Treynor Ratio

C is correct. Fund C has the highest Treynor ratio: (13% - 3%) / 1.1 = 10% / 1.1 = 9.09. This indicates Fund C generates the most excess return per unit of systematic risk (beta), making it the most efficient choice for a diversified portfolio.

Fund A has Treynor ratio of (15% - 3%) / 1.4 = 12% / 1.4 = 8.57. While Fund A has the highest absolute return (15%) and highest excess return (12%), it requires significantly more systematic risk (beta 1.4) to achieve those returns, making it less efficient. Fund B has Treynor ratio of (11% - 3%) / 0.9 = 8% / 0.9 = 8.89. Option B incorrectly calculates Fund B's ratio. Fund C provides superior bang-for-your-beta-buck.

B is correct. The Treynor ratio is calculated as (Portfolio Return - Risk-Free Rate) / Beta. It measures excess return per unit of systematic risk (beta). Beta represents the sensitivity to market movements and captures only non-diversifiable risk.

A describes the components of the Sharpe ratio, not the Treynor ratio. The key distinction is that Sharpe uses standard deviation (total risk) while Treynor uses beta (systematic risk only). C describes elements related to alpha calculation and CAPM analysis. D includes correlation and benchmark return, which are not direct inputs to the Treynor ratio formula.

B is correct. Calculate: Treynor Ratio = (18% - 3%) / 1.5 = 15% / 1.5 = 10.00. This means the fund generates 10% of excess return for each unit of systematic risk (beta) taken.

A (5.00) incorrectly uses a different calculation, possibly dividing 15% by 3 (the risk-free rate) instead of by beta. C (12.00) incorrectly uses 18% / 1.5 without subtracting the risk-free rate first, which is a common error. D (15.00) represents only the excess return (18% - 3%) but fails to complete the division by beta, confusing excess return with the Treynor ratio itself.

C is correct (the EXCEPT answer). The Treynor ratio uses beta (systematic risk) in the denominator, NOT standard deviation (total risk). This is the key distinction between Treynor and Sharpe ratios. The Sharpe ratio uses standard deviation to measure total risk, while Treynor focuses only on systematic (market) risk measured by beta.

A is accurate: Higher Treynor ratios indicate more excess return generated per unit of systematic risk, signaling superior risk-adjusted performance for diversified portfolios. B is accurate: Treynor is most appropriate for well-diversified portfolios because it assumes unsystematic risk has been eliminated through diversification, leaving only systematic (beta) risk as relevant. D is accurate: The numerator (Return - Risk-Free Rate) measures excess return above the risk-free rate, just like the Sharpe ratio.

D is correct. All four statements (1, 2, 3, and 4) are accurate.

Statement 1 is TRUE: Fund Y's Treynor ratio = (10% - 4%) / 0.8 = 6% / 0.8 = 7.50.

Statement 2 is TRUE: Fund X has a Treynor ratio of 8.33 compared to Fund Y's 7.50, indicating Fund X provides better risk-adjusted returns per unit of systematic risk (8.33% of excess return per beta unit versus 7.50%).

Statement 3 is TRUE: The Treynor ratio assumes portfolios are well-diversified, meaning unsystematic (company-specific) risk has been eliminated. If either fund held concentrated positions, beta alone would not capture total risk, and the Sharpe ratio (using standard deviation) would be more appropriate for evaluation.

Statement 4 is TRUE: Fund Y has a beta of 0.8 (meaning 80% of market volatility) while Fund X has beta of 1.2 (120% of market volatility). Lower beta indicates lower systematic (market) risk, making Fund Y more defensive than Fund X.