Alpha (Investing)

Alpha is the part of an investment's return that cannot be explained by the market risk it carried. It measures how much a fund, a portfolio manager or a trading strategy earned above, or below, what a passive exposure of the same riskiness would have delivered. A positive alpha suggests skill or an edge; a negative alpha means the investor would have done better with a cheaper market proxy.

Alpha is usually reported next to beta, which captures the market-driven part of a return, and R-squared, which shows how much of the return the market explains. Fund rating services, consultants and institutional investors use it to judge active managers against a benchmark. In everyday speech the word is looser: traders call any excess return over an index "alpha", whether or not risk has been adjusted for.

Picture two delivery drivers. One drives on a quiet highway, the other through a crowded city centre. Counting deliveries alone is unfair, because the highway driver had an easier road. A fair comparison asks how many deliveries each made compared with what a typical driver would manage on that same road.

Alpha does the same for investments. A fund that holds riskier shares should earn more when markets rise, simply because of the road it chose. Alpha strips out that expected reward and asks what is left over. If something is left over, the manager added value. If the figure is below zero, the manager took the bumpy road and still arrived late.

The standard version is Jensen's alpha, introduced by Michael Jensen in a 1968 study of mutual fund performance between 1945 and 1964, published in the Journal of Finance. It is the actual return minus the return predicted by the capital asset pricing model (CAPM):

• $\alpha$ is the alpha, the return not explained by market exposure.
• $R_p$ is the portfolio's actual return over the period.
• $R_f$ is the risk-free rate, often the yield on three-month Treasury bills.
• $\beta_p$ is the portfolio's beta against the market.
• $R_m$ is the return of the market index used as the benchmark.

Suppose a fund returned 12% in a year when the market returned 10% and Treasury bills paid 4%. The fund's beta is 1.2. The CAPM expects 4% + 1.2 × (10% − 4%) = 4% + 7.2% = 11.2%. The fund's alpha is 12% − 11.2% = 0.8 percentage points. Note that the fund beat the market by 2 points, but most of that came from taking more market risk; only 0.8 points is alpha.

Alpha rests on the CAPM, developed in the early 1960s by Jack Treynor and set out in published form by William Sharpe in 1964, John Lintner in 1965 and Jan Mossin in 1966. The model says that, in equilibrium, an asset's expected return depends only on its exposure to the whole market, because company-specific risk can be removed through diversification. Sharpe shared the 1990 Nobel memorial prize in economics with Harry Markowitz and Merton Miller for this line of work.

Jensen's 1968 paper applied the model to 115 mutual funds and found that, on average, they did not earn positive alpha once their expenses were counted. That finding helped build the case for low-cost index funds in the following decade. Sharpe's companion measure, the Sharpe ratio, ranks funds by return per unit of total risk instead of market risk.

Later research showed that market beta alone does not explain the returns of many portfolios. Eugene Fama and Kenneth French added size and value factors in 1993, and Mark Carhart added momentum in 1997. In a multi-factor model, alpha is what remains after the portfolio's exposure to all of these factors has been accounted for. A manager who beats the CAPM simply by owning small-cap stocks or cheap value stocks may show no alpha at all under a factor model, because those exposures can now be bought cheaply through rules-based funds.

This is why alpha figures always depend on the model and the benchmark chosen. The same fund can show positive alpha against the S&P 500 and negative alpha against a small-cap value index.

Active fund managers, hedge funds and private equity firms all market themselves on alpha. Common uses include:

• Manager selection. Pension plans and other institutions screen managers by their historical alpha, usually over three to five years, alongside tracking error.
• Fee justification. An active fund's alpha has to exceed the extra cost of its expense ratio over an index fund for the investor to be better off.
• Portable alpha. Some institutions hold derivatives to get cheap market exposure and invest the cash with managers expected to add alpha on top.

Alpha also appears on fund pages and in third-party data. Morningstar, for example, reports alpha alongside beta and R-squared in its risk statistics.

Alpha is an estimate, not a fact. Several problems weaken it:

• Short histories are noisy. A few years of returns cannot reliably separate skill from luck, and historical alpha is a weak predictor of future alpha.
• The benchmark matters. If the benchmark does not match the fund's holdings, beta and alpha are both distorted, which is why a low R-squared makes alpha hard to read.
• Hidden risks. Strategies that sell insurance-like protection, such as writing options, can show steady positive alpha for years before a large loss.
• Survivorship bias. Funds that performed badly are often closed or merged, so averages of surviving funds overstate typical alpha.

Across the whole market, alpha is close to a zero-sum game before costs: one investor's outperformance is another's underperformance. After fees, the average active dollar must trail the market, a point stressed by Sharpe in his 1991 article "The Arithmetic of Active Management".

• The Sveriges Riksbank Prize in Economic Sciences 1990 (Nobel Prize)