Derivatives: Markets, Valuation, and Risk Management

APPENDIX A

Elementary Statistics

The purpose of this appendix is to provide a quick and informative review of elementary statistics. Statistics is used in almost every facet of every life form aviation to weather prediction. In the field of finance, one of its primary uses is to characterize the rate of return distributions of risky securities or portfolios of securities, although the principles apply to prices changes, earnings, or cash flows of almost any sort. To clarify the use of the statistical concepts used in this appendix, numerous illustrations are provided. To make the concepts in the illustrations as usable as possible, we demonstrate how the computations the computations can be performed using Microsoft Excel add-ins.

OBJECTIVES

After reviewing this Appendix, you should be able to:

1. Understand the difference between a population and a sample.
2. Understand the statistical properties of a probability distribution.
3. Understand the properties of expectation operators.
4. Estimate properties of population from a sample of observations drawn from the distribution.
5. Understand the properties of important continuous distributions including the normal distribution, the chi-square distribution, the t-distribution, and the F- distribution.
6. Test the hypothesis that a given data series approximates the normal distribution.
7. Test the hypothesis that the mean of a population is zero.
8. Test the hypothesis that the means of two samples are equal when the samples have equal and unequal variances. ...