WFU Law School
Law & Valuation
2.2.2 Expected Return

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
2.2.2 Expected Return

©2003 Professor Alan R. Palmiter

This page was last updated on: March 16, 2004