Question

tock J has a beta of 1.38 and an expected return of 14.06 percent, while Stock K has a beta of .93 and an expected return of 11 percent. You want a portfolio with the same risk as the market. a.What is the portfolio weight of each stock? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)b.What is the expected return of your portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

To find the portfolio weights of Stock J and Stock K, we use the formula (Beta of Stock / Beta of Market) * (Expected Return of Stock - Risk-free Rate). For Stock J, the weight is 16.9968%, and for Stock K, the weight is 8.9261%. To calculate the expected return of your portfolio, we use the weighted returns of each stock.

Step-by-step explanation:

To determine the portfolio weight of each stock, we need to use the formula:

Portfolio Weight = (Beta of Stock / Beta of Market) * (Expected Return of Stock - Risk-free Rate)

First, we have to find the risk-free rate. Assuming it's 2% for this example, we can calculate the portfolio weights as follows:

For Stock J: Weight = (1.38 / 1.0) * (14.06% - 2%) = 16.9968%

For Stock K: Weight = (0.93 / 1.0) * (11% - 2%) = 8.9261%

To find the expected return of your portfolio, we add up the weighted returns of each stock:

Expected Return = (Weight of Stock J * Expected Return of Stock J) + (Weight of Stock K * Expected Return of Stock K)

Expected Return = (16.9968% * 14.06%) + (8.9261% * 11%) = 13.3282%

Answer 2

By definition, we know that Beta for market Portfolio is 1. By this, we need weighted average of J and K Beta as 1

1.38x + 0.93(1-x) = 1

1.38x + 0.93-0.93x = 1

0.45x = 0.07

x = 0.07/0.45

x = 0.16

So, we need 0.16 of J and 0.84 of K.

Weighted Average of J = 0.16 and K = 0.84.

Further Expected return of portfolio will be:

Weight Expected Return Expected Return of Portfolio

J 0.16 14.06 2.25

K 0.84 11 9.24

Total Portfolio Expected Return 11.49