Alpha (investment)
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Alpha is a measure of the
active return In finance, active return refers to the financial return, returns produced by an investment portfolio due to active management decisions made by the portfolio manager that cannot be explained by the portfolio's exposure to returns or to risks in the ...
on an
investment Investment is traditionally defined as the "commitment of resources into something expected to gain value over time". If an investment involves money, then it can be defined as a "commitment of money to receive more money later". From a broade ...
, the performance of that investment compared with a suitable market index. An alpha of 1% means the investment's
return on investment Return on investment (ROI) or return on costs (ROC) is the ratio between net income (over a period) and investment (costs resulting from an investment of some resources at a point in time). A high ROI means the investment's gains compare favorab ...
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 with
beta Beta (, ; uppercase , lowercase , or cursive ; or ) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Ancient Greek, beta represented the voiced bilabial plosive . In Modern Greek, it represe ...
, is one of two key coefficients in the
capital asset pricing model In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a Diversification (finance), well-diversified Portfolio (f ...
used in
modern portfolio theory Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of Diversificatio ...
and is closely related to other important quantities such as
standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...
,
R-squared In statistics, the coefficient of determination, denoted ''R''2 or ''r''2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s). It is a statistic used in t ...
and the
Sharpe ratio In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment such as a security or portfolio compared to a risk-free asset, after adjusting for ...
. In modern financial markets, where
index fund An index fund (also index tracker) is a mutual fund or exchange-traded fund (ETF) designed to follow certain preset rules so that it can replicate the performance of a specified basket of underlying investments. The main advantage of index fun ...
s are widely available for purchase, alpha is commonly used to judge the performance of
mutual fund A mutual fund is an investment fund that pools money from many investors to purchase Security (finance), securities. The term is typically used in the United States, Canada, and India, while similar structures across the globe include the SICAV in ...
s 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 a flight of capital to index funds and non-traditional
hedge fund A hedge fund is a Pooling (resource management), pooled investment fund that holds Market liquidity, liquid assets and that makes use of complex trader (finance), trading and risk management techniques to aim to improve investment performance and ...
s. It is also possible to analyze a portfolio of investments and calculate a theoretical performance, most commonly using the
capital asset pricing model In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a Diversification (finance), well-diversified Portfolio (f ...
(CAPM). Returns on that portfolio can be compared with the theoretical returns, in which case the measure is known as
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 the ...
. This is useful for non-traditional or highly focused funds, where a single stock index might not be representative of the investment's holdings.


Definition in capital asset pricing model

The alpha coefficient (\alpha_i) is a parameter in the
single-index model The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. The model has been developed by William Sharpe in 1963 and is commonly used in the finance industry. Mathematically the SIM is expre ...
(SIM). It is the intercept of the
security characteristic line Security characteristic line (SCL) is a regression line, plotting performance of a particular security or portfolio against that of the market portfolio at every point in time. The SCL is plotted on a graph where the Y-axis is the excess return ...
(SCL), that is, the coefficient of the constant in a market model regression. :\mathrm : R_ - R_ = \alpha_i + \beta_i\, ( R_ - R_ ) + \varepsilon_ where the following inputs are: * R_i: the realized return (on the portfolio), * R_M: the market return, * R_f: the
risk-free rate The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payments over a fixed period of time that is assumed to meet all payment obligations. Since the risk-free r ...
of return, and * \beta_: the
beta Beta (, ; uppercase , lowercase , or cursive ; or ) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Ancient Greek, beta represented the voiced bilabial plosive . In Modern Greek, it represe ...
of the portfolio. * ''ε''''i'',''t'' : the non-systematic or diversifiable, non-market or idiosyncratic risk It can be shown that in an
efficient market The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted basis ...
, 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: *\alpha_i < 0 : the investment has earned too little for its risk (or, was too risky for the return) *\alpha_i = 0 : the investment has earned a return adequate for the risk taken *\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 of CAPM and not to a market index, it would be more accurate to use the term of
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 the ...
.


Origin of the concept

Efficient market hypothesis The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted basis ...
(EMH) states that
share prices A share price is the price of a single Share (finance), share of a number of saleable share capital, equity shares of a company. In layman's terms, the stock price is the highest amount someone is willing to pay for the stock, or the lowest amount ...
reflect all information, therefore stocks always trade at their
fair value In accounting, fair value is a rational and unbiased estimate of the potential market price of a good, service, or asset. The derivation takes into account such objective factors as the costs associated with production or replacement, market c ...
on exchanges. This would mean consistent alpha 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 Passive may refer to: * Passive voice, a grammatical voice common in many languages, see also Pseudopassive * Passive language, a language from which an interpreter works * Passivity (behavior), the condition of submitting to the influence of ...
portfolio. A belief in EMH spawned the creation of market capitalization weighted
index fund An index fund (also index tracker) is a mutual fund or exchange-traded fund (ETF) designed to follow certain preset rules so that it can replicate the performance of a specified basket of underlying investments. The main advantage of index fun ...
s, 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. The best examples for the US are the
S&P 500 The Standard and Poor's 500, or simply the S&P 500, is a stock market index tracking the stock performance of 500 leading companies listed on stock exchanges in the United States. It is one of the most commonly followed equity indices and in ...
and the
Wilshire 5000 The Wilshire 5000 Total Market Index, or more simply the Wilshire 5000, is a market-capitalization-weighted index of the market value of all American stocks actively traded in the United States. As of December 31, 2023, the index contained 3,40 ...
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, 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 the
expected return The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. It is calculated ...
of the beta adjusted return of the market is called "Alpha".


Relation to beta

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 (see
index fund An index fund (also index tracker) is a mutual fund or exchange-traded fund (ETF) designed to follow certain preset rules so that it can replicate the performance of a specified basket of underlying investments. The main advantage of index fun ...
), the price of the stock market as a whole fluctuates 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.


References


Further reading

* Bruce J. Feibel. ''Investment Performance Measurement''. New York: Wiley, 2003.


External links


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

Seeking Alpha - New York hedge fund creates value trading index options {{DEFAULTSORT:Alpha (Investment) Finance theories Financial ratios Investment indicators Mathematical finance