A well-diversified portfolio has …………

Question

BlackTom AI · Accepted Answer

Systematic risk cannot be diversified away, so a well-diversified portfolio retains only systematic risk.

1) Relevant knowledge points and concepts
- Total risk of a security or portfolio = systematic risk (market-wide, non-diversifiable) + non-systematic risk (idiosyncratic, firm-specific, diversifiable).
- Diversification reduces non-systematic risk by combining many uncorrelated securities; it does not reduce systematic risk which affects all assets (e.g., interest rates, recessions).
- In CAPM, expected return depends only on systematic risk (beta).

2) Complete reasoning process step by step
- Denote total portfolio variance Var_p = Var_systematic + Var_unsystematic.
- For an equal-weighted portfolio of n identical, independent assets, you can model:
  Var_p = β_p^2 Var(Market) + (1/n) σ_e^2,
  where σ_e^2 is the average idiosyncratic variance and β_p^2 Var(Market) represents systematic variance.
- As n increases (portfolio becomes well-diversified), the idiosyncratic component (1/n) σ_e^2 → 0.
- Therefore, Var_p → β_p^2 Var(Market), i.e., only systematic variance remains.

3) Intermediate calculation steps (illustrative)
- Start with Var_p = β_p^2 Var(M) + (1/n) σ_e^2.
- Take the limit as n → ∞: lim_{n→∞} (1/n) σ_e^2 = 0.
- Thus lim_{n→∞} Var_p = β_p^2 Var(M).

4) Why the correct answer is correct
- A “well-diversified” portfolio implies n is large enough that idiosyncratic risks cancel out. The remaining risk that cannot be eliminated by diversification is the systematic (market) risk. This is the risk investors are compensated for, and it is measured by beta in CAPM.

5) Why other options are incorrect
- “Non-systematic risk” (idiosyncratic) is precisely the component that diversification eliminates, so it is not what a well-diversified portfolio “has.”
- “Total risk” is incorrect because a well-diversified portfolio does not retain the diversifiable portion of total risk.
- “None of the answers are correct” is false because one option, systematic risk, is correct.

6) Conclusion
Therefore, the correct answer is Systematic risk, which matches the provided answer.

A well-diversified portfolio has ………… 单项选择题

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