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:
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Possible Outcomes
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Probability
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X
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Y
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|
1
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0.2
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-3
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1
|
|
2
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0.5
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1
|
0
|
|
3
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0.3
|
2
|
2
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(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.
1. 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: β = σAB/σ2A. σAB represents the covariance between A and B and σ2A 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 https://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?