Performance Evaluation

Question 1

Sharpe Ratio

Answer 1

Sharpe Ratio

SR = R_p - r_f

σ_p

• denominator = total risk, doesn’t difference between good/bad risk
• penalizes for upside risk which is a penalty for all volatility, even good volatility

Question 2

Treynor Ratio

Answer 2

Treynor Ratio

TR = Rp - rf

σ_ß

• Sim to SR, but uses Beta (systematic risk) instead of σ (total risk)
• only used in highly diversified portfolios, it’s only considering systematic, not idiosyncratic risk
• when benchmarks assume efficient markets

Question 3

Information Ratio (IR)

Answer 3

Information Ratio

IR = E(R_p) - E(R_B)

σ(R_p - R_B)

• active return per unit of active risk (tracking risk)
• active risk: weight each asset class in a portfolio by it’s active risk%² and sum

Square root the answer

Question 4

Appraisal Ratio

Answer 4

Appraisal Ratio

AR = alpha

σ_e

• alpha computed from any factor model
• σ_e = std dev of the residual unsystemic risk
• may only be given R² (explained risk)

therefore, 1 - R² = unexplained risk (residual)

1 - R² x σ² = X

Square root of X = σ_e

Question 5

Sortino Ratio

Answer 5

Sortino Ratio

SR = R_p - R_t

σ_d

• R_t = target return (MAR)
• σ_d = semi-deviation - measuring downside deviation
• penalizes managers for only bad volatility
• higher = better
• used for funds with non-symmetrical or skewed return distributions