Question 8 (Pairs trading). This problem set is based on the Excel sheet Pairs Trading.xlsx.

You will explore the potential prots of trading twin stocks. The spreadsheet contains the

return index (adjusted for dividends, corporate actions, etc.) at close of 16 stocks, corresponding

to two share classes for the following eight companies: A.P. Mller Mrsk (Denmark),

Industrivarden, Investor, Svenska Handelsbanken and Volvo (Sweden), Volkswagen

(Germany), Hyundai Motors (Korea) and Store Enso (Finland).

(a) (Pair correlation). Calculate the daily returns for each stock and then use these

daily returns to calculate the correlation between daily returns for the stocks in the

each pair. Make a bar plot of the correlations.

(Pair co-movement). Standardize all return indices such that they have a value equal

to 100 on the September 8, 2004. Plot the return indices for stocks in the same pair

together and discuss if there are potential arbitrage strategies for any of the pairs.

(c) (Pairs trading based on absolute prices). Implement the following strategy: At

close on the last day of each year, take a self-nancing 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.

{ Why might this strategy be protable?

Hint: What happens if the share price is unchanged from rebalancing to rebalancing?

{ Calculate the yearly excess return per pair, the Sharpe ratio, and test whether the

yearly excess returns are statistically signicant from zero (under the assumption

that returns are independent and normally distributed).

{ Form a portfolio consisting of all eight pairs, equally weighted, and compute the

excess returns and Sharpe ratio of the portfolio. Also test if the excess returns of

the portfolio are signicantly dierent from zero.

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

(d) Explain how you could improve the trading strategy from part (c).