You want your portfolio beta to be 0.90. Currently, your portfolio consists of $4,000 invested in stock A with a beta of 1.47 and $3,000 in stock B with a beta of 0.54. You have another $9,000 to invest and want to divide it between an asset with a beta of 1.74 and a risk-free asset. How much should you invest in the risk-free asset

31.47%

Explanation:

Total investment = 4000 + 3000 +9000 = $16,000

% of investment in A = 4000/16000 = 25%

% of investment in B = 3000/16000 = 18.75%

% of investment in Asset beta and risk-free asset = 100% - 25% -18.75% = 56.25%

Let the % of investment in asset with beta of 1.74 is A, % of investment in risk free asset is B.

We have the following simultaneous equations:

0.9 = (0.25 x 1.47) + (0.1875 x 0.54) + (A x 1.74) + (B x 0)

A+B = 56.25%

From the first equation, we get A = 24.78%

--> B = 56.25% - 24.78% = 31.47%

*** Note: Portfolio beta is the weighted sum of individual asset betas, according to the proportions of the investments in the portfolio

*** Note: Beta of risk free asset is 0