The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

QUESTIONS

1.

a. What are the main assumptions of arithmetic random walks?

b. What are their main disadvantages when modeling asset prices?

2.

a. What are the main assumptions of geometric random walks?

b. What is the probability distribution of asset prices that follow geometric random walks?

3.

a. What are the main assumptions of mean reversion?

b. When would you model asset prices using mean-reverting walks instead of arithmetic or geometric random walks?

4. Explain in detail how you would simulate a geometric random walk when the volatility is assumed to follow a mean-reverting process.

5. Let us evaluate a simple trading strategy whose goal is to limit downside risk. Suppose you are holding one share of stock. You sell the stock as soon your loss (relative to the original price of stock) exceeds 10% of the original stock value; otherwise you keep the stock. Once you have sold the stock, you do not buy it back for three months. If you have not sold the stock, you sell it at the end of three months.

Pick a stock, and determine its drift and volatility from historical data. Check also if a mean-reverting process appears to apply. Implement a simulation model in which the price of the stock is assumed to follow (1) an arithmetic random walk, (2) a geometric random walk, (3) mean reversion, and (4) geometric mean reversion with the parameters you estimated. Discuss the performance of the trading strategy depending on the process the price of the stock is assumed to follow. ...