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Let's assume we have two long short equity strategies A, B with a Sharpe ratio of 2 each. Ignoring scalability, trading costs, turnover etc. We want to simply compare how efficient two strategies are using their capital.

Strategy A returns 10% on it's capital yearly and strategy B returns 1% on it's capital yearly. This could be possible if strategy B just has very low volatility. Obviously A is better because its using it's capital more efficiently. This calculation is very simple when we are comparing % returns. But % returns only makes sense of the capital allocation is roughly constant i.e. we have for example a constant 10m $ invested in each strategy.

A third strategy C - also with a Sharpe ratio of 2 - has highly non-constant capital allocation let's say between 1m $ and 10m $ invested. It wouldn't make sense to keep strategy C at a constant allocation because of the way it trades. Let's say for example it reacts to events that unevenly distributed.

How can I compare how efficiently the strategies are using their capital and rank them? Are there any established metrics for that?

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    $\begingroup$ In my opinion a good approach is to assume you have no funding, and pretend that when you take a position you have to first short an asset of comparable risk (for stock investing: the S&P) in the amount required. Naturally the return of the short position is included in the return of the overall strategy. When you free up some capital it goes to cover as much of the short position as you can, reducing the drag on performance. A similar method used in Private equity is the so-called Kaplan-Schoar PME. $\endgroup$ – noob2 Jan 4 at 19:41
  • $\begingroup$ Sorry - this wasn't clear. These strategies are fully hedged. To simplify we can assume they are hedged with SPY so S&P. So when I talk about return on capital 1% is the the return on the trades plus the hedges. $\endgroup$ – Joachim Jan 4 at 20:39
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"How can I compare how efficiently the strategies are using their capital and rank them? Are there any established metrics for that?"

The strategies will incur financing costs when using capital so those which are invested for a higher proportion of the time will incur higher financing costs.

You could also look at return per unit of time in the market. But I'm not aware of any standard metrics and I haven't seen this used in practice, though I have seen quant strategies where the backtest reports % of time in the market.

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