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In: Finance

A portfolio generates the following returns over the past 10 years: Year Return (%) 1 14...

A portfolio generates the following returns over the past 10 years:

Year Return (%)
1 14
2 2
3 -15
4 20
5 18
6 16
7 -17
8 24
9 -10
10 -4

Calculate the test statistic to test whether the standard deviation of this portfolio's return is different from the benchmark portfolio standard deviation of 23.

The answer should be 4.075. Please use Excel and show formulas that are used. Thank you!

Solutions

Expert Solution

A B C D E F G H I J
2
3 To test the claim about standard deviation and variance, the chi-square test statistic is used.
4
5 The hypothesis will be
6 Null Hypothesis: Standard Deviation is σ0 i.e. σ = σ0
7 Alternate Hypothesis: Standard Deviation is σ0 i.e. σ ≠ σ0
8
9 The test statistic is
10 χ2= [(n-1)s2]/σ02
11
12 Where n is the sample size, s is sample standard deviation and σ0 is the target standard deviation.
13
14 Given the following data:
15
16 Year Return (%)
17 1 14
18 2 2
19 3 -15
20 4 20
21 5 18
22 6 16
23 7 -17
24 8 24
25 9 -10
26 10 -4
27
28 Sample Standard Deviation (s) 15.4761465 =STDEV.S(D17:D26)
29 n 10
30 σ0 23
31
32 The test statistic is
33 χ2= [(n-1)s2]/σ02
34 or
35 χ2= 4.075 =(D29-1)*((D28/D30)^2)
36
37 Hence test statistic is 4.075
38

jeff jeffy answered 1 year ago
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