Question13 An investor invests 25% of her wealth in the optimal portfolio of risky assets P* with an expected rate of return of 0.17 and a variance of 0.08. The risk-free rate is 0.045. Her optimal complete portfolio C* has an expected return and standard deviation of _________ and _________, respectively. Select one alternative: a. 0.076; 0.071 b. 0.087; 0.124 c. 0.114; 0.126 d. 0.076; 0.020 ResetMaximum marks: 1 Flag question undefined单项选择题
A
a. 0.076; 0.071
B
b. 0.087; 0.124
C
c. 0.114; 0.126
D
d. 0.076; 0.020

Question

Question13 An investor invests 25% of her wealth in the optimal portfolio of risky assets P* with an expected rate of return of 0.17 and a variance of 0.08. The risk-free rate is 0.045. Her optimal complete portfolio C* has an expected return and standard deviation of _ and _, respectively. Select one alternative: a. 0.076; 0.071 b. 0.087; 0.124 c. 0.114; 0.126 d. 0.076; 0.020 ResetMaximum marks: 1 Flag question undefined单项选择题

A

a. 0.076; 0.071

B

b. 0.087; 0.124

C

c. 0.114; 0.126

D

d. 0.076; 0.020

BlackTom AI · Accepted Answer

Combining a risky portfolio and a risk-free asset: the complete portfolio expected return is the weighted average of the risky and risk-free returns, and its standard deviation equals the risky weight times the risky portfolio’s standard deviation (since the risk-free asset has zero variance and zero covariance).

1) Relevant knowledge points
- Expected return of a two-asset combination (risk-free r_f and risky P*): E[R_C] = w_P E[R_P] + (1 - w_P) r_f.
- Variance of the complete portfolio: Var(R_C) = w_P^2 Var(R_P) (because the risk-free asset has zero variance and zero covariance), so standard deviation sigma_C = |w_P| sigma_P.
- sigma_P = sqrt(Var(P*)).

2) Step-by-step reasoning and calculations
- Given: w_P = 0.25, E[R_P] = 0.17, Var(P*) = 0.08, r_f = 0.045.
- Compute sigma_P: sigma_P = sqrt(0.08).
  - sqrt(0.08) = sqrt(8 × 10^-2) = sqrt(8) × 0.1 ≈ 2.82842712 × 0.1 = 0.282842712.
- Expected return of complete portfolio:
  - E[R_C] = 0.25 × 0.17 + 0.75 × 0.045
  - = 0.0425 + 0.03375 = 0.07625 ≈ 0.076 (rounded).
- Standard deviation of complete portfolio:
  - sigma_C = 0.25 × 0.282842712 = 0.070710678 ≈ 0.071 (rounded).

3) Intermediate steps shown above (square root and multiplication steps included).

4) Why the correct answer is correct
- The expected return computed as a weighted average yields 0.07625 (rounded to 0.076). The risk-free asset contributes no volatility, so the portfolio’s volatility scales linearly with the risky weight, giving 0.07071 (rounded to 0.071). These match option a.

5) Why other options are incorrect
- b (0.087; 0.124): both values are inconsistent with the 25% weighting and given parameters (sigma too large and return too high).
- c (0.114; 0.126): implies a much larger weight in the risky asset (return and sigma both too high).
- d (0.076; 0.020): expected return matches, but sigma = 0.020 would correspond to a much smaller risky weight (~7%), not the given 25%.

6) Conclusion
The correct complete-portfolio expected return and standard deviation are 0.076 and 0.071, respectively, so answer a. 0.076; 0.071 is confirmed.

类似问题

Question1.3 An investor’s optimal risky allocation y* is required to identify the______: Optimal Complete Portfolio C. Global Minimum Variance Portfolio (GMVP). Optimal risky portfolio P. Capital Allocation Line (CAL). Efficient frontier. ResetMaximum marks: 2.5 Flag question undefined

Constraining MSR portfolio weights to the (0%, 100%) range compared to allowing unconstrained (short-selling) weights tends to:

The Global Minimum Variance (GMV) portfolio is defined as the portfolio that:

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