Which of the following statements regarding unsystematic risk is accura

Question

BlackTom AI · Accepted Answer

Unsystematic risk is firm-specific risk (also called idiosyncratic risk), so it can be effectively eliminated by holding a well-diversified portfolio.

1) Relevant knowledge points and concepts
- Total risk = systematic (market) risk + unsystematic (firm-specific) risk.
- Systematic risk cannot be diversified away; unsystematic risk can.
- Beta measures sensitivity to market (systematic) risk. Standard deviation measures total volatility (both systematic and unsystematic). In CAPM, only systematic risk (beta) is priced; investors are compensated via the risk premium for bearing market risk, not idiosyncratic risk.

2) Step-by-step reasoning
- Consider returns decomposed into market-driven component and firm-specific shock: R_i = α_i + β_i R_m + ε_i, where ε_i is idiosyncratic.
- In a portfolio of N equally weighted stocks (w_i = 1/N), portfolio return variance = Var(R_p) = Var(β̄ R_m) + Var(average ε_i) + cross terms. If idiosyncratic shocks ε_i are uncorrelated across firms, Var(average ε_i) = (1/N^2) Σ Var(ε_i) ≈ (1/N)·average Var(ε).
- As N increases, the (1/N) term → 0, so idiosyncratic variance vanishes and only market (systematic) variance remains.

3) Intermediate/formula steps shown
- Var(R_p) = Σ w_i^2 σ_i^2 + Σ_{i≠j} w_i w_j Cov(i,j). For independent idiosyncratic terms, Cov(i,j)≈β_iβ_j Var(R_m). With equal weights: Var(R_p) ≈ Var(R_m)·(average β)^2 + (1/N)·average Var(ε). Limit as N→∞ leaves only the market term.

4) Why the correct answer is correct
- Because unsystematic risk is idiosyncratic and tends to cancel out across many independent securities, diversification reduces it toward zero. Hence it can be effectively eliminated.

5) Why other options are incorrect
- "It is related to the overall economy": that's systematic risk, not unsystematic. 
- "It is measured by beta": beta measures systematic market sensitivity. 
- "It is measured by standard deviation": standard deviation measures total risk (systematic + unsystematic), not specifically unsystematic. 
- "It is compensated for by the risk premium": CAPM implies only systematic risk (beta) is rewarded; idiosyncratic risk is not priced.

6) Conclusion
The correct choice is "It can be effectively eliminated by portfolio diversification." This matches the provided answer.

Which of the following statements regarding unsystematic risk is accura单项选择题

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