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Measure of risk-adjusted performance. Some refer to the alpha as the difference between the investment return and the benchmark return. However, this does not properly adjust for risk. More appropriately, an alpha is generated by regressing the security or mutual fund's excess return on the benchmark (for example 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. The alpha depends on the benchmark used. For example, it may be the intercept in a multifactor model that includes risk factors in addition to the S&P 500. Related: Risk-adjusted return.
Copyright © 2012, Campbell R. Harvey. All Rights Reserved.


1. The measure of the performance of a portfolio after adjusting for risk. Alpha is calculated by comparing the volatility of the portfolio and comparing it to some benchmark. The alpha is the excess return of the portfolio over the benchmark. It is important to Markowitz portfolio theory and is used as a technical indicator.

2. The excess return that a portfolio makes over and above what the capital asset pricing model estimates.
Farlex Financial Dictionary. © 2012 Farlex, Inc. All Rights Reserved


The mathematical estimate of the return on a security when the market return as a whole is zero. Alpha is derived from a in the formula Ri = a + bRm which measures the return on a security (Ri) for a given return on the market (Rm) where b is beta. See also capital-asset pricing model, characteristic line.
Wall Street Words: An A to Z Guide to Investment Terms for Today's Investor by David L. Scott. Copyright © 2003 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved. All rights reserved.


Alpha measures risk-adjusted return, or the actual return an equity security provides in relation to the return you would expect based on its beta. Beta measures the security's volatility in relation to its benchmark index.

If a security's actual return is higher than its beta, the security has a positive alpha, and if the return is lower it has a negative alpha.

For example, if a stock's beta is 1.5, and its benchmark gained 2%, it would be expected to gain 3% (2% x 1.5 = 0.03, or 3%). If the stock gained 4%, it would have a positive alpha.

Alpha also refers to an analyst's estimate of a stock's potential to gain value based on the rate at which the company's earnings are growing and other fundamental indicators.

For example, if a stock is assigned an alpha of 1.15, the analyst expects a 15% price increase in a year when stock prices are generally flat. One investment strategy is to look for securities with positive alphas, which indicates they may be undervalued.

Dictionary of Financial Terms. Copyright © 2008 Lightbulb Press, Inc. All Rights Reserved.
References in periodicals archive ?
WolframAlpha gives all sets of complex solutions (like log(4) + i[pi](2n+1)/log(2) or i(2[pi[n + [pi]) (denoted as Branches(Cn), Domain(C)); Sage gives one complex solution (like i[pi] + log(4)/log(2)) (denoted as Branches(Cl), Domain(C)).
In case of unequal bases (like [2.sup.2-x] = [3.sup.2-x] and [4.sup.x+1] - [3.sup.x] = [3.sup.x+2] - [4.sup.x]), WolframAlpha gives the expected answers; Maxima and Sage give numerical answers with the help of find-root.
The exponential logarithmic equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is solved only by WolframAlpha.
WolframAlpha gives the answer x =1 and log (b) [not equal to] 0, while Axiom only gives 1.
The number of the solutions could be one (Axiom, Sage) or two (WIRIS), or a general solution could be given (WolframAlpha).
In case of Maxima, Sage and WolframAlpha, the inverse function appears in case of 'less likeable' answers (e.g., sin x = 1/10).
Are x = n[pi] and x = [(-1).sup.n] [pi]/2 + n [pi] as found in textbooks equivalent to x = 2[pi]n, x = 2[pi]n + [pi] and x = 1/2 (4[pi]n+ [pi]) as given by WolframAlpha (Form(periodic)).
WolframAlpha also allows more complex regression examples such as:
WolframAlpha responds in typical detail when asked to describe a 120[degrees] rotation; however, I was disappointed that users cannot apply transformations to simple user-defined shapes.
WolframAlpha presents very nice translucent representations of 3D solids such as this dodecahedron, but I was disappointed that it cannot construct the Mathematica logo using an hyperbolised dodecahedron.
They could use WolframAlpha to look up things they had not learned properly.
At some stage, applications such as WolframAlpha are going to become so attractive that we will rethink our assessment strategies and our students will use their iPods in class and as homework tools more than they use them for music and games.