Question

Suppose that you have a risky asset that provides you with an expected return of 12% per year with 20% volatility (standard deviation). Consider a risk-free asset that provides you with a 3% risk-free return. a. If you have $100,000 and invest 80% into the risky asset and 20% into the 6. b. How much will your portfolio be worth if the realized return on the risky c. If you cannot borrow money, what is the maximum possible expected return d. If you are allowed to borrow money at the risk-free rate, how can you get a risk-free asset, what is the expected return and risk of your portfolio? asset is 15%? on your portfolio, and what is the minimum? portfolio with an 18% expected return and what is the risk of this portfolio?

Answer 1

1. Invested Capital = $100,000

Investment in risky asset = 0.8 * 100,000 = 80,000

Investment in risk free asset = 0.2 * 100,000 = 20,000

Expected return on risk free asset = E(R) = 12%

Return on risk free asset = 3%

Expected return of the portfolio = E(R) = weighted average of portfolio assets returns = (w1*R1) + (w2*R2)(R1 risky asset, R2 risk free asset)

Therefore, E(R) for our portfolio = 80% *12% + 20%*3%

= 0.8*0.12 + 0.2*0.03

= 0.102 = 10.2%

The risk of our portfolio is equal to the standard deviation of two asset portfolio =

Portfolio variance = w²_A*σ²(R_A) + w²_B*σ²(R_B) + 2*(w_A)*(w_B)*Cov(R_A, R_B) ..[Variance = std. dev²]

But since, in our portfolio, the other asset is a risk free asset (std dev of risk free asset = 0), the equation for our portfolio, simply becomes,

Risk of the portfolio = Weight of risky asset * std. dev of risky asset

= 80% * 20%

= 0.8 * 0.2 = 0.16 = 16%

1. Realised return on risky asset = 15%

Realised return on portfolio = return on risky asset + return on risk free asset

Return on risky asset = 15% * 80,000 = 12,000

Return on risk free asset = 3% * 20,000 = 600

Hence, Return on portfolio = 12,000 + 600

= 12,600

Hence portfolio worth = Capital invested + realised return

= 100,000 + 12,600

= $112,600

1. Since, there is no borrowing in the portfolio, the minimum and maximum expected return of our portfolio will be = Expected return * (+- (standard deviation * expected return))

= 10.2% * (+-(16%*10.2%))

Hence, maximum expected return = 0.102 + (0.16*0.102) = 11.832%

minimum expected return = 0.102 - (0.16*0.102) = 8.568%