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