Sharpe Ratio, Traynor Ratio and Jensens Alpha

Portfolios contain groups of securities that are selected to achieve the highest return for a given level of risk. How well this is achieved depends on how well the portfolio manager or investor is able to forecast economic conditions and the future prospects of companies, and to accurately assess the risk of each security under consideration.

Portfolio returns come in the form of current income and capital gains. Current income includes dividends on stocks and interest payments on bonds. There are several ways of comparing portfolio returns with each other and with the market in general. A simple comparison is to simply compare their returns. However, returns by themselves do not account for the risk taken. If 2 portfolios have the same return, but one has lower risk, then that would be the preferable, more efficient portfolio.

There are three common ratios that measure a portfolios risk-return tradeoff: Sharpe’s ratio, Treynor’s ratio and Jensen’s Alpha.

SHARPE RATIO:

The Sharpe ratio or Sharpe measure is the ratio of Risk premium to Standard Deviation of portfolio.

Where,

Risk premium = Total portfolio Return – Risk free Rate

Sharpe ratio = Risk premium/ Standard Deviation of Portfolio

Higher the Sharpe ratio, the better the performance and the greater the profits for taking on additional risk.

TREYNOR RATIO:

While the Sharpe ratio measures the risk premium of the portfolio over the portfolio risk, or its standard deviation, treynors ratio compares the portfolio risk premium to the systematic risk of the portfolio as measured by its beta.

Treynor ratio = Risk premium/ portfolio beta.

Since, the Beta of market is equal to 1.The treynor ratio for market will be equal to risk premium.

JENSEN’S ALPHA:

Jensen’s alpha is a measure of a securities excess return with respect to the expected return given by the Capital Asset Pricing Model.

Jensen’s Alpha = Total Portfolio return – Risk free rate-{portfolio bets * (market return-risk free rate)}

Jensens alpha can be positive, negative or zero. Note that, by definition, Jensens alpha of the market is zero. If the alpha is negative, then the portfolio is underperforming the market, thus higher alphas re more desirable.

For a well diversified fund, you can use either sharpe or Treynor for estimating itsrisk-adjusted returns. This is because a well diversified fund is only exposed to the market risks and both measures of risk-standard deviation vigourously captures the total risks.

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