A stock has a beta of 1.3 and an expected return of 15 percent. A risk-free asset currently earns 3.9 percent.
| a. | What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.) |
| Expected return | % |
| b. | If a portfolio of the two assets has a beta of .17, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the “%” sign in your response.) |
| Portfolio Weight | |
| xS | % |
| xrf | % |
| c. | If a portfolio of the two assets has an expected return of 12.75 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.) |
| Beta |
| d. | If a portfolio of the two assets has a beta of 1.48, what are the portfolio weights? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the “%” sign in your response.) |
| Porfolio Weight | |
| xS | % |
| xrf | % |
a) Expected return of the portfollio
E(r) of the portfolio = (0.50)0.039 + (0.50)0.15
= 0.0195 + 0.075
= 0.0945, or 9.45% rounded
b) weights of the portfolio
0.17= weight of stock*1.3
weight of stock = 0.17/ 1.3
= 0.1308, round 2 places: 13.08%
weight of risk-free asset = 1 – weight of stock = 1 – 0.1308 = 0.8692 rounded: 86.92%
| Porfolio Weight | |
| xS | 13.08% |
| xrf | 86.92 |
c) if the two asset portfolio has an E(r) of 12.75%, then the weights must be:
0.1275 = weight stock(0.15) + (1 – weight of stock)(0.039)…
0.1275 = 0.15X + 0.0.39(1 – X)
0.1275=0.15X+0.039-0.039X
0.1275-0.039=0.15X-0.039X
0.0885=0.111X
X=0.7973
“X”, weight of stock =0.7973
(1 – X), weight of Rf= (1 – weight of stock) = 0.2027(RFRs have beta = 0), so…
weight of stock * beta of stock = beta of portfolio = 0.7973 * 1.15 =1.036
d) 1.48 = 1.3(weight stock “X”) + 0 (1- weight of stock), reduces to:
1.48 = 1.3X
X= 1.1385 <weight of stock…= 113.85%, means “weight” of RFR is: 1 – 1.1385 = (0.1385) or NEGATIVE -0.1385%…(this essentially means you have borrowed at the risk free rate, perhaps to help finance the purchase of the stock in the portfolio – i.e. a leveraged portfolio)
