(a) Explain the so called pairs trading rule in statistical arbitrage.

Suppose a stock A is currently valued at 80 and another stock B is valued at 110. How would you design a pairs trading rule that generates profits when the two prices converge?

(7 marks)

(b) A portfolio has total variance 16%, and an average return of 9%. The market index has total variance 9% and an average return of 8%. The correlation between the return on the portfolio and the return on the market index is 0.6. The risk-free return is 4%.

Work out the Sharpe ratio and the Treynor ratio for the portfolio.

(9 marks)

(c) Suppose you hold an equally weighted portfolio of 16 stocks. Each stock has a beta of 0.8 and total variance 16%. The market index has variance 9%. Assume that the unsystematic risk is independent across the stocks.

Calculate the total risk, market risk and unsystematic risk of the portfolio.