FBE 506 Quantitative Methods in Finance
Assignment #4
1. Given the following observations on X:
X: 14, 20, 18, 10, 8, 14, 16, 17, 9, 16, 16, 22, 20, 25, 15
a. Find the point estimate of the sample mean ......................................
b. Find the point estimate of the sample variance .......................................
c. Find the point estimate of the sample standard deviation .......................................
d. Find the point estimate of the population mean .......................................
e. Find the point estimate of the population variance .............................
f. Find the point estimate of the population standard deviation .......................................
g. Find the point estimate of the standard deviation of the sample mean ........................
h. Find the point estimate of the variance of the sample mean ........................
2. A financial analyst is testing the performance of two portfolios where the end of the year index on each portfolio for the past nine years are indexed as follows: (Note: For each question you are required to define your hypothesis clearly, find the relevant statistics, and express, statistically, what your conclusions are.)
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Portfolios
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2011 2012 2013
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2014 2015
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2016 2017
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2018 2019
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A
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123.5 121.3 106.5
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102.8 118.9
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129.6 137.9
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142.9 153.7
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B
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108.6 101.4 93.8
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101.9 112.0
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119.6 128.7
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139.5 145.8
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a. Test the hypothesis that the mean return for portfolio A during 2011-2019 is no different from the mean return on government’s T-Bill of 2.6% for the same time period.
b. Test the hypothesis that the mean return for portfolio B during 2011-2019 is no different from the mean return on government’s T-Bill of 2.6% for the same time period.
c. Test the hypothesis that the mean returns of the two portfolios are not statistically different from each other.
d. Test the hypothesis that the risk of the two portfolios (measured by the variances of the returns) are not statistically different from each other.
e. A financial analyst claims that portfolio A has higher performance than portfolio B. Test for the claim of the financial analyst? Do you agree?
3. Given the distribution of the following variable (X), find the mean, E(X), and the variance V(X) of the variable X.
X: 10, 6, 5, 8, 3, 4, 4.5
Probability: .1, .15, .3, .2, .05, .1, .1
a. E(X) = __________________
What does E(X) represent? ________________________________________________
b. V(X) = ____________________
What does V(X) represent? ________________________
c. Y is a variable with E(Y) = 5, V(Y) = 82, and E(XY) = 15.2 .
d. Find E(Z), where Z = 10X + 3Y ____________________________________
e. Find V(Z). _______________________________
f. Find covariance of X and Y. __________________
g. Find the correlation coefficient between X and Y.
4. Given that E(X) = 5, E(Y) = 8, E(X2) = 68, E(Y2) = 75 and rx,y = .35, find the followings.
a. Find V(X) _________________ b. Find V(Y) _________________
c. Find E(5 + 3X) ____________ d. Find E(2X - 2Y) _____________
e. Find E(5XY) _______________ f. Find E(3X2)__________________
g. Find V(2 + 4Y) ____________ h. Find V(5X - 2Y) _____________
i. Find V(X*Y) _______________ j. Find Cov(X,Y) _________________