Practice Question
An investor invests $800 in a risky asset with an expected rate of return of 18% and a standard deviation of 25%. The investor also invests $200 in a Treasury bill with a 4% rate of return. Her portfolio's expected rate of return and standard deviation are ______and ______, respectively.
Answer +
A
Explanation +
Expected Rate of Return
The expected rate of return on the portfolio is the weighted average of the expected returns of the risky asset and the Treasury bill.
- Risky asset: $800, Expected return: 18% (0.18)
- Treasury bill: $200, Expected return: 4% (0.04)
Total investment = $1000
Weights:
- Risky asset: 0.8
- Treasury bill: 0.2
E[Rp] = (0.8 × 0.18) + (0.2 × 0.04)
= 0.144 + 0.008
= 0.152 or 15.2%Standard Deviation
The Treasury bill is risk-free (σ = 0), so only the risky asset contributes to portfolio risk.
σp = Weight_risky × σ_risky
= 0.8 × 0.25
= 0.20 or 20%Final Answer
Expected rate of return: 15.2%
Standard deviation: 20%
Answer: A