Question21 The expected return for an investor's Optimal Complete Portfolio is E(rC*) = 12%. The expected return for the Optimal Risky Portfolio is E(rP*) = 10.5%. The risk-free rate is rf = 3%. What is the investor's optimal risky share y*? 120% 88% Cannot be determined without the standard deviations 114% 83% ResetMaximum marks: 3 Flag question undefined单项选择题
A
120%
B
88%
C
Cannot be determined without the standard deviations
D
114%
E
83%

Question

Question21 The expected return for an investor's Optimal Complete Portfolio is E(rC) = 12%. The expected return for the Optimal Risky Portfolio is E(rP) = 10.5%. The risk-free rate is rf = 3%. What is the investor's optimal risky share y*? 120% 88% Cannot be determined without the standard deviations 114% 83% ResetMaximum marks: 3 Flag question undefined单项选择题

A

120%

B

88%

C

Cannot be determined without the standard deviations

D

114%

E

83%

BlackTom AI · Accepted Answer

The two-fund separation relation (complete portfolio as a combination of the risk-free asset and the optimal risky portfolio) gives the key linear equation: E(rC*) = rf + y*(E(rP*) − rf).

1. Relevant knowledge points and concepts
- Two-fund separation: any investor’s optimal complete portfolio is a weighted combination of the risk-free asset and the same optimal risky portfolio, P*.
- E(rC*) is the expected return of the complete portfolio; E(rP*) is the expected return of the optimal risky portfolio; rf is the risk-free rate; y is the fraction invested in the risky portfolio (can exceed 100% if leveraged).

2. Complete step-by-step reasoning
Start with the formula:
E(rC*) = rf + y*(E(rP*) − rf).

Substitute the given numbers:
E(rC*) = 12% (0.12),
E(rP*) = 10.5% (0.105),
rf = 3% (0.03).

So:
0.12 = 0.03 + y*(0.105 − 0.03).

3. All intermediate calculation steps
Compute the excess return of the risky portfolio over the risk-free rate:
0.105 − 0.03 = 0.075 (7.5%).

Rearrange to solve for y:
0.12 − 0.03 = y * 0.075
0.09 = y * 0.075
y = 0.09 / 0.075
y = 1.2 = 120%.

4. Why the correct answer is correct
The algebra directly gives y = 120%, meaning the investor should allocate 120% of wealth to the optimal risky portfolio and finance the extra 20% by borrowing at the risk-free rate. No volatility or standard deviation information is required because the relationship uses expected returns only.

5. Why the other options are incorrect
- 88%, 114%, 83% are simple numerically incorrect given the algebra above.
- "Cannot be determined without the standard deviations" is false because the two-fund separation formula for the expected return of the complete portfolio does not require standard deviations; it only requires the expected returns and the risk-free rate.

6. Conclusion
Solving rf + y*(E(rP*) − rf) = E(rC*) yields y = 120%, which matches the provided correct answer: 120%.

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:

Portfolio optimization requires an accurate understanding of costs and overhead cost allocation.

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