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For example, if the stock market went up by 20% in a given year, and a manager had a portfolio with a market-beta of 2.0, this portfolio should have returned 40% in the absence of specific stock picking skills. This is measured by the alpha in the market-model, holding beta constant. Occasionally, other betas than market-betas are used.
[] / [] is the "beta", return mentioned — the covariance between the asset's return and the market's return divided by the variance of the market return — i.e. the sensitivity of the asset price to movement in the market portfolio's value (see also Beta (finance) § Adding an asset to the market portfolio).
An estimation of the CAPM and the security market line (purple) for the Dow Jones Industrial Average over 3 years for monthly data.. 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 well-diversified portfolio.
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How to calculate beta Beta is calculated by taking the covariance between the return of an asset and the return of the market and dividing it by the variance of the market.
To calculate beta, investors divide the covariance of an individual stock (say, Apple) with the overall market, often represented by the Standard & Poor’s 500 Index, by the variance of the ...
Under the assumption of normality of returns, an active risk of x per cent would mean that approximately 2/3 of the portfolio's active returns (one standard deviation from the mean) can be expected to fall between +x and -x per cent of the mean excess return and about 95% of the portfolio's active returns (two standard deviations from the mean) can be expected to fall between +2x and -2x per ...
With this equation, only the betas of the individual securities and the market variance need to be estimated to calculate covariance. Hence, the index model greatly reduces the number of calculations that would otherwise have to be made to model a large portfolio of thousands of securities.