Given: Two funds- Vanguard Stock Index Funds(VSIF) and Vanguard Balanced Index funds(VBIF). Do bonds reduce the overall risk of an investment portfolio? Let "X" be a random variable representing annual percent return for the Vanguard Total Stock Index(all stocks). Let "Y" be a random variable representing annual return for the Vanguard Index Fund(60% stock and 40%bond). Make reasonable assumptions whether it is a sample or population. You can choose either one. For the past several years assume the following data:X: 13 0 37 24 32 26 27 -12 -12  -24Y: 8 -2 26 15 25 18 15 -3 -4 -9 1. Compute the Coefficient of variation(CV) for each fund. Round your answers to the nearest tenth 2. If CV represents risk per unit of return,which fund appears to be better? Explain 3. Compute a 75% Chebyshev's interval around the mean for the X and Y values

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Asked Sep 26, 2019
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Given: Two funds- Vanguard Stock Index Funds(VSIF) and Vanguard Balanced Index funds(VBIF). 

Do bonds reduce the overall risk of an investment portfolio? Let "X" be a random variable representing annual percent return for the Vanguard Total Stock Index(all stocks). Let "Y" be a random variable representing annual return for the Vanguard Index Fund(60% stock and 40%bond). Make reasonable assumptions whether it is a sample or population. You can choose either one.

 

For the past several years assume the following data:

X: 13 0 37 24 32 26 27 -12 -12  -24

Y: 8 -2 26 15 25 18 15 -3 -4 -9

 

1. Compute the Coefficient of variation(CV) for each fund. Round your answers to the nearest tenth

 

2. If CV represents risk per unit of return,which fund appears to be better? Explain

 

3. Compute a 75% Chebyshev's interval around the mean for the X and Y values

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Expert Answer

Step 1

Checking whether the values are from population or sample:

It is given that the random variable X represent the annual percent return for VSIF and the random variable Y represent the annual return for VBIF.

Since only a few observations, that is, 10 observations from two large populations is considered, the given data is the sample data.

Step 2

The sample means are calculated below:

Σ
159
10
=15.9
Συ
n
89
10
=8.9
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Image Transcriptionclose

Σ 159 10 =15.9 Συ n 89 10 =8.9

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Step 3

The sample standard deviati...

1
η
Σ&-3)
n-1
=17.89
1
п
Υ-2-J).
n-1
=12.72
help_outline

Image Transcriptionclose

1 η Σ&-3) n-1 =17.89 1 п Υ-2-J). n-1 =12.72

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