Question

1. you want to create a portfolio equally as risky as the market, and you have $100,000 to invest. In your portfolio, you want to invest in Stock A, Stock B, and a risk-free asset. You want to invest $30,000 in Stock A and the beta of Stock A is 0.80. The beta of Stock B is 30.

1. What is the market beta? What is the beta of the risk-free asset?
2. How much should you invest in Stock B and the risk-free asset to create this portfolio?

Answer 1

A) The beta measures how much a the return of an asset changes with respect to 1% change in market return. Since the asset we are considering is the market, the beta of market is 1.

B) The beta of a risk-free asset is 0 because if the market return changes the risk-free asset return doesn't change.

C) Weight of stock A = 30,000/100,000 = 0.30

The beta of portfolio = 1

1 = Weight of stock A * beta of stock A + Weight of stock B * beta of stock B + Weight of risk-free asset * beta of risk-free asset

1 = 0.30 * 0.8 + Wb * 30 + Wr * 0

1 = 0.24 + Wb * 30

Wb = (1 - 0.24)/30

Wb = 0.02533333333

Wa + Wb + Wr = 1

0.30 + 0.02533333333 + Wr = 1

Wr = 1 - 0.30 - 0.02533333333

Wr = 0.6746666667

The amount to be invested in stock B = 0.02533333333 * 100,000 = $2,533.333333

The amount to be invested in = 0.6746666667 * 100,000 = $67,466.66667