Beta can be used to indicate the contribution of an individual asset to the market risk of a portfolio when it is added in small quantity.
Beta is the hedge ratio of an investment with respect to the stock market.
Thus insured, movements of the overall stock market no longer influence the combined position on average.
Beta measures the contribution of an individual investment to the risk of the market portfolio that was not reduced by diversification.
It does not measure the risk when an investment is held on a stand-alone basis.
In practice, few stocks have negative betas (tending to go up when the market goes down).
occasions, is defined by (and best obtained via) a linear regression of the rate of return
The reverse is not the case: A coin toss bet has a zero beta but not zero risk.
The new portfolio is defined by The variance can be computed as For small values of
In practice, the choice of index makes relatively little difference in the market betas of individual assets, because broad value-weighted market indexes tend to move closely together.
Academics tend to prefer to work with a value-weighted market portfolio due to its attractive aggregation properties and its close link with the capital asset pricing model (CAPM).
[3] When used within the context of the CAPM, beta becomes a measure of the appropriate expected rate of return.
Due to the fact that the overall rate of return on the firm is weighted rate of return on its debt and its equity, the market-beta of the overall unlevered firm is the weighted average of the firm's debt beta (often close to 0) and its levered equity beta.
(The CAPM has only one risk factor, namely the overall market, and thus works only with the plain beta.)
For example, a beta with respect to oil price changes would sometimes be called an "oil-beta" rather than "market-beta" to clarify the difference.
[4] Utility stocks commonly show up as examples of low beta.
These have some similarity to bonds, in that they tend to pay consistent dividends, and their prospects are not strongly dependent on economic cycles.
However, this effect is not as good as it used to be; the various markets are now fairly correlated, especially the US and Western Europe.
Whereas Beta relies on a linear model, an out of the money option will have a distinctly non-linear payoff.
(True also - but here, far less pronounced - for volatility, time to expiration, and other factors.)
Thus "beta" here, calculated traditionally, would vary constantly as the price of the underlying changed.
Accommodating this, mathematical finance defines a specific volatility beta.
[5] Here, analogous to the above, this beta represents the covariance between the derivative's return and changes in the value of the underlying asset, with, additionally, a correction for instantaneous underlying changes.
A true beta (which defines the true expected relationship between the rate of return on assets and the market) differs from a realized beta that is based on historical rates of returns and represents just one specific history out of the set of possible stock return realizations.
The true market-beta is essentially the average outcome if infinitely many draws could be observed.
Despite these problems, a historical beta estimator remains an obvious benchmark predictor.
It is obtained as the slope of the fitted line from the linear least-squares estimator.
The OLS regression can be estimated on 1–5 years worth of daily, weekly or monthly stock returns.
The choice depends on the trade off between accuracy of beta measurement (longer periodic measurement times and more years give more accurate results) and historic firm beta changes over time (for example, due to changing sales products or clients).
When long-term market-betas are required, further regression toward the mean over long horizons should be considered.