Question

ou invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04.

What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.11?

Select one:

a. 53.8% and 46.2%

b. 75% and 25%

c. 62.5% and 37.5%

d. 46.2% and 53.8%

e. Cannot be determined.

Answer 1

The % is computed as shown below:

Let the amount invested in risky stock be Y. Then the amount to be invested in risk free asset will be ($ 1,000 - Y)

Expected return of portfolio = Return of risky asset x investment in risky asset + Return of T-bill x investment in T -bill

0.11 x $ 1,000 = 0.17 x Y + 0.04 x ($ 1,000 - Y)

$ 110 = 0.17 Y + $ 40 - 0.04 Y

0.13 Y = $ 70

Y = $ 538 Approximately

So, investment in T-bill will be:

= $ 1,000 - $ 538

= $ 462

So, % will be as follow:

= $ 538 / $ 1,000 and $ 462 / $1,000

= 53.8% and 46.2%

So, the correct answer is option a.

Feel free to ask in case of any query relating to this question