What is Jensen’s Alpha?

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. 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.

What Does Jensen’s Alpha Mean?

Financial analysts use Jensen’s alpha when they seek to determine the highest possible return on investment with the lowest level of risk. Therefore, the main assumption of alpha is that a portfolio is adequately diversified to generate a high return while leveraging the portfolio risk.

Also, as alpha represents the portfolio performance, it is always evaluated in comparison to a benchmark, under the assumption that the portfolio’s return on investment is not related to the market like the beta (systematic risk), but to the individual selections of the fund manager. Hence, an alpha equal to zero simply means that the portfolio is perfectly correlated to the benchmark index.

History

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.

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.

Example

Marion is a fund manager at Morgan Stanley, and she handles the portfolios of several clients. All portfolios are well-diversified, including large cap equity, small cap equity, emerging markets equities, bonds, and T-bills. Marion wants to calculate the alpha of a portfolio that is underperforming the market over the past few months to determine the highest possible return on investment at the lowest level of risk.

Hence, Marion uses the capital price asset model (CAPM) to calculate alpha:

alpha = rs – [Rf + b (Rm – Rf)]

where:

• rs = the portfolio return
• rf = risk-free rate
• b = the portfolio’s beta (systematic risk)
• rm = market return

Marion calculates the average portfolio return and the average market return for 2015, and she finds that the portfolio return (rs) is 3.29%, whereas the market return (rm) is 1.60%. The risk-free rate (rf) is 1.25%.

Marion can now calculate the portfolio beta and the portfolio alpha as follows:

In Excel, beta is calculated using the covariance. p function and the variance. p function. Therefore, beta = (covariance. p of the portfolio return and the market return cells) /variance. p (market return). Doing these calculations, Marion finds that the portfolio beta is 0.45.

Then, she calculates alpha by applying the above formula. Therefore:

Given the low beta of the portfolio, the positive alpha of 2.20% suggests that Marion earns more than a sufficient return given the level of risk undertaken in this portfolio.

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.

Why Does Jensen’s Measure Matter?

Jensen’s measure is a measurable way to determine whether a manager has added value to a portfolio, because alpha is the return attributable to the skill of the portfolio manager rather than the general market conditions.

The very existence of alpha is controversial, however, because those who believe in the efficient market hypothesis (which says, among other things, that it is impossible to beat the market) believe alpha is attributable to luck rather than skill; they support this idea with the fact that many active portfolio managers don’t make much more for their clients than those managers who simply follow passive, indexing strategies. Thus, investors who believe managers add value accordingly expect above-market or above-benchmark returns – that is, they expect alpha.

Summary

Define Alpha: Jensen’s alpha means a financial performance metric that investors use to gauge their portfolio performance.

• The Jensen’s alpha measure is the difference in how much a person returns vs. the overall market.
• Jensen’s alpha measure is commonly referred to as alpha. When a manager outperforms the market concurrent to risk, they have “delivered alpha” to their clients.
• The measure accounts for the risk-free rate of return for the time period.