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 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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