Question

You want a portfolio as risky as the market. Given the information below, compute the weight of the risk-free asset.

Enter your answer in percentages, rounded off to two decimal points. Do not enter % in the answer box.

Asset	Investment	Beta
Stock A	40.00%	1.4
Stock B	25.00%	0.9
Stock C	?	2.25
Risk-free asset	?	?

Answer 1

The risk-free asset will have a beta of 0 and the market has a beta of 1.

To construct a portfolio with stocks A, B, C, and the risk-free assets to be as risky as the market, the weighted average beta should be equal to 1.

Let's say the Weight of stock C is x and the weight of the risk-free asset is y.

We have,

1 = 0.4 * 1.4 + 0.25 * 0.9 + x * 2.25 + y * 0

This is just the sum of the product of beta with weights.

1 = 0.785 + x * 2.25

x = 0.215 / 2.25

x = 0.095555 or 9.55555%

We know that the sum of the weights must be equal to 100%

0.4 + 0.25 + 0.0955555 + y = 1

or y = 1 - 0.7455555555

y = 0.254444 or the weight of the risk-free asset = 25.44%

answered by: anonymous