Problems

The following problems utilize data in the file Gesim.xlsx.

1. Assume that the current price of Microsoft stock is $28 per share. What is the probability that in two years the price of Microsoft stock will be at least $35?

2. Solve Problem 1 again, but this time with the assumption that during the next two years, Microsoft will on average perform 6 percent better per year than it performed during the 1997–2002 period for which we have data.

3. Assume that the current price of Intel is $20 per share. What is the probability that during the next three years, we will earn at least a 30 percent return (for the three-year period) on a purchase of Intel stock? Problems 1 through 3 utilize data in the file Asselallsim.xlsx.

4. Suppose you believe that over the next five years, stocks will produce returns that are 5 percent worse per year, on average, than our 1972–2001 data. Find an asset allocation between stocks, T-Bills, and bonds that yields an expected annual return of at least 6 percent yet minimizes risk.

5. Suppose you believe that it is two times more likely that investment returns for each of the next five years will be more like the period 1992–2001 than the period 1972–1991. For example, the chance that next year will be like 1993 has twice the probability that next year will be like 1980. This belief causes your bootstrapping analysis to give more weight to the recent past. How would you factor this belief into your portfolio optimization model?

6. Many mutual funds and investors hedge the risk that stocks will go down by purchasing put options. (See Chapter 63, “Fun and Games: Simulating Gambling and Sporting Event Probabilities,” for more discussion of put options.) How could our asset allocation model be used to determine an optimal hedging strategy that uses puts?

7. Determine the correlations (based on our 1972–2001 data) between annual returns on stocks, T-Bills, and bonds. Then determine the correlation (based on our 1000 scenarios created by bootstrapping) between the final values for stocks, T-Bills, and assets. Does it appear that the bootstrapping approach picks up the interdependence between the returns on stocks, T-Bills, and bonds?