Explanation

The question asks for the factor with the smallest downside risk as measured by the weighted average of all losses that exceed a threshold. This definition corresponds to Conditional Value at Risk (CVaR), also known as Expected Shortfall.

Key Points:

• CVaR (95%) represents the average loss in the worst 5% of cases
• Lower CVaR indicates smaller downside risk
• From the table:
  • Factor 1: CVaR = 12.1%
  • Factor 2: CVaR = 15.7%
  • Factor 3: CVaR = 16.8%

Analysis:

• Factor 1 has the lowest CVaR (12.1%), indicating the smallest downside risk
• This makes sense because CVaR measures exactly what the question describes: the weighted average of losses beyond the VaR threshold

Why not VaR or Maximum Drawdown?

• VaR only shows the threshold loss, not the average beyond it
• Maximum drawdown shows the largest peak-to-trough decline, not the average of extreme losses

Conclusion: Factor 1 has the smallest downside risk as measured by Conditional VaR.