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

Answer 1

A) The beta of market is 1. This is by definition of beta.

B) The beta of risk-free asset is 0 because the returns on the market has no effect on the risk-free asset return.

C) We need to create a portfolio that has a beta of 1

1 = Wa * Beta of A + Wb * Beta of B + Wr * Beta of risk-free asset

1 = 30,000/100,000 * 0.80 + Wb * 3.0 + Wr * 0

1 = 0.3 * 0.80 + Wb * 3

Wb = 0.76/3

Wb = 0.2533333333

Wb = 0.2533333333 * 100,000

The amount to be invested in stock B = $25,333.33333

The amount to be invested in risk-free asset = 100,000 - 30,000 - 25,333.33333

The amount to be invested in risk-free asset = $44,666.66667