How do you calculate Sharpe on a position with a dynamic size? Asking for a friend... who is doing something.
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For each day sum up total *net* P&L from all positions held at start of the day and all trades during the day, inc financing costs, slippage, comms etc. Daily return is daily P&L / start of day account size and Sharpe ratio is E(daily ret)/StDev(daily ret). Annualize if you like.
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problem you would have is if trading becomes infrequent Lily. Then is sharpe a good measure etc...
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Yeah if you have a significant number of days with zero P&L (ie no positions held at sod and no trading) then you probably want to use a different metric.
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If you wanted to aggregate for a period, would you do like a simple arithmetic/geo average or something like a dollar weighted on the sod capital?
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Or maybe some kinda inverse stdev weight?
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