ScholarMatic: Explanation & Answer

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FIN

Problem
Set #1

1. There
are two random variables, X and Y. X
takes on values of -3, 1, and 2, while Y can take the values of 2, 0, and
1. The probability for X and Y at each
state is given as follows:

(a)
Compute the expected value of X and Y,
i.e., E(X) and E(Y).

(b)
Compute the variances of X and Y, i.e.
Var(X), and Var(Y).

(c)
What is the covariance between X and Y,
i.e. Cov(X, Y)?

(d)
Compute the correlation between X and Y.

2. You are
interested in two investments, Fidelity Low Price Stock Fund (FLPSF) and Spider
(SPY). The followings are their annual
returns you’ve recorded from finance.yahoo.com:

Year
FLPSX SPY

1999 4.67% 20.36%

2000 18.73% -9.78%

2001 26.64% -12.06%

2002 -6.17% -21.58%

2003 40.86% 28.17%

2004 22.01% 10.70%

(a)
What are the respective average returns
of the two funds?

(b)
What are the standard deviations in the returns
of each fund?

(c)
Compute the covariance between returns
of the two funds.

3. When
you plot the returns of FLPSX against the returns of SPY (using Excel) in
Problem 2, you will see a relationship between the two. Using regression analysis in Excel, find the
linear relationship between the returns of the two funds, i.e., regressing returns
of FLPSX on returns of SPY. Actually,
the slope coefficient β from the regression can be computed using the following
formula:.gif”>. .gif”> represents the
covariance between A and B and .gif”>represents the variance of A.

Confirm your computation using
the results from Question 2 (see my lecture notes for example). The results
will be slightly different due to the scale by n-1 in the Excel program when
calculating variance.

4. (Note: This problem will be further developed as a
project) In order to help you understand
the investment process, you are required to form a hypothetical portfolio of
five stocks. To start, you can pick any
five stocks or ETFs or mutual funds of your interest by researching on .yahoo.com/”>http://finance.yahoo.com. After deciding on the assets you can find
their tick symbols from the same website and download their past five year
monthly prices from July 2010 to
July 2015 by clicking on “Historical
Prices” on the left up corner under “Quotes.”
Select the start date to be the first trading day of July 2010 and the end date
to be the first trading day of July 2015 and choose “Monthly” as your data
frequency. After downloading the data, please answer the following questions.

(a)
First compute returns from “Adjusted
Closing Price” (“Adj. Close*”) in Excel.

(b)
With these return data, calculate the
average returns, standard deviations, pair wise covariance, and correlations
for the five stocks.

5.
After Merrill Lynch analyst
upgraded Coca-Cola stock on June 20, 2005, you bought on margin 5,000 shares at
the price of $43.91 per share. The initial percentage margin is 60% and the
maintenance margin is 30%. The annual
cost of the margin loan is 6%.

(a) Determine your initial
margin requirement.

(b) To what price must Coca-Cola fall for you to receive a margin call?

(c) On August 19, 2005, you sold your Coca-Cola shares at the
price of $44.39 per share. What was the return
on your investment?

ScholarMatic: Explanation & Answer

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