Question

You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 20% 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 8%?

Answer 1

Risky asset Expected return = 20%

Risk-free rate of return = 5%

Desired portfolio expected return = 8%

Portfolio expected return = (weight of Risky asset * Exp. return of Risky asset) + (Weight of Risk free asset * Exp. return of risk free asset)

Assume weight of risk free = x, risky = 1-x

8 = ( (1-x) * 20) + (x * 5)

8 = 20 - 20x + 5x

-12 = -15x

x = 12/15 = 0.80

So, weight of risk free asset = 0.80,

Weight of risky asset = 1-0.80 = 0.20

Amount invested in risk-free asset = 10000 * 0.80 = $8,000

Amount invested in risky asset = 10000 * 0.20 = $2,000