Calculate Daily Returns for Sharpe Ratio

For the purposes of Sharpe ratio, I calculate a trading strategy's daily returns using realized P/L only: $$\frac{K(t + 1) - K(t)}{K(t)},$$ where $K(t)$ is the cash balance after market close on day $t$. Assume no transfer is made from or to the account.

Recently, someone suggested I use account balance(cash balance + market value of all positions) instead, to include the day's unrealized P/L.

Which one should I use?

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I would absolutely use a mark-to-market value in your daily pnl for the purposes of evaluating performance (e.g. Sharpe). So, yes, that would include the value of open positions in addition to your cash balance.

If you hold something for a year, that performance was earned one day at a time, not all at once. If you only look at cash, you will have a large cash flow when you exit a position, and that will overstate the volatility of your returns. The difference in standard deviation between [0,0,0,0,0,0,0,0,99] vs [11,11,11,11,11,11,11,11,11] is significant, even though they total the same.

The effect of interest might be relevant (as BlueTrin as suggested), but is secondary to the importance of using mark-to-market.

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Thanks, I totally missed the part about MTM – BlueTrin Jan 14 '14 at 9:51

For a single day as long as $K(t+1)$ includes the intraday cash flows it is the same, however if you do not simulate your cash balance interest rate you forget that your cash get compounded over time, which is slightly incorrect.

This is why someone suggested you simulate your cash balance. This is more correct as well if you are not always 100% invested or if you have access to leverage as you get interest or get charged for being in credit/debit.

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