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Extreme Events – Specimen Question A.2.1(a) – Answer/Hints

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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 in-built 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 built-in 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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