You want your portfolio beta to be 1.10. Currently, your portfolio consists of $3,000 invested in stock A with a beta of 1.65 and $2,000 in stock B with a beta of .72. You have another $5,000 to invest
And want to divide it between an asset with a beta of 1.48 and a risk-free asset. How much should
You invest in the risk-free asset?
A) $0
B) $775
C) $1,885
D) $3,115
E) $5,000

Question

Quizplus · Accepted Answer

The first step is to calculate the current beta of the portfolio:

Portfolio beta = (Amount invested in stock A / Total portfolio value) * Beta of stock A + (Amount invested in stock B / Total portfolio value) * Beta of stock B
Portfolio beta = (3,000 / 5,000) * 1.65 + (2,000 / 5,000) * 0.72
Portfolio beta = 1.188

To increase the portfolio beta to 1.10, we need to find the beta contribution of the new investment:

New beta contribution = (Amount to be invested in asset with beta 1.48 / Total portfolio value + Amount to be invested in risk-free asset * 0) * Beta of asset with beta 1.48
1.10 = (3,000 / (3,000 + 2,000 + Amount to be invested)) * 1.188 + (Amount to be invested in asset with beta 1.48 / (3,000 + 2,000 + Amount to be invested)) * 1.48

Solving for Amount to be invested, we get:
Amount to be invested = $1,885.25

Therefore, the amount to be invested in the risk-free asset is:
$5,000 - $1,885.25 - $3,000 - $2,000 = $114.75

The closest answer choice is C) $1,885.

You Want Your Portfolio Beta to Be 1