Question

2. A friend brags that she expects to earn a return of 10.25% on her portfolio with a beta of 0.825. Can you match her performance with Stock X (12% return and a beta of 1.1) and the risk free asset that earns a 5% return? With what portfolio weights?

Answer 1

To match a friend's portfolio return of 10.25% and beta of 0.825, invest 75% in Stock X (12% return, 1.1 beta) and 25% in a risk-free asset with a 5% return. Solve simultaneous equations to find these weights.

Step-by-step explanation:

A friend expects to earn a return of 10.25% with a portfolio that has a beta of 0.825. To evaluate whether you can match her performance with Stock X (with a 12% return and a beta of 1.1) and a risk-free asset earning a 5% return, you can use the Capital Asset Pricing Model (CAPM) and the following formulas:

• Expected return on the portfolio = weight of Stock X * return on Stock X + weight of risk-free asset * return on risk-free asset
• Portfolio beta = weight of Stock X * beta of Stock X + (1 - weight of Stock X)

To match your friend's expected return of 10.25% and beta of 0.825, you need to set up the equations:

1. 0.1025 = weight of Stock X * 0.12 + (1 - weight of Stock X) * 0.05
2. 0.825 = weight of Stock X * 1.1

By solving these simultaneous equations, you can determine the weight of Stock X in the portfolio.

To find the portfolio weights, solve for the weight of Stock X from equation (2):

• 0.825 = weight of Stock X * 1.1
• weight of Stock X = 0.825 / 1.1 = 0.75

Then, using the weight of Stock X found, solve for the weight of the risk-free asset:

• Weight of risk-free asset = 1 - weight of Stock X = 1 - 0.75 = 0.25

Therefore, to match your friend's performance, you should invest 75% of your portfolio in Stock X and the remaining 25% in a risk-free asset.