A stock has a beta of 1.56 and an expected return of 17.3 percent. A risk-free asset currently earns 5.1 percent. If a portfolio of the two assets has a beta of 1.06, what are the portfolio weights

Stock 0.68 and 0.32 for a market stock

Explanation:

Given Beta = 1.56 for a stock

Expected Return 17.3

Risk free Return = 5.1%

Portfolio beta = 1.06

From the given information the other stock is a t bill or risk free stock

β of a Portfolio = sum of weights of individual assets and associated betas

We know the Beta of a market stock is 1 we will denote the weight of The stock as x and the weight of market stock as 1-x

1.06 = 1.56 (x) + 1 (1-x)

1.06 = 1.56x + 1-x

x = 0.68 is the weight of stock

Market index

1-x = 1-0.68 = 0.32

The weight of the risky stock is 67.95% while that of the risk free asset is 32.05%

Explanation:

The two stock portfolio is made up of a risk free asset and a risky asset. Thus the portfolio beta is the weighted average of the individual sstock's betas. The beta for the risk free asset is zero.

Using the portfolio beta equation, we can calculate the weight of each stock in the portfolio.

Portfolio beta = rA * beta of A + rB * beta of B

Let x be the weight of the risk free asset in the portfolio. The weight of risky asset will be 1-x.

1.06 = x * 0 + (1-x) * 1.56

1.06 = 1.56 - 1.56x

1.06 - 1.56 = - 1.56x

-0.5 / - 1.56 = x

x = 32.05%

Thus, the weight of the risk free asset be 1 - 0.3205 = 0.6795 or 67.95%