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Alpha is a measure of theactive return on aninvestment, the performance of that investment compared with a suitablemarket index. An alpha of 1% means the investment'sreturn on investment over a selected period of time was 1% better than the market during that same period; a negative alpha means the investment underperformed the market.

Alpha, along withbeta, is one of two key coefficients in thecapital asset pricing model used inmodern portfolio theory and is closely related to other important quantities such asstandard deviation,R-squared and theSharpe ratio.^[1]

In modern financial markets, whereindex funds are widely available for purchase, alpha is commonly used to judge the performance ofmutual funds and similar investments. As these funds include various fees normally expressed in percent terms, the fund has to maintain an alpha greater than its fees in order to provide positive gains compared with an index fund. Historically, the vast majority of traditional funds have had negative alphas, which has led to aflight of capital to index funds and non-traditionalhedge funds.

It is also possible to analyze a portfolio of investments and calculate a theoretical performance, most commonly using thecapital asset pricing model (CAPM). Returns on that portfolio can be compared with the theoretical returns, in which case the measure is known asJensen's alpha. This is useful for non-traditional or highly focused funds, where a single stock index might not be representative of the investment's holdings.

Thealpha coefficient (${\displaystyle {\alpha }_i}$) is a parameter in thesingle-index model (SIM). It is theintercept of thesecurity characteristic line (SCL), that is, the coefficient of the constant in a market model regression.

${\displaystyle \mathrm{S}\mathrm{C}\mathrm{L}:R_{i,t}-R_f={\alpha }_i+{\beta }_i(R_{M,t}-R_f)+{\epsilon }_{i,t}}$

where the following inputs are:

• ${\displaystyle R_i}$: therealized return (on the portfolio),
• ${\displaystyle R_M}$: themarket return,
• ${\displaystyle R_f}$: therisk-free rate of return, and
• ${\displaystyle {\beta }_{iM}}$: thebeta of the portfolio.
• ε_i,t : the non-systematic or diversifiable, non-market or idiosyncratic risk

It can be shown that in anefficient market, the expected value of the alpha coefficient is zero. Therefore, the alpha coefficient indicates how an investment has performed after accounting for the risk it involved:

• : the investment has earned too little for its risk (or, was too risky for the return)
• ${\displaystyle {\alpha }_i=0}$: the investment has earned a return adequate for the risk taken
• ${\displaystyle {\alpha }_i>0}$: the investment has a return in excess of the reward for the assumed risk

For instance, although a return of 20% may appear good, the investment can still have a negative alpha if it's involved in an excessively risky position.

In this context, because returns are being compared with the theoretical return ofCAPM and not to a market index, it would be more accurate to use the term ofJensen's alpha.

Efficient market hypothesis (EMH) states thatshare prices reflect all information, therefore stocks always trade at theirfair value onexchanges. This would mean consistentalpha generation (i.e. better performance than the market) is impossible, and proponents of EMH posit that investors would benefit from investing in a low-cost,passive portfolio.^[2]

A belief in EMH spawned the creation of market capitalization weightedindex funds, which seek to replicate the performance of investing in an entire market in the weights that each of the equity securities comprises in the overall market.^[3][4] The best examples for the US are theS&P 500 and theWilshire 5000 which approximately represent the 500 most widely held equities and the largest 5000 securities respectively, accounting for approximately 80%+ and 99%+ of the total market capitalization of the US market as a whole.

In fact, to many investors,^{[citation needed]} this phenomenon created a new standard of performance that must be matched: an investment manager should not only avoid losing money for the client and should make a certain amount of money, but in fact should make more money than the passive strategy of investing in everything equally (since this strategy appeared to be statistically more likely to be successful than the strategy of any one investment manager). The name for the additional return above theexpected return of the beta adjusted return of the market is called "Alpha".

Besides an investment manager simply making more money than a passive strategy, there is another issue:although the strategy of investing in every stock appeared to perform better than 75 percent of investment managers (seeindex fund), the price of the stock market as a wholefluctuates up and down, and could be on a downward decline for many years before returning to its previous price.

The passive strategy appeared to generate the market-beating return over periods of 10 years or more. This strategy may be risky for those who feel they might need to withdraw their money before a 10-year holding period, for example. Thus investment managers who employ a strategy that is less likely to lose money in a particular year are often chosen by those investors who feel that they might need to withdraw their money sooner.

Investors can use both alpha and beta to judge a manager's performance. If the manager has had a high alpha, but also a high beta, investors might not find that acceptable, because of the chance they might have to withdraw their money when the investment is doing poorly.

These concepts not only apply to investment managers, but to any kind of investment.

• Bruce J. Feibel.Investment Performance Measurement. New York: Wiley, 2003.ISBN 0-471-26849-6

• International Association of CPAs, Attorneys, and Management (IACAM) (Free Business Valuation E-Book Guidebook)
• The financial-dictionary entry on alpha
• Investopedia Alpha Definition
• Five Technical Risk Ratios
• Alpha analysis for global equities Free alpha look-up
• Traders Magazine Seeking Alpha - New York hedge fund creates value trading index options

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