Which type of risk is eliminated through diversification?

Question

BlackTom AI · Accepted Answer

Unsystematic risk—also called idiosyncratic, firm-specific, or diversifiable risk—can be reduced or essentially eliminated by holding a sufficiently diversified portfolio.

1) Relevant concepts
- Unsystematic risk: risk specific to a company or industry (e.g., management decisions, product recalls).
- Systematic risk: market-wide risk (e.g., recessions, interest-rate changes) that affects all assets.
- Diversification: holding many independent or low-correlated assets to reduce firm-specific fluctuations.
- Variance decomposition: portfolio variance depends on individual variances and covariances.

2) Step-by-step reasoning
- Portfolio variance formula: Var(Rp) = Σ wi^2 Var(Ri) + Σ_{i≠j} wi wj Cov(Ri,Rj).
- For simplicity, consider n equal-weighted assets: wi = 1/n. Then
  Var(Rp) = (1/n^2) [n Var̄ + n(n−1) Cov̄] = (1/n) Var̄ + (1−1/n) Cov̄,
  where Var̄ is average individual variance and Cov̄ is average covariance.
- If asset-specific shocks are uncorrelated (Cov̄ ≈ 0), Var(Rp) ≈ (1/n) Var̄. As n increases, (1/n) Var̄ → 0.
- Thus idiosyncratic (unsystematic) variance can be driven to near zero by increasing n; the remaining variance is driven by common covariance (systematic risk).

3) Intermediate-step emphasis
- Show limit: lim_{n→∞} Var(Rp) = Cov̄, so only common (systematic) components remain.
- If Cov̄ = market variance components, diversification cannot remove them.

4) Why the correct answer is correct
- Unsystematic risk arises from individual asset events and is diversified away by pooling many independent exposures. That makes “Unsystematic risk” the correct choice.

5) Why other options are incorrect
- Systematic risk: cannot be eliminated by diversification; it affects the whole market.
- Market risk: synonymous with systematic risk, not diversifiable.
- Interest rate risk: a specific form of systematic risk (affects many assets) and is not eliminated by diversification across typical securities.

6) Conclusion
- The eliminated risk through diversification is Unsystematic risk, matching the provided answer.

Which type of risk is eliminated through diversification?Single choice

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