A backtest ranks stocks on the closing price and fills at that same close. The signal has an information coefficient of 0.04 against close to close returns and 0.025 against returns measured from the next open. By what percentage does the achievable Sharpe ratio fall?

A backtest ranks stocks on the closing price and fills at that same close. The signal has an information coefficient of 0.04 against close to close returns and 0.025 against returns measured from the next open. By what percentage does the achievable Sharpe ratio fall?

Approach: At fixed breadth the information ratio moves in proportion to the information coefficient, so compare the two coefficients directly and then ask which part of the forecast was already in the traded price.

37.5%. At fixed breadth the information ratio is proportional to the information coefficient, so the achievable ratio scales by 0.025/0.04 = 0.625 and falls 37.5%. The missing 0.015 is the part of the forecast already contained in the closing price the backtest assumed it could trade at, and using it is a look-ahead bias because the ranking consumes information published at the same instant as the fill. Any fill assumption has to lag the data by the time needed to compute the signal and reach the exchange, so a close based equity signal is tested from the next open at the earliest. The same error hides in restated fundamentals, index membership dated at announcement rather than effect, and any database that overwrites history in place.

Follow-up: How would you quantify the look-ahead in a fundamental signal that uses fiscal period end rather than filing date?

Key concepts: look-ahead bias, information coefficient, fill assumption, backtest.