Exercises for Efficiently Inefficient

9.8 Pair correlation. First calculate the daily returns for each stock. Then calculate the correlation between daily returns for the stocks in the each pair. Make a bar plot of the correlations.

9.9 Pair co-movement. Adjust all the return indices to 100 on the September 8, 2004. Plot the return indices for stocks in the same pair together and assess whether you think there may be an arbitrage strategy. Do you see any unusual or surprising patterns?

9.10 Spreads. Calculate and plot the relative spread between the stock prices in the same pair (i.e., one price divided by the other minus 1) and assess whether you think there may be an arbitrage strategy. Do you see any unusual or surprising patterns?

9.11 Pairs trading based on absolute prices. Implement the following strategy: At close on the last day of each year, take a self-financing position in each pair where you go long the stock with the lowest price and short the one with the highest price. The initial value of each long position should be $1 and, similarly, the initial value of each short position should be $1. Hold the position for a year and rebalance again at close on the last day of the year.

a. Why might this strategy be profitable? Hint: What happens if the share price is unchanged from rebalancing to rebalancing?

b. Calculate the yearly excess return per pair, the SR, and test whether the yearly excess returns are statistically significant from zero (under the assumption that returns are independent and normally distributed).

c. Same as question b for a portfolio consisting of all eight pairs, equally weighted.

d. Which costs would you incur if you were to implement this strategy in practice?