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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 ...
The average magnitude of the observations is merely an approximation of the standard deviation of the market index. Assuming that the market index daily changes are normally distributed with mean zero and standard deviation σ, the expected value of the magnitude of the observations is √(2/ π)σ = 0.798σ. The net effect is that this crude ...
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 ...
The MPT is a mean-variance theory, and it compares the expected (mean) return of a portfolio with the standard deviation of the same portfolio. The image shows expected return on the vertical axis, and the standard deviation on the horizontal axis (volatility). Volatility is described by standard deviation and it serves as a measure of risk. [7]
A stock certificate is a legal document that specifies the number of shares owned by the shareholder, and other specifics of the shares, such as the par value, if any, or the class of the shares. In the United Kingdom, Republic of Ireland, South Africa, and Australia, stock can also refer, less commonly, to all kinds of marketable securities. [4]
He pointed out that the standard deviation from the 11.7% average annual return is 19.6 percentage points. That means any return from a 7.8% decline to a 31.2% increase could be considered ...
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).
S&P 500 with 20-day, two-standard-deviation Bollinger Bands, %b and bandwidth. Bollinger Bands (/ ˈ b ɒ l ɪ n dʒ ər /) are a type of statistical chart characterizing the prices and volatility over time of a financial instrument or commodity, using a formulaic method propounded by John Bollinger in the 1980s.