Question

a stock has a beta of 1.08 and an expected return of 13.2 percent. a risk-free asset currently earns 1.2 percent. the beta of a portfolio comprised of these two assets is .94. what percentage of the portfolio is invested in the stock?

Answer 1

To calculate the percentage of the portfolio invested in the stock with a beta of 1.08 and a portfolio beta of 0.94, we find that approximately 87.04% of the portfolio is invested in the stock.

Step-by-step explanation:

To determine what percentage of a portfolio is invested in a stock with a beta of 1.08, an expected return of 13.2 percent, a risk-free asset earning 1.2 percent, and a portfolio beta of 0.94, we use the formula for the beta of a portfolio, which is a weighted average of the betas of its constituents.

The formula for the portfolio beta (Bp) is:

Bp = x(Bs) + (1-x)(Br)

Where:

• Bs = Beta of stock
• Br = Beta of risk-free asset (which is 0)
• x = The proportion of the portfolio invested in the stock
• (1-x) = The proportion of the portfolio in the risk-free asset

Solving for x gets us:

0.94 = x(1.08) + (1-x)(0)

0.94 = 1.08x

x = 0.94 / 1.08

x ≈ 0.87037

Therefore, approximately 87.04% of the portfolio is invested in the stock.

Answer 2

To determine the percentage of the portfolio invested in the stock, we used the weighted average formula for the portfolio beta and found it to be approximately 87.04% invested in the stock.

Step-by-step explanation:

To calculate the percentage of the portfolio invested in the stock, we can use the formula for the beta of a portfolio, which is a weighted average of the betas of the individual investments in the portfolio. In this case, we are given that the beta of the portfolio is 0.94, the beta of the stock is 1.08, and the beta of the risk-free asset is 0, since it has no systematic risk.

Let x be the fraction of the portfolio invested in the stock and (1-x) be the fraction invested in the risk-free asset. The beta of the portfolio can be written as:

beta of portfolio = (beta of stock)(x) + (beta of risk-free asset)(1-x)

Plugging in the values we get:

0.94 = (1.08)(x) + (0)(1-x)

Solving for x gives us the proportion of the portfolio invested in the stock:

0.94 = 1.08x

x = 0.94 / 1.08

x = 0.87037 or 87.04%

Therefore, approximately 87.04% of the portfolio is invested in the stock.