1. Investing in the stock market:

Johnson & Johnson (JNJ) is trading at 68.15 (Sep 12th 2012 close). JNJ is a large health care conglomerate. It has done well so far this year (though not as well as the market) and may continue to do well. You believe that it is less vulnerable to the risks of the “fiscal cliff” and decide to take a closer look at it.
After careful analysis you conclude that in one year the price will be (44, 58, 71, 76, 91) with associated probabilities of (0.1, 0.2, 0.4, 0.2, 0.1). Looking at the company’s past record you determine that JNJ will pay a dividend of 2.52 (two quarterly dividends of 0.61 and two quarterly dividends of 0.65). If you invest your funds risk-free in the money market you will receive 1%.

a. What is the expected return of JNJ stock? What is the risk premium of JNJ stock?

b. find out the standard deviation of the return of JNJ stock (remember that you are using probabilities to do this, not historical data).
You become convinced that this investment opportunity is a good one. In the current conditions JNJ seems like a safe investment. You decide to buy JNJ stock on margin. You purchase 200 shares, financing half with your own investment and borrowing half from your broker.

c. How much do you borrow from your broker? What is your initial margin?
Tomorrow bad news reaches the economy and the price of JNJ stock drops to 44 immediately.

d. What is the new margin on the account? Do you receive a margin call? If you do, assume that you close your position immediately.

e. find out the return on your investment. What would the return have been if you had not borrowed any funds (Hint: what is the return on JNJ stock)?

2. Different choices: Risk-free investment and inflation:

You decide to invest 1000 in a 5-year Treasury Inflation protected bond that each year offers a return of -1.5% plus the rate of inflation. You assume 1-year inflation rates over the next five years of (1.5%, 2%, 2.5%, 2.75%, 3%). This means that the rate of return in the first year is zero.

a. What is the total value of your investment in five years?

b. What is the constant nominal interest rate that would lead to the same value in five years?

c. How would your answers to a. and b. change if inflation is higher than you expected?

3. Stock market investment and average excess returns:

Download annual NYSE stock return (holding period return) data from CRSP. The data is accessible through WRDS. Follow the steps in “Access CRSP on WRDS” (on LATTE). Choose the date range 1960 to 2011. Add this data to the data in “PS1.xls” on LATTE which contains annual risk-free returns (from Ken French’s website).

a. What was the average and standard deviation of NYSE stock returns?

b. What was the average and standard deviation of risk-free returns? What was the average  excess return (the average difference between the stock return and the risk-free return)?

c. Imagine that at the beginning of 1960 you invested 100 each in stocks and the risk-free security. What are the values of your two investments at the end of 2011?

d. What are the two values when starting with 100 in 2001 and investing until the end of 2008?

4. Collect stock return data and analyze it using Excel:

You are interested in analyzing historical stock return data for four U.S. companies that are included in the S&P500: Microsoft, IBM, Exxon Mobil, and Chevron. The ticker symbols for these companies are (MSFT IBM XOM CVX). You can enter them directly like this (no comma).
Download monthly stock return (holding period return) data from CRSP, which is accessible through WRDS. Follow the steps in “Access CRSP on WRDS” (see above). Choose a date range of Jan 1990 to Dec 2011. Open the file in Excel. Note that the output data uses “PERMNO” to identify the firms. These numbers are: MSFT: 10107, IBM: 12490, XOM: 11850, CVX: 14541.

a. For the four series, find out the monthly sample average return. Multiply by 12 to get the annual average return. Which company has the highest, which the lowest return?

b. For the four series, what is the standard deviation of the monthly returns? Multiply by the square root of 12 (3.464) to get the annual standard deviations. How does the standard deviation of these stocks compare to the standard deviation of returns on a portfolio of large stocks (Hint: look at the lecture notes)?

c. Looking at the numbers, do you think it would be a good idea to invest all of your money in one of these stocks?

d. find out the correlations between all pairs of stock returns (a total of six correlations). Which correlations are high, which are low? Why could this be the case?

Some useful Excel commands:

Suppose you have data in cell ranges A1:A10 and B1:B10.
Mean of series A: = AVERAGE(A1:A10)
Variance of series A: =VAR(A1:A10)
Standard deviation of series A: =STDEV(A1:A10)
Covariance between series A and B: =COVAR(A1:A10, B1:B10)
Coefficient of correlation between series A and B: =CORREL(A1:A10, B1:B10)
Square root of a number: SQRT()

5. VaR – value at risk:

Using the data on the four stock return series you downloaded in the previous problem, compare VaR using the normal distribution and VaR from the monthly return data.

a. Based on the monthly sample average returns and standard deviations, what are the values at risk of the monthly stock returns based on the normal distribution? That is, what are the 5th percentiles of the return distributions if you assume that returns are normally distributed?

b. For each series rank the monthly observations (a total of 264 numbers, 5% of which is close to 13.2). Find the 5th percentile of the return distribution by finding the 13th smallest returns.

c. What do you conclude regarding using the normal distribution as an approximation when calculating the size of a large loss (VaR)?