = $3,500)

(D ) The expected return on the portfolio will be :

= weight of potpourri * expected return of potpourri + Weight of Magnolia * expected return of magnolia

= 0.65 * 0.167 + 0.35*0.125

= 0.1086 + 0.0438

= 15.235%

= 15.24%

So, the expected return on the portfolio is 15.24%.