7 estimating volatility

# 7 estimating volatility - What Practitieners Need te Knew....

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What Practitieners Need te Knew. .. by Mark Kritzman Windham Capital Management . . . About Estimating Volatility Parti Volatility is important to financial analysts for several reasons. Perhaps most obvious, estimates of volatil- ity, together with information about central ten- dency, allow us to assess the likelihood of experienc- ing a particular outcome. For example, we may be interested in the likelihood of achieving a certain level of wealth by a particular date, depending on our choice of alternative investment strategies. In order to assess the likelihood of achieving such an objective, we must estimate the volatility of returns for each of the alternative investment strategies. Financial analysts are often faced with the task of combining various risky assets to form efficient port- folios—portfolios that offer the highest expected re- turn at a particular level of risk.' Again, it is necessary to estimate the volatility of the component assets. Also, the valuation of an option requires us to esti- mate the volatility of the underlying asset. These are but a few examples of how volatility estimates are used in financial analysis. Historical Volatility The most commonly used measure of volatility in financial analysis is standard deviation. Standard deviation is computed by measuring the difference between the value of each observation in a sample and the sample's mean, squaring each difference, taking the average of the squares and then determin- ing the square root of this average. Suppose, for example, that during a particular month we observe the daily returns shown in column 1 in Table I. The average of the returns in column 1 equals 0.28 per cent. Column 2 shows the difference between each observed return and this average re- turn. Column 3 shows the squared values of these differences. The average of the squared differences— 0.0167 per cent—equals the variance of the returns. (In computing the variance, we divide by the number of observations less one, because we used up one degree of freedom to compute the average of the returns.) The square root of the variance—1.2904 per cent—equals the standard deviation of the daily re- turns. Table I Standard Deviations of Return Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Average Square Root 1 Return (%) 1.00 1.50 2.10 -0.40 1.00 -1.40 0.45 -0.75 1.00 1.40 -2.00 1.00 -1.50 0.35 -0.30 1.00 0.00 -0.60 -1.20 2.90 0.28 2 Return - Average (%) 0.72 1.22 1.82 -0.68 0.72 -1.68 0.17 -1.03 0.72 1.12 -2.28 0.72 -1.78 0.07 -0.58 0.72 -0.28 -0.88 -1.48 2.62 3 Squared Difference (%) 0.0052 0.0149 0.0332 0.0046 0.0052 0.0281 0.0003 0.0106 0.0052 0.0126 0.0519 0.0052 0.0316 0.0001 0.0033 0.0052 0.0008 0.0077 0.0218 0.0688 0.0167 1.2904 In this example, the standard deviation measures the volatility of daily returns. It is typical in financial analysis to annualize the standard deviation. Unlike rates of return, which increase proportionately with hme, standard deviations increase with the square root of hme. We can take two approaches to convert-

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## This note was uploaded on 08/13/2010 for the course FINS 2624 R taught by Professor Yippie during the Three '10 term at University of New South Wales.

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7 estimating volatility - What Practitieners Need te Knew....

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