# FBE 506 University of Southern Quantitative Methods in Finance Questions

UNIVERSITY OF SOUTHERN CALIFORNIAMarshall School of Business

FBE 506 Quantitative Methods in Finance

M. Safarzadeh

Assignment #4

Student Name: _______________

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.)

Portfolios

2011

2012

2013

2014

2015

2016

2017

2018

2019

A

123.5 121.3

106.5

102.8

118.9

129.6

137.9

142.9

153.7

B

108.6 101.4

93.8

101.9

112.0

119.6

128.7

139.5

145.8

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:

Probability:

10,

.1,

6,

.15,

5,

.3,

8,

.2,

3,

.05,

4,

.1,

4.5

.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) _________________