Fixed Income Markets: Management, Trading and Hedging, 2nd Edition

APPENDIX A Statistical Concepts

MEAN AND STANDARD DEVIATION

In finance, two fundamental concepts are the mean and standard deviation of a series of numbers. Imagine that there are five dot-com companies that are suffering cash-flow problems. The year-end operating losses for these companies are £1,000, £2,000, £3,000, £5,000, and £9,000. The mean or average loss suffered by the companies is

(1,000 + 2,000 + 3,000 + 5,000 + 9,000)/5 or £4,000

An analyst of this particular dot-com sector may wish to know how much variation (or perhaps “dispersion”) away from the mean value has occurred. Therefore, we require a measure of the variance of the raw data. This is a measure of the dispersion for each item away from the mean (here denoted as X). Individual measures may be either positive or negative, and so to remove the effects of the sign we take the square of each deviation before adding them together. This is shown below.

X	(X – )	(X – )2
1,000	–3,000	9,000,000
2,000	–2,000	4,000,000
3,000	–1,000	1,000,000
5,000	1,000	1,000,000
9,000	5,000	25,000,000
40,000,000

If we are calculating variance for a sample of the population, rather than the entire population itself, then the total of the squared sums is divided by (n – 1) where n is the number of observations ...