The objective function in Markowitz portfolio model is to:

Question

BlackTom AI · Accepted Answer

Modern portfolio theory (Markowitz) balances expected return against risk measured by variance; the model optimizes the trade-off rather than simply maximizing or minimizing one of those quantities alone.

1) Relevant knowledge points and concepts
- Expected return: the weighted average of asset expected returns in the portfolio.
- Risk (variance or standard deviation): the portfolio variance = w'Σw, where w is the weight vector and Σ is the covariance matrix.
- Markowitz objective: either (a) minimize portfolio variance subject to a given target expected return, or (b) maximize expected return subject to a target variance, or (c) maximize a mean-variance utility U = E[R_p] − (λ/2)Var(R_p) for some risk-aversion parameter λ. All formulations reflect a trade-off, not maximizing risk or minimizing return as stand-alone goals.

2) Step-by-step reasoning
- Standard constrained formulation: minimize w'Σw subject to w'μ = R_target and sum(w)=1 (and possibly no-short-sale constraints). This explicitly minimizes variance for a required return.
- Alternative: maximize w'μ subject to w'Σw ≤ σ_target^2 and sum(w)=1. This maximizes return for a constrained risk.
- Utility form: maximize w'μ − (λ/2) w'Σw. This balances return and variance simultaneously.

3) Intermediate expressions (no numeric calculation required)
- Portfolio variance: σ_p^2 = w'Σw
- Portfolio expected return: μ_p = w'μ
- Mean-variance utility: U(w) = μ_p − (λ/2)σ_p^2

4) Why the correct answer is correct
Each offered option contradicts the Markowitz intent: the model never seeks to maximize variance or minimize return; it balances return and variance. Thus none of the listed choices describe the objective properly.

5) Why other options are incorrect
- "maximize return while maximizing risk": Wrong — Markowitz does not aim to maximize risk; risk is either constrained or penalized.
- "maximize portfolio variance": Wrong — variance is the measure of risk to be minimized or constrained, not maximized.
- "minimize return": Wrong — minimizing return is the opposite of the goal.

6) Conclusion
Therefore the correct choice is "none of these are correct," which matches the provided answer.

The objective function in Markowitz portfolio model is to:单项选择题

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