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In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.
How to calculate alpha. ... Differences between alpha and beta. Though both greek letters, alpha and beta are quite different from each other. Alpha is a way to measure excess return, while beta ...
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 ...
With = generates a gamma distributed random number in time that is approximately constant with &alpha. The acceptance rate does depend on α , with an acceptance rate of 0.95, 0.98, and 0.99 for α = 1, 2, and 4.
The formulas given in the previous section allow one to calculate the point estimates of α and β — that is, the coefficients of the regression line for the given set of data. However, those formulas do not tell us how precise the estimates are, i.e., how much the estimators α ^ {\displaystyle {\widehat {\alpha }}} and β ^ {\displaystyle ...
The Blume beta shrinks the estimated OLS beta towards a mean of 1, calculating the weighted average of 2/3 times the historical OLS beta plus 1/3. A version based on monthly rates of return is widely distributed by Capital IQ and quoted on all financial websites.
Alpha is a measure of the active return on an investment, the performance of that investment compared with a suitable market index.An alpha of 1% means the investment's return 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.
The beta (β) of a stock or portfolio is a number describing the volatility of an asset in relation to the volatility of the benchmark that said asset is being compared to. This benchmark is generally the overall financial market and is often estimated via the use of representative indices , such as the S&P 500 .