Answer: 0.13

## Explanation The Treynor Performance Index (TPI), also known as the Treynor Ratio, measures the risk-adjusted return of a portfolio considering its systematic risk (beta). To calculate the Treynor Ratio, use the following formula: $$ \text{TPI} = \frac{\mathrm{E}(R_p) - R_f}{\beta_p} $$ where: - $\mathrm{E}(R_p)$ = Expected return of the portfolio = 7.7% - $R_f$ = Risk-free rate = 2.5% - $\beta_p$ = Beta of the portfolio = 0.4 $$ \text{TPI} = \frac{7.7\% - 2.5\%}{0.4} = \frac{5.2\%}{0.4} = 0.13 $$ **Key Points:** - The Treynor Ratio measures excess return per unit of systematic risk (beta) - It uses beta rather than total volatility (unlike Sharpe Ratio) - Higher Treynor Ratio indicates better risk-adjusted performance - The volatility of 17% is not used in this calculation as Treynor focuses only on systematic risk

Author: Tanishq Prabhu