Investors speak of a “bear market” when security prices fall substantially and i

Question

Investors speak of a “bear market” when security prices fall substantially and investors become pessimistic. The table below shows all declines of 10% or more in the Standard & Poor’s 500-stock index between 1940 and 2008. The data show how far the index fell from its peak.

Year           Decline           Year           Decline           Year           Decline

’40-‘42           42%             ‘66                22%              ‘98               28%

‘46                 27%           ’68-‘70            36%           ’00-‘02            48%

‘50                 14%           ’73-‘74            48%           ’08-‘09            56%

‘53                 15%           ’81-‘82            26%

‘55                 10%           ’83-‘84            14%

’56-‘57            22%          ‘87                  34%

’59-‘60            26%          ‘90                  20%

1. Conduct a descriptive statistical analysis of the data in the table above.

a. Make a split-stem plot of the % declines.

b. Thoroughly describe the shape of this distribution.

c. Compute the mean and standard deviation.

d. Compute the 5-number summary.

e. An investor asks you: “How far do stocks tend to fall in a “bear” market? “ What would you tell them?

Explanation / Answer

we will use minatab to compute this answer

a) thw stem and leaf plot is

Stem-and-leaf of C3 N = 17
Leaf Unit = 0.010

3 1 044
4 1 5
7 2 022
(4) 2 6678
6 3 4
5 3 6
4 4 2
3 4 88
1 5
1 5 6

b) the distibution will not be and standard distribution. But the distribution looks like that has more frequency at 4 then at 7 and 3.

c) mean and standard deviation

Variable Mean StDev
0.2871   0.130519

d) summary

Variable Minimum Q1 Median Q3 Maximum
0.1000 0.1750 0.2600 0.3900 0.5600

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