How to deal with different amount of td's in computing Sharpe Ratio

Question

In calculating the Sharpe Ratio, should I take into account the days were I have 0 return due to non-trading day? Another user posted a similar question but this was related to trading days with no open position. This is actually the same issues but then related to return history and inactive trading days. When analyzing the return history of several firms in the Asia Pacific region I noticed that there are some irregularities when it comes to trading days.

For example, X has 239 td’s on the TSE while Y has 250 td’s on the SGX. Squaring both daily returns by 252 would give biased returns/Sharpe ratios. My gut feeling says to square it by the amount of actual td’s rather than using the common 252 days. It also sometimes occurs within, for example the Japanese market, that different listed firms produce 0 return four times in a row, while others have on those same days a positive/negative return. The data is downloaded from the DataStream database.

Thanks in advance.

Answer 1

I can only repeat myself because your mentioned previously asked question is essentially identical:

=> I would say do not include non-trading days, do not include days with zero position, do not include days where the asset did not trade for whatever other reason.

Here some reasons and pointers:

• Sharpe measures excess returns scaled by volatility. The whole big picture of using such metrics is to gauge risk and risk adjusted returns. When a security does not trade, when you do not have a position then you do not carry risk at least not on that day. Nothing moves, hence, you are not subject to risk nor returns (on that particular day)
• You should always scale by the number days that you include in your calculation. So, if a security trades on January 1-31, then trading is halted because of filing irregularities or gross corporate illegal conduct or for whatever reason and for the rest of the year the security does not trade then you end up with those number days that you had a position in this security in January and on which such security traded. Hence you also scale by such number trades. The point is that this one single security does not make up your whole portfolio nor investment horizon (I hope not) but that you properly reflect such risk even if you need to extrapolate risk and returns out over the remainder of the year even though the security did not trade. You are sometimes unfairly penalized for that, at other times you are unfairly rewarded by applying such procedure but the whole point is that such event risk is properly reflected in your whole portfolio risk metrics.