- Jensen's alpha
In finance,

**Jensen's alpha**(or**Jensen's Performance Index**,**ex-post alpha**) is used to determine the excess return of a security or portfolio of securities over the security's theoretical expected return.The security could be any asset, such as stocks, bonds, or derivatives. The theoretical return is predicted by a market model, most commonly the

Capital Asset Pricing Model (CAPM) model. The market model uses statistical methods to predict the appropriate risk-adjusted return of an asset. The CAPM for instance uses beta as a multiplier.Jensen's alpha was first used as a measure in the evaluation of

mutual fund managers byMichael Jensen in the 1970s. The CAPM return is supposed to be 'risk adjusted', which means it takes account of the relative riskiness of the asset. After all, a riskier assets will have higher expected returns than less risky assets. If an asset's return is even higher than the risk adjusted return, that asset is said to have "positive alpha" or "excess returns". Investors are constantly seeking investments that have higher alpha.In the context of CAPM, calculating alpha requires the following inputs:

* the realized return (on the portfolio),

* the market return,

* therisk-free rate of return, and

* the beta of the portfolio.**"Jensen's alpha = Portfolio Return - (Risk Free Rate + Portfolio Beta * (Market Return - Risk Free Rate))**"

$alpha\_J\; =\; R\_i\; -\; (R\_f\; +\; eta\_\{iM\}\; cdot\; (R\_M\; -\; R\_f))$Since

Eugene Fama , many academics believe financial markets are too efficient to allow for repeatedly earning positive Alpha, unless by chance. To the contrary, empirical studies of mutual funds spearheaded byRuss Wermers usually confirm managers' stock-picking talent, finding positive Alpha. However, they also show that after fees and expenses are deducted, the effective Alpha for investors is negative. (These results also explain whypassive investing is increasingly popular.)Nevertheless, Alpha is still widely used to evaluate mutual fund and portfolio manager performance, often in conjunction with the

Sharpe ratio and theTreynor ratio .**ee also***

Alpha (investment)

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