Pairs trading with costly short-selling

We study an optimal pairs trading model with costly short-selling. When the investor has logarithm utility function, we derive the solution in closed form, which shows that: the optimal allocation functions are piece-wise linear in the pair's relative price; stock borrowing fees asymmetrically reduce the optimal size of the long/short position; and for risk-hedging purpose, it can be optimal to short sell even when the stock borrowing fees outweigh the expected return earned from short selling. When the investor has power utility function, we propose analytical allocation functions adopting which only causes a small utility loss. When the investor is constrained from borrowing funds, the margin requirement for short selling can significantly affect the trading strategy. Empirically, we demonstrate the importance of incorporating short selling costs when trading pairs in China's stock market and verify the model-implied relation between short selling costs and profitability of pairs trading.