ints) Dybvig Incorporation stock has a beta of 1.13 and an expected return of 12
ID: 420880 • Letter: I
Question
ints) Dybvig Incorporation stock has a beta of 1.13 and an expected return of 12.1 s (10 ercent. A risk-free asset currently earns 5 percent. What is the expected return on a portfolio that is equally invested in the two assets b. If a portfolio of the two assets has a beta of .50, what are the portfolio weights? c. Ifa portfolio of the two assets has an expected return of 10 percent, what is its beta? d. If a portfolio of the two assets has a beta of 2.26, what are the portfolio weights? e. How do you interpret the weights for the two assets in case (d)? Explain.Explanation / Answer
a. As the portfolio is equally invested in 2 assets the expected return will be the average return of the 2 assets = (12.1+5)/2 = 8.55%
b. Let the weight of the stock be x and so the weight of risk free asset = 1-x. Portfolio beta = sum of weighted average of the beta of 2 stocks.
Thus 0.50 = x*1.13 + (1-x)*0 (kindly note that beta of risk free asset is 0)
Or, 0.50 = 1.13x
Or, x = 0.50/1.13 = 0.4425.
So weight of stock = 0.4425 or 44.25% and weight of risk free asset = 100 – 44.25 = 55.75%
c. Expected return = weight of stock*return on stock + (1-weight of stock)*return on risk free asset
Let the weight of the stock be y. Thus 10 = 12.1y+(1-y)*5
Or 10 = 7.1y+5
Or y = 5/7.1 = 0.7042. Thus weight of stock = 70.42% and weight of risk free asset = 100-70.42 = 29.58%
Beta = 70.42%*1.13 + 29.58%*0 = 0.7958 or 0.80 (rounded off to 2 decimal places)
d. This is similar to “b” solved above.
Thus 2.26 = x*1.13 + (1-x)*0
Or, x = 2.26/1.13 = 2
Thus weight of stock = 2 or 200% and weight of risk free asset = 1-2 = -1 or -100%
e. In “d” weight of risk free asset is negative. It means that the risk free asset is seeing short selling. In other words the portfolio manager is borrowing from the risk free asset to invest in the stock. In other words the portfolio is long on the stock and short on the risk free asset.
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