Homework Assignment #3

Due date:  March 25
 
 

1. When looking for a good stock-return forecasting model, we sometimes do not distinguish between forecasting "which stocks out of 1000 individual stocks will do better over the next period" (i.e., cross-sectional forecasting) and forecasting "how well the S&P 500 index will do over the next period" (i.e., time-sequential forecasting for a single stock or index).  To make this more specific, suppose that using momentum, firm size, book/market ratio and other valuation measures, you can predict individual stock returns in the future with 70% accuracy. That is, in cross-sectional forecasting, your forecasts are directionally accurate for 7 stocks out of 10 (on average). With this model, you decide to buy an equal dollar ammount of the 100 best-forecast stocks and hold them until the next portfolio rebalancing time in one month, at which time you re-do the forecasting and select the new 100 best-forecast stocks and form the new equally-weighted portfolio, and so on. Let's call this the "cross-sectional strategy".
     On the other hand, using historical data, you find that using the default premium, term premium, T-bill interest rate, put-option-volume to call-option-volume ratio and so on, you can predict the future direction of the S&P 500 index (just one index) with 70% accuracy. That is, out of 10 future months, your directional predictions will on average be right in 7 months. Upon finishing the development of this model, you decide to apply it to trade S&P 500 futures: whenever your model forecast is positive for next month, you put all of your fund's capital into a long position in the S&P 500 futures (the futures position's notional value is made equal to the total capital of your fund); Whenever your forecast is negative for next month, you short an amount of the S&P 500 futures that is, in notional value, equal to the total capital of your fund. Let's call this the "time-sequential strategy".

1.1. Assume you are starting a hedge fund and are free to choose either of the above two strategies. Your investors are not willing to have their capital locked in for any period of time, as they would like to keep the option to withdraw from the fund. They all follow the "three strikes in a row, you are out" investment principle, especially for new funds. Then, which of the two strategies would you prefer? Do the two strategies offer the same level of "business risk"? Explain you ranswer.

1.2. Suppose your investors are willing to lock in their investment in your fund for a period of time. Then, how long would you want the lock-in period to be? Why?

2. The S&P 500 index has a dividend yield of 1.8% per year, and is currently at 1120. The T-bill rate is 3%. The June S&P 500 futures (with 4 months to expiration) is traded at 1121. Does there exist an arbitrage opportunity? If yes, construct an exact arbitrage strategy and explain whether you will need to do any rebalancing before the June expiration date. Will you lose money if the S&P 500 index goes down to 1050 in June? What if the index goes up to 1250 in June?

3. Problem 2 of Chapter 20, the BKM textbook.

4. Problem 21 of Chapter 20, the BKM textbook.

5. Problem 22 of Chapter 20, the BKM textbook.

6. Problem 11 of Chapter 22, the BKM textbook.

7. Problem 16 of Chapter 22, the BKM textbook.

8. Problem 19 of Chapter 22, the BKM textbook.