Question

Stock J has a beta of 1.37 and an expected return of 14.01%. Stock K has a beta of .92 and an expected return of 10.95%.

You want a portfolio with the same risk as the market.


What is the portfolio weight of each stock?

Answer 1

To achieve a portfolio with market-level risk, one should invest 47.75% in stock J with a beta of 1.37 and 52.25% in stock K with a beta of 0.92.

Step-by-step explanation:

To create a portfolio with the same risk as the market, which typically has a beta of 1, we need the weighted average of the portfolio's beta to be equal to 1.

We solve this by setting up the following equation where w_J is the weight of stock J, and w_K is the weight of stock K:

w_J(1.37) + w_K(0.92) = 1
w_J + w_K = 1 (since the total portfolio weight must equal 100%)

Since we have two equations and two unknowns, we can solve for one variable in terms of the other using the second equation, and then substitute into the first to find the weights.

Solving these equations simultaneously gives us:

w_J = (1 - 0.92w_K) / 1.37
w_K = 1 - w_J

Plugging the expression for w_J into the first equation, we get:

1 = (1 - 0.92w_K) / 1.37 + 0.92(1 - ((1 - 0.92w_K) / 1.37))

Solving this, we find:

w_J = 1.0936 / 2.29

= 0.4775 or 47.75%
w_K = 1 - 0.4775

= 0.5225 or 52.25%

Thus, to have the same risk as the market, you would invest 47.75% in stock J and 52.25% in stock K.