Jensen's alpha
Encyclopedia
In finance, Jensen's alpha (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.
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 by Michael Jensen
in 1968. The CAPM return is supposed to be 'risk adjusted', which means it takes account of the relative riskiness of the asset. After all, 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 "abnormal returns". Investors are constantly seeking investments that have higher alpha.
In the context of CAPM, calculating alpha requires the following inputs:
Jensen's alpha = Portfolio Return − [Risk Free Rate + Portfolio Beta * (Market Return − Risk Free Rate)]
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 by Russ 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 why passive 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 the Treynor ratio
.
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.
Portfolio (finance)
Portfolio is a financial term denoting a collection of investments held by an investment company, hedge fund, financial institution or individual.-Definition:The term portfolio refers to any collection of financial assets such as stocks, bonds and cash...
of securities over the 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
Capital asset pricing model
In finance, the capital asset pricing model is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk...
(CAPM) model. The market model uses statistical methods to predict the appropriate risk-adjusted return of an asset. The CAPM for instance uses beta
Beta coefficient
In finance, the Beta of a stock or portfolio is a number describing the relation of its returns with those of the financial market as a whole.An asset has a Beta of zero if its returns change independently of changes in the market's returns...
as a multiplier.
Jensen's alpha was first used as a measure in the evaluation of mutual fund
Mutual fund
A mutual fund is a professionally managed type of collective investment scheme that pools money from many investors to buy stocks, bonds, short-term money market instruments, and/or other securities.- Overview :...
managers by Michael Jensen
Michael Jensen
Michael Cole "Mike" Jensen is an American economist working in the area of financial economics. He is currently the managing director in charge of organizational strategy at Monitor Group, a strategy consulting firm, and the Jesse Isidor Straus Professor of Business Administration, Emeritus at...
in 1968. The CAPM return is supposed to be 'risk adjusted', which means it takes account of the relative riskiness of the asset. After all, 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 "abnormal 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 returnMarket portfolioMarket portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the proportions that they exist in the market, with the necessary assumption that these assets are infinitely divisible....
, - the risk-free rate of return, and
- the betaBeta coefficientIn finance, the Beta of a stock or portfolio is a number describing the relation of its returns with those of the financial market as a whole.An asset has a Beta of zero if its returns change independently of changes in the market's returns...
of the portfolio.
Jensen's alpha = Portfolio Return − [Risk Free Rate + Portfolio Beta * (Market Return − Risk Free Rate)]
Since Eugene Fama
Eugene Fama
Eugene Francis "Gene" Fama is an American economist, known for his work on portfolio theory and asset pricing, both theoretical and empirical. He is currently Robert R...
, 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 by Russ 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 why passive investing
Passive management
Passive management is a financial strategy in which an investor invests in accordance with a pre-determined strategy that doesn't entail any forecasting...
is increasingly popular.)
Nevertheless, Alpha is still widely used to evaluate mutual fund and portfolio manager performance, often in conjunction with the Sharpe ratio
Sharpe ratio
The Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return per unit of deviation in an investment asset or a trading strategy, typically referred to as risk , named after William Forsyth Sharpe...
and the Treynor ratio
Treynor ratio
The Treynor ratio , named after Jack L. Treynor, is a measurement of the returns earned in excess of that which could have been earned on an investment that has no diversifiable risk , per each unit of market risk assumed.The Treynor ratio relates...
.
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.
See also
- Alpha (investment)Alpha (investment)Alpha is a risk-adjusted measure of the so-called active return on an investment. It is the return in excess of the compensation for the risk borne, and thus commonly used to assess active managers' performances...
- Modigliani Risk-Adjusted PerformanceModigliani Risk-Adjusted PerformanceModigliani risk-adjusted performance or M2 or M2 or Modigliani–Modigliani measure or RAP is a measure of the risk-adjusted returns of some investment portfolio. It measures the returns of the portfolio, adjusted for the deviation of the portfolio , relative to that of some benchmark...
- Operating Alpha
- Sharpe RatioSharpe ratioThe Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return per unit of deviation in an investment asset or a trading strategy, typically referred to as risk , named after William Forsyth Sharpe...
- Sortino ratioSortino ratioThe Sortino ratio measures the risk-adjusted return of an investment asset, portfolio or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target, or required rate of return, while the Sharpe ratio penalizes both upside and downside...
- Treynor ratioTreynor ratioThe Treynor ratio , named after Jack L. Treynor, is a measurement of the returns earned in excess of that which could have been earned on an investment that has no diversifiable risk , per each unit of market risk assumed.The Treynor ratio relates...
- Upside potential ratioUpside potential ratioThe Upside-Potential Ratio is a measure of a return of an investment asset relative to the minimal acceptable return. The measurement allows a firm or individual to choose investments which have had relatively good upside performance, per unit of downside risk....