Financial Risk Manager Part 1

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What is the Treynor Performance Index of a portfolio, given its expected return of 7.7%, volatility of 17%, beta of 0.4, and a risk-free rate of 2.5%, as calculated by an investment performance analyst?

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TTanishq

0.305

0.052

0.13

3.72

Explanation:

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

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