You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 15% and a standard deviation of 21% and a Treasury bill with a rate of return of 5%. How much money should be invested in the risky asset to form a portfolio with an expected return of 11%

$6,000

Explanation:

The computation of the amount invested in the risky asset is shown below;

Let us assume

R = Proportion of risky asset

T = T-bill proportion

We can say that

R + T = 100% and 100% be considered as 1

So, T = R - 1

First we have to determine the R which is calculated by the following formula

the expected return of portfolio = (Return of risky asset × proportion of risky asset) +  (Return of T-bill × proportion of t-bill)

11% = (15% × R) + (5% × (1 - R)

11% = 15%R + 5% - 5%R

R = 60%

Now the amount invested is

= Total amount invested × R

= $10,000 × 60%

= $6,000

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