# Measuring a Portfolio’s Performance

many investors mistakenly base the success of their portfolios on returns alone. few investors consider the risk involved in achieving those returns. Since the 1960s, investors have known how to quantify and measure hazard with the unevenness of returns, but no one measure actually looked at both hazard and return together. today, there are three sets of performance measurement tools to assist with portfolio evaluations. The Treynor, Sharpe, and Jensen ratios combine risk and return performance into a single value, but each is slenderly different. Which one is best ? possibly, a combination of all three.

### Key Takeaways

• Portfolio performance measures are a key factor in the investment decision.
• There are three sets of performance measurement tools to assist with portfolio evaluations—the Treynor, Sharpe, and Jensen ratios.
• Portfolio returns are only part of the story—without evaluating risk-adjusted returns, an investor cannot possibly see the whole investment picture.

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## Treynor measure

Jack L. Treynor was the first to provide investors with a composite measuring stick of portfolio operation that besides included risk. Treynor ‘s objective was to find a operation measure that could apply to all investors careless of their personal gamble preferences. Treynor suggested that there were actually two components of hazard : the risk produced by fluctuations in the stock marketplace and the risk arising from the fluctuations of individual securities .

Treynor introduced the concept of the security market telephone line, which defines the relationship between portfolio returns and market rates of returns whereby the gradient of the line measures the proportional volatility between the portfolio and the market ( as represented by beta ). The beta coefficient is the volatility measure of a stock portfolio to the marketplace itself. The greater the line ‘s slope, the better the risk-return tradeoff .

The Treynor measure, besides known as the reward-to- excitability proportion, is defined as :

Treynor Measure = P R − R F R β where : P R = portfolio reappearance R F R = risk-free rate β = beta \begin { aligned } & \text { Treynor measure } = \frac { PR – RFR } { \beta } \\ & \textbf { where : } \\ & PR=\text { portfolio fall } \\ & RFR=\text { risk-free rate } \\ & \beta=\text { beta } \\ \end { aligned } ​Treynor Measure=βPR−RFR​where : PR=portfolio returnRFR=risk-free rateβ=beta​

The numerator identifies the risk premium, and the denominator corresponds to the portfolio risk. The resulting value represents the portfolio ‘s fall per unit of measurement risk.

To illustrate, suppose that the 10-year annual reappearance for the S & P 500 ( market portfolio ) is 10 % while the average annual reappearance on Treasury bills ( a good proxy for the risk-free rate ) is 5 %. then, assume the evaluation is of three distinct portfolio managers with the following 10-year results :