hrishikesh d vinod - preparing for the worst

[...]... b Therefore the average of x - m = m - m = 0 3 If the standard deviation of x = s, then the standard deviation of a(x) = a(s) (Note: The variance of a(x) = a2s2.) 4 If the standard deviation of x = s, then the standard deviation of (x + b) = s Therefore the standard deviation of (x - m)/s = (1/s)s = 1 Through standardization, tables of the area under the standard normal distribution can be used for. .. early years The more distant these dividends are, the harder they are to forecast Dividends also create a tax burden for the investor because they are taxed as current income, whereas capital gains from holding the stock are not taxed until the stock is sold This double taxation of dividends at the corporate and individual levels leads many to question the use of dividends at all, and has led many firms... distributions with any average and standard deviation To use the tables, one converts the x value under the normal distribution to the standardized z statistic under the standard normal and looks up the z value in the table The probability relates back to the original x value, which is then the number of standard deviations from the mean With the wide availability of Excel software workbooks, nowadays... portfolio, and what can be done to identify and prepare for the downside We take the view that downside risk can be incorporated into current methods of stock valuation and portfolio management Therefore we introduce commonly used theories in order to show how the status quo often misses the downside, and where to include it The importance of downside risk is evident to any investor in the market No... prices in the calculation of standard deviations over several days By taking the high and low price instead of the opening and closing prices, one does not run the risk of artificially smoothing the data and ignoring the rest of the day The high and low can come at any time during the day Once the expected return and volatility of returns are calculated, our next step is to understand the distribution... change dramatically with changes of the parameters Increases in the average will shift the location of the normal distribution Increases in the standard deviation will widen the normal distribution Decreases in the standard deviation will narrow the distribution Because the normal distribution changes with a change in the average or standard deviation, a useful tool is standardization This way the random... be measured in units of the number of standard deviations measured from the mean: z= x -m s (1.3.5) If x is normally distributed with mean m and standard deviation s, then the standardized value z will be standard normally distributed with mean of zero, and standard deviation equal to one In statistical literature this relation is often stated by using the compact notation: x ~ N(m, s2) and z ~ N(0,... double-exponential distribution density Azzalini skew-normal density Left panel: SN density for l = 0 (dark line, unit normal), l = 1 (dotted line), and l = 2 (dashed line) Right panel: l = -3 (dark line), l = -2 (dotted line), and l = -1 (dashed line) Figure 4.4.5 Variance of Azzalini SN distribution as l increases Figure 4.4.6 Plot of empirical pdf (solid line) and fitted adjusted skew-normal density Figure... on the buy side On the sell side, there is an individual who already owns the stock and wishes to liquidate all or part of the investment With so much heterogeneity in the amalgam that is the stock market, our task of finding a common framework for all players seems Preparing for the Worst: Incorporating Downside Risk in Stock Market Investments, by Hrishikesh D Vinod and Derrick P Reagle ISBN 0-4 7 1-2 344 2-7 ... of volatility has the same units as the average For the S&P 500, the standard deviation is 0.1496, for T-bills, 0.0115 The advantage in using the standard deviation is that all available data can be utilized Also some works have shown that alternate definitions of a deviation can be used Rather than strictly as deviations from the mean, risk can be defined as deviations from the risk-free rate (CAPM, . skew-normal density. Left panel: SN density for l=0 (dark line, unit normal), l=1 (dotted line), and l=2 (dashed line). Right panel: l =-3 (dark line), l =-2 (dotted line), and l =-1 (dashed line). appears at the end of this volume. Preparing for the Worst Incorporating Downside Risk in Stock Market Investments HRISHIKESH D. VINOD Fordham University Department of Economics Bronx, NY DERRICK. Stochastic Dominance (1SD), 139 6.3.7. Second-Order Stochastic Dominance (2SD), 140 6.3.8. Third-Order Stochastic Dominance (3SD), 141 6.3.9. Fourth-Order Stochastic Dominance (4SD), 142 6.3.10. Empirical