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For any fund that evolves randomly with time, volatility is defined as the standard deviation of a sequence of random variables, each of which is the return of the fund over some corresponding sequence of (equally sized) times. Thus, "annualized" volatility σ annually is the standard deviation of an instrument's yearly logarithmic returns. [2]
Stock A over the past 20 years had an average return of 10 percent, with a standard deviation of 20 percentage points (pp) and Stock B, over the same period, had average returns of 12 percent but a higher standard deviation of 30 pp. On the basis of risk and return, an investor may decide that Stock A is the safer choice, because Stock B's ...
are the residual (random) returns, which are assumed independent normally distributed with mean zero and standard deviation These equations show that the stock return is influenced by the market (beta), has a firm specific expected value (alpha) and firm-specific unexpected component (residual).
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 ...
It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk. It was named after William F. Sharpe, [1] who developed it in 1966.
That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. [ 1 ] [ 2 ] Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure ) measures both the upside and downside risk.
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.
By using the relationship between standard deviation and variance, and the definition of correlation, (,) (), market beta can also be written as =,, where , is the correlation of the two returns, and , are the respective volatilities.