Question

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08? Select one: a. 30% and 70% b. 50% and 50% c. 60% and 40% d. 40% and 60% e. Cannot be determined.

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03.

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 0.08?

Select one:

a. 85% and 15%

b. 75% and 25%

c. 62.5% and 37.5%

d. 57% and 43%

e. Cannot be determined.

Answer 1

Let % of money invested in Risky assets is x

Let % of money invested in Risk-free assets would be (1-x)

Variance of Portfolio = (X²_ASd²_A)+(X²_BSd²_B ) +(2X_AX_B(Sd_ASd_Br_AB)

0.08² = x²_A*0.20²

x²*0.20² = 0.08*0.08

x² = 0.16

= 0.40

And (1-x) = 0.60

Therefore option (d) is the correct option i.e. 40% of Risky assets and 60% of Risk-free asset.

Note: Standard deviation of a risk-free will always be zero.

Correlation of coefficient of any asset with risk-free assets will always be zero.

Return of Risky asset = 0.11

Return of Risk-free asset = 0.03

Calculation of % of money invested in the portfolio formed by Risky assets and risk free asset:

Let % of money invested in Risky assets is x

Let % of money invested in Risk-free assets would be (1-x)

Expected return of the Portfolio = Σ Weights*Return

8 = x*0.11+(1-x)*3

11x-3x = 8-3

X = 5/8

= 0.625

and (1-x) = 0.375

Therefore option (c) is the correct option i.e. 62.5% of Risky assets and 37.5% of Risk-free asset