 • Table of Contents • Introduction • 1-Time Value • 2-Risk/Return • 3-Accounting • 4-Securities • 5-Business • 6-Regulatory • Case Studies • Student Papers ## 2.2.3 Standard Deviation

This variability can be measured. That is, risk can be quantified! The most common measure of risk is the standard deviation -- a numerical measure of the dispersion around the expected value. Here is how the standard deviation (designated by s ) is calculated for our two dice probability distributions:

• compute the expected return;
• square the variance of each return from the expected return;
• multiply this by the probability;
• sum these weighted values;
• calculate the square root of this sum (the standard deviation).

This gives a numerical indication of how far the returns are dispersed from the average.

There are various measures of risk: beta, standard deviation, R-squared. (See a comparison of these three measures of risk.) cFor an excellent primer on risk in securities markets, see Vanguard's Investing Primer.

 Return Square of variance Probability Weighted square \$2 (7 - 2)2 = 25 1/36 = .028 0.694 \$3 (7 - 3)2 = 16 2/36 = .056 0.889 \$4 (7 - 4)2 = 9 3/36 = .083 0.750 \$5 (7 - 5)2 = 4 4/36 = .111 0.444 \$6 (7 - 6)2 = 1 5/36 = .139 0.139 \$7 (7 - 7)2 = 0 6/36 = .167 0.000 \$8 (7 - 8)2 = 1 5/36 = .139 0.139 \$9 (7 - 9)2 = 4 4/36 = .111 0.444 \$10 (7 - 10)2 = 9 3/36 = .083 0.750 \$11 (7 - 11)2 = 16 2/36 = .056 0.889 \$12 (7 - 12)2 = 25 1/36 = .028 0.694 Statistics: Sum of weighted squares 5.833 Standard deviation (square root of sum) 2.415
 This page was last updated on: March 16, 2004