Question9 When borrowing and lending at the risk-free rate are allowed, which capital allocation line (CAL) should the investor choose to combine with the efficient frontier? I. The one with the highest Sharpe ratio.II. The one identifying the optimal complete portfolio at the point of tangency with the efficient frontier.III. The one with the steepest slope.IV. The one which passes through the GMVP. II and IV I and IV I, II, and III I only I and III ResetMaximum marks: 3 Flag question undefined单项选择题
A
II and IV
B
I and IV
C
I, II, and III
D
I only
E
I and III

Question

Question9 When borrowing and lending at the risk-free rate are allowed, which capital allocation line (CAL) should the investor choose to combine with the efficient frontier? I. The one with the highest Sharpe ratio.II. The one identifying the optimal complete portfolio at the point of tangency with the efficient frontier.III. The one with the steepest slope.IV. The one which passes through the GMVP. II and IV I and IV I, II, and III I only I and III ResetMaximum marks: 3 Flag question undefined单项选择题

A

II and IV

B

I and IV

C

I, II, and III

D

I only

E

I and III

BlackTom AI · Accepted Answer

The investor should choose the capital allocation line that maximizes the Sharpe ratio because that CAL is the steepest line from the risk-free rate that is tangent to the efficient frontier and therefore identifies the optimal complete portfolio.

1) Relevant concepts
- Efficient frontier: the set of risky portfolios offering maximum expected return for a given risk.  
- Risk-free asset: allows straight-line combinations (CAL) between risk-free and any risky portfolio.  
- Sharpe ratio (reward-to-risk): S = (E[R_p] − R_f) / σ_p; it equals the slope of the CAL.  
- Tangency (optimal) portfolio: the risky portfolio where the CAL with maximum slope touches the efficient frontier.  
- GMVP (global minimum variance portfolio): the risky portfolio with minimum variance, not necessarily the tangency portfolio.

2) Step-by-step reasoning
- Any CAL through the risk-free rate and a risky portfolio p has slope S_p = (E[R_p] − R_f)/σ_p (definition).  
- The investor maximizes expected utility for mean-variance preferences by maximizing return per unit of risk, i.e., maximizing the Sharpe ratio. Thus choose the CAL with maximum S_p.  
- Geometrically, the CAL with maximum slope is the steepest CAL from R_f and is tangent to the efficient frontier; the tangency point is the optimal risky portfolio. Combining that risky tangency portfolio with borrowing/lending yields the optimal complete portfolio.

3) Calculation/Intermediate steps (symbolic)
- For portfolios on the efficient frontier, maximize S_p = (E[R_p] − R_f)/σ_p. The maximizer yields the tangency portfolio p*. The CAL slope = S_p* (steepest).

4) Why the correct answer is correct
- Statement I (highest Sharpe ratio) is equivalent to choosing the CAL with the steepest slope (III) because Sharpe ratio = slope. Statement II restates that the tangency identifies the optimal complete portfolio. All three are true and mutually consistent.

5) Why other options are incorrect
- IV (passes through the GMVP) is not generally true: GMVP minimizes variance but need not maximize Sharpe ratio, so the optimal CAL need not pass through the GMVP. Any answer including IV is therefore wrong. Options omitting II or III leave out correct implications of maximizing Sharpe.

Conclusion: I, II, and III are correct — matching the provided answer.

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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