If an investor wants to earn a sizable risk premium, they should focus on stocks with a high volatility of their past realized returns.

Question

BlackTom AI · Accepted Answer

High past realized volatility does not automatically imply a larger expected risk premium.

1) Relevant concepts:
- Risk premium = expected return minus risk-free rate. Investors are compensated for systematic (non-diversifiable) risk, not for diversifiable (idiosyncratic) volatility.
- CAPM relation: E[R_i] − R_f = β_i × (E[R_m] − R_f). Beta measures covariance with the market (systematic risk). Total volatility (σ_i) includes both systematic and idiosyncratic components.
- Realized volatility is a historical measure; it may not equal future or systematic volatility.

2) Step-by-step reasoning:
- An investor seeking a risk premium cares about expected excess return, which in simple equilibrium models depends on β, not on total historical σ.
- High historical volatility can be driven by idiosyncratic shocks (diversifiable). If you hold a well-diversified portfolio those idiosyncratic risks cancel and do not increase expected premium.
- Therefore, focusing on stocks with high past realized volatility does not necessarily increase exposure to market risk that earns compensation.

3) Illustrative calculation (intermediate steps):
- Suppose market risk premium E[R_m] − R_f = 6%.
- Stock A: β_A = 1.0, idiosyncratic σ_e = 5% → expected premium = 1.0 × 6% = 6%.
- Stock B: β_B = 1.0, idiosyncratic σ_e = 20% → expected premium = 1.0 × 6% = 6%.
Despite B having much higher total realized volatility, both have identical expected risk premium because their betas are the same.

4) Why the correct answer is correct:
- Equilibrium pricing compensates for systematic risk, not total realized volatility. Historical high volatility alone is an unreliable predictor of future risk premium.

5) Why the other option (True) is incorrect:
- It assumes a direct link between past total volatility and future expected premium, ignoring differences between systematic and idiosyncratic risk and empirical anomalies (e.g., low-volatility anomaly).

6) Conclusion:
- The correct answer is False, which matches the provided answer.

If an investor wants to earn a sizable risk premium, they should focus on stocks with a high volatility of their past realized returns.判断题

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