Problem 1. Investing in the stock market:
Johnson and Johnson (JNJ) is trading at 68.15. JNJ is a large health care conglomerate. It has done well so far this year (though not as well as the market) and will 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 find that in one year the price will be (44, 58, 71, 76, 91) with related probabilities of (0.1, 0.2, 0.4, 0.2, 0.1). Looking at the company's past record you evaluate 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. Evaluate the expected return of JNJ stock? Evaluate the risk premium of JNJ stock?
b. Determine 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?
d. What is the new margin on the account? Do you get a margin call? If you do, consider that you close your position immediately.
e. Evaluate the return on your investment. What could the return have been if you had not borrowed any funds
Problem 2. Risk-free investment and inflation:
You decide to invest 1000 in a 5-year Treasury Inflation protected bond that every year offers a return of -1.5% plus the rate of inflation. You consider 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. Determine the total value of your investment in five years?
b. compute the constant nominal interest rate that would lead to the same value in five years?
Problem 3. Stock market investment and average excess returns:
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. Suppose 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?
Problem 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 added in the S&P500: Microsoft, IBM, Exxon Mobil, and Chevron.
c. Looking at the numbers, do you think it could be a good idea to invest all of your money in one of these stocks?
d. Determine 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?
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)
Problem 5. VaR - value at risk:
a. Based on the monthly sample average returns and standard deviations, Determine 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 consider that returns are normally distributed?
b. For each series rank the monthly observations. Evaluate 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 evaluating the size of a large loss (VaR)?