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# Alpha

Alpha is the return over and above that predicted by an equilibrium model like the capital asset pricing model (CAPM) and is a proxy for an (active) investment manager’s skill.

Alpha is a risk-adjusted measure of the so-called "excess return" on an investment. It is a common measure of assessing active manager's performance.
The difference between the fair and actually expected rates of return on a stock is called the stock's alpha.
Wikipedia (2006)
Alpha (Investment) - Wikipedia

"The abnormal rate of return on a security in excess of what would be predicted by an equilibrium model like CAPM or APT."
Bodie, Kane and Marcus (2005)

"The difference between the fair and actually expected rates of return on a stock is called the stock's alpha, denoted α."
Bodie, Kane and Marcus (2005), page 291

"The alpha of a stock is its expected return in excess of (or or below) the fair expected return as predicted by the CAPM. If the stock is fairl priced, its alpha must be zero."
Bodie, Kane and Marcus (2005), page 328

"Jensen's measure is the average return on the portfolio over and above that predicted by the CAPM, given the portfolio's beta and the average market return. Jensen's measure is the portfolio's alpha value."
Bodie, Kane and Marcus (2005), page 868

"Alpha = Excess return - (Beta × Market excess return)"
Bodie, Kane and Marcus (2005), page 873

To estimate Joe's portfolio alpha from the security characteristic line (SCL), we regress the portfolio excess returns on the market index.
Bodie, Kane and Marcus (2005), page 877

Alpha.
"Used in a number of different senses, including the y-intercept of the characteristic line, and the difference between a secutity's expected return and the equilibrium return predicted by the capital asset pricing model."
Lofthouse (1994), page 533

"The element of risk attributable to the constituency of a portfolio"
Global Fund Analysis

"Alpha measures the returns in excess of the benchmark produced by a fund manager. There are a variety of measures, including the Information, Sortino and Treynor ratios and Jensen's alpha."

"The abnormal (or manager specific) rate of return on the hedge fund in excess what would be predicted by the market return and risk measure (beta)."

"Alpha measures the difference between a fund's actual returns and its expected returns given its risk level as measured by its beta. A higher alpha is better, but a high alpha is only reliable in the presence of a high R-squared value. Some investors see alpha as a measurement of the value added or subtracted by a fund's manager.
A positive alpha figure indicates the fund has performed better than its beta would predict. A negative alpha indicates a fund has underperformed, given the expectations established by the fund's beta.
There are limitations to alpha's ability to accurately depict a manager's added or subtracted value. In some cases, a negative alpha can result from the expenses that are present in the fund figures but are not present in the figures of the comparison index. Alpha is completely dependent on the accuracy of beta as measured by R-squared: If the investor accepts beta as a conclusive definition of risk, a positive alpha would be a conclusive indicator of good fund performance.
The mathematical definition of alpha that Morningstar uses is below. Morningstar deducts the current return of the 90-day T-bill from the total return of both the fund and the benchmark index. The difference is called the fund's excess return.
Alpha = Excess Return -- ((Beta x (Benchmark - Treasury))
Benchmark = Total Return of Benchmark Index
Treasury = Return on Three-month Treasury Bill"
MSN Money

"Measures the value that an investment manager produces, by comparing the manager's performance to that of a risk-free investment (usually a Treasury bill). For example, if a fund had an alpha of 1.0 during a given month, it would have produced a return during that month that was one percentage point higher than the benchmark Treasury. Alpha can also be used as a measure of residual risk, relative to the market in which a fund participates."
HedgeCo.Net

"Alpha is a measure of how the fund is performing under the assumption that the market return is zero. For example, a fund with an alpha of 1, based on the S&P index, would have returned 1% if the index had returned zero."
hedgefocus

"A numerical value indicating excess rate of return relative to a benchmark. As it applies to hedge funds, it is a manager's "value-added" in selecting securities."
LJH Global Investments

"A numerical value indicating a manager's risk-adjusted excess rate of return relative to a benchmark. Measures a manager's "value-added" in selecting individual securities, independent of the effect of overall market movements."
HedgeWorld

"The premium an Investment earns above a set standard. This is usually measured in terms of the Dow Industrials or the SP 500. How the Stock performs independent of the market. Measure of risk-adjusted performance. An Alpha is usually generated by regressing the security or mutual fund`s excess Return on the S&P 500 excess return. The Beta adjusts for the Risk (the slope coefficient). The alpha is the intercept. Example: Suppose the mutual fund has a return of 25%, and the short-term Interest rate is 5% (excess return is 20%). During the same time The Market excess return is 9%. Suppose the beta of the mutual fund is 2.0 (twice as risky as the S&P 500). The expected excess return given the risk is 2 x 9%=18%. The actual excess return is 20%. Hence, the alpha is 2% or 200 Basis points. Alpha is also known as the Jensen Index. Related: Risk-adjusted return."