Calculating Cumulative Returns for a Short Position

Summary

The document examines why compounding the asset’s period returns does not match the holding-period return of a short position when the short is evaluated using its initial notional. Its example uses a price path of 5, 6, 4, and 2.5, with the short asset returns shown as −20%, 33%, and 37.5%. Multiplying those period figures produces a result that differs from the 50% gain implied by the initial and final prices.

The answer explains that the asset’s returns should first be compounded to obtain cumulative asset performance, after which the initial short weight is applied. This distinguishes cumulative asset returns from the returns of a position whose exposure and capital base may vary over time. The answer is brief and does not discuss margin, financing, rebalancing, or alternative conventions for measuring a short strategy, so its calculation should be understood in the stated setup rather than as a general account of short portfolio returns.

Key ideas

• Compounding an asset’s period returns gives the asset’s cumulative return, not automatically the short position’s return.
• For a fixed initial short weight, apply that weight to the asset’s cumulative return.
• The example’s price path implies a 50% gain for the short based on its starting and ending prices.
• The answer does not account for margin, financing, or changing position size.

Tags

# compounding in short positions


# compounding in short positions












Why does compounding doesn't work in short positions? Let's say I have following mini time series 5 6 4 2.5

Returns are -20%, 33% and 37.5%. So compounding return equals to 46.67% = 0.8 * 1.33 * 1.375. But the return is 50% = 1 - 2.5/5.

How one can reconcile these numbers? Why do we get two different returns?

## Answer by Enrico Schumann (score 1)

https://quant.stackexchange.com/a/79575

The 'trick' with short positions is to first compound the asset's returns, and only then to apply the position weights, i.e. -1 in your case. See also this answer How to calculate holding period return of a long-short strategy? The cumulative asset returns are 20%, -20% and -50%. Multiply by the initial weight of -1, and you get the expected outcome.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.