Jensen's alpha

In finance, Jensen's alpha^[1] (or Jensen's Performance Index, ex-post alpha) is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. It is a version of the standard alpha based on a theoretical performance index instead of a market index.

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). 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.

History

Jensen's alpha was first used as a measure in the evaluation of mutual fund managers by Michael Jensen in 1968.^[2] The CAPM return is supposed to be 'risk adjusted', which means it takes account of the relative riskiness of the asset.

This is based on the concept that riskier assets should 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 "abnormal returns". Investors are constantly seeking investments that have higher alpha.

Since Eugene Fama, many academics believe financial markets are too efficient to allow for repeatedly earning positive Alpha, unless by chance. Nevertheless, Alpha is still widely used to evaluate mutual fund and portfolio manager performance, often in conjunction with the Sharpe ratio and the Treynor ratio.

Calculation

In the context of CAPM, calculating alpha requires the following inputs:

the realized return (on the portfolio),
the market return,
the risk-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}+\beta _{{iM}}\cdot (R_{M}-R_{f})]

An additional way of understanding the definition can be obtained by rewriting it as:

\alpha _{J}=(R_{i}-R_{f})-\beta _{{iM}}\cdot (R_{M}-R_{f})

If we define the excess return of the fund (market) over the risk free return as $\Delta _{R}\equiv (R_{i}-R_{f})$ and $\Delta _{M}\equiv (R_{M}-R_{f})$ then Jensen's alpha can be expressed as:

\alpha _{J}=\Delta _{R}-\beta _{{iM}}\Delta _{M}

Use in Quantitative Finance

Jensen's alpha is a statistic that is commonly used in empirical finance to assess the marginal return associated with unit exposure to a given strategy. Generalizing the above definition to the multifactor setting, Jensen's alpha is a measure of the marginal return associated with an additional strategy that is not explained by existing factors.

We obtain the CAPM alpha if we consider excess market returns as the only factor. If we add in the Fama-French factors, we obtain the 3-factor alpha, and so on. If Jensen's alpha is significant and positive, then the strategy being considered has a history of generating returns on top of what would be expected based on other factors alone. For example, in the 3-factor case, we may regress momentum factor returns on 3-factor returns to find that momentum generates a significant premium on top of size, value, and market returns.^[3]^[4]

References

Financial markets

Types of markets	Primary market Secondary market Third market Fourth market

Types of stocks	Common stock Golden share Preferred stock Restricted stock Tracking stock

Share capital	Authorised capital Issued shares Shares outstanding Treasury stock

Participants	Broker-dealer Day trader Floor broker Floor trader Investor Market maker Proprietary trader Quantitative analyst Regulator Stock trader

Exchanges	Electronic communication network List of stock exchanges Opening times Multilateral trading facility Over-the-counter

Stock valuation	Alpha Arbitrage pricing theory Beta Bid–ask spread Book value Capital asset pricing model Dividend discount model Dividend yield Earnings per share Earnings yield Net asset value Security characteristic line Security market line T-model

Trading theories and strategies	Algorithmic trading Buy and hold Concentrated stock Contrarian investing Day trading Dollar cost averaging Efficient-market hypothesis Fundamental analysis Growth stock Market timing Modern portfolio theory Momentum investing Mosaic theory Pairs trade Post-modern portfolio theory Random walk hypothesis Sector rotation Style investing Swing trading Technical analysis Trend following Value investing

Related terms	Block trade Cross listing Dark liquidity Dividend Dual-listed company DuPont analysis Efficient frontier Flight-to-quality Haircut Initial public offering Margin Market anomaly Market capitalization Market depth Market manipulation Market trend Mean reversion Momentum Open outcry Public float Public offering Rally Returns-based style analysis Reverse stock split Share repurchase Short selling Slippage Speculation Stock dilution Stock market index Stock split Trade Uptick rule Volatility Voting interest Yield

This article is issued from Wikipedia - version of the 4/28/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.

Jensen's alpha

History

Calculation

Use in Quantitative Finance

References

See also