A long short book turns over 50% of its gross notional a day in one direction, pays 5 basis points of traded notional in spread and impact, and grosses 12% a year at 8% volatility. What is the net Sharpe ratio?

A long short book turns over 50% of its gross notional a day in one direction, pays 5 basis points of traded notional in spread and impact, and grosses 12% a year at 8% volatility. What is the net Sharpe ratio?

Approach: Annualise the one way turnover, multiply by the cost per side, and take the result off the gross return before dividing by an unchanged volatility.

0.71. One way turnover of 50% a day is 0.5*252 = 126 times gross notional a year, and at 5 basis points a side that is 126*0.0005 = 6.3% of gross paid away annually. Net return is 12 - 6.3 = 5.7% against an unchanged 8% volatility, so the net Sharpe ratio is 0.71 where the gross alpha implied 1.50. Transaction costs are linear in turnover while the alpha available at a shorter horizon grows at best with the square root of the frequency, so a book at this turnover is a cost problem before it is a forecasting problem. Raising the cost estimate to 8 basis points leaves 1.9% and a Sharpe ratio of 0.24, so the entire result sits inside the uncertainty of one input.

Follow-up: What cost per side makes this strategy exactly break even, and how would you measure the realised figure?

Key concepts: turnover, transaction costs, net sharpe ratio, gross alpha.