Extreme Events – Specimen Question A.2.1(a)
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Q. Calculate the mean,
(sample) standard deviation, skew and (excess) kurtosis of [Index A’s] log
returns over the period covered by the above table.
The logged returns of A, i.e. are:
Period

A (logged return)

1

0.2890163

2

0.0009995

3

0.2167230

4

0.0760347

5

0.0140989

6

0.0049875

7

0.0060181

8

0.0099503

9

0.0704585

10

0.1278334

11

0.0069756

12

0.0079682

13

0.0387408

14

0.0276152

15

0.0439519

16

0.0120726

17

0.0725707

18

0.0629748

19

0.0353671

20

0.0178399

The mean, (sample) standard deviation, skew and (excess)
kurtosis of A’s log returns can be calculated in a variety of ways, including:
i.
In a Microsoft Excel spreadsheet using the inbuilt functions AVERAGE,
STDEV, SKEW and KURT respectively;
ii. In
a Microsoft Excel spreadsheet using the Nematrian web functions MnMean, MnStdev, MnSkew and MnKurt respectively;
iii. In
VBA, the builtin programming language packaged with Microsoft Excel, using:

The VBA equivalents to (i), i.e. Excel.WorksheetFunction.Average,
Excel.WorksheetFunction.StDev, Excel.WorksheetFunction.Skew and
Excel.WorksheetFunction.Kurt respectively; or

The VBA equivalents to (ii), which if you have e.g. used the Nematrian
website’s, automatic
code generator or have loaded up a prepopulated spreadsheet from the Nematrian
spreadsheet library will also be called MnMean, MnStdev, MnSkew and MnKurt respectively;
iv. Interactively,
via the MnMean, MnStdev, MnSkew and MnKurt webpages.
In each case the answers supplied (possibly with some
rounding error) are:
Statistic

Value

mean

0.0033204

stdev

0.0954161

skew

0.9253403

kurt

4.6238918

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