A stock has a beta of 1.37 and an expected return of 13.5 percent. A risk-free a
ID: 2727667 • Letter: A
Question
A stock has a beta of 1.37 and an expected return of 13.5 percent. A risk-free asset currently earns 4.65 percent.
What is the expected return on a portfolio that is equally invested in the two assets?
If a portfolio of the two assets has a beta of 0.97, what are the portfolio weights?
If a portfolio of the two assets has an expected return of 12.7 percent, what is its beta?
If a portfolio of the two assets has a beta of 2.57, what are the portfolio weights?
A stock has a beta of 1.37 and an expected return of 13.5 percent. A risk-free asset currently earns 4.65 percent.
Explanation / Answer
a) E(r) of the portfolio = (0.50)* 4.65% + (0.50)* 13.5% = 0.02325 + 0.0675 = 0.09075, or 9.1% rounded
b) 0.97 = weight of stock*1.37
weight of stock = 0.97 / 1.37 = 0.708, round 2 places: 70.8%
weight of risk-free asset = 1 - weight of stock = 1 - 0.708 = 0.292, rounded: 29.2%
c) if the two asset portfolio has an E(r) of 12.7%, then the weights must be:
12.7% = weight stock(13.5%) + (1 - weight of stock)(4.65%)
0.127 = 0.135X + 0.0465(1 - X)
"X", weight of stock = 0.9096
(1 - X), weight of RFR = (1 - weight of stock) = 0.09039 (RFRs have beta = 0),
so.
weight of stock * beta of stock = beta of portfolio = 0.9096 * 1.37 = 1.246152. round to 3 places = 1.246
d) 2.57 = 1.37(weight stock "X") + 0 (1- weight of stock), reduces to:
2.57 = 1.37X
X= 1.8759 <weight of stock...= 187.59%, means "weight" of RFR is: 1 - 1.8759= (0.8759) or NEGATIVE 87.59%.
(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)
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