Comparing Long-Short Returns Across Holding Periods

Summary

The document raises a portfolio-return calculation question: how to compare long-short stock strategies that hold positions for more than one month. The investor has monthly stock returns and wants to evaluate a shared holding period for the long and short sides. For a one-month period, the proposed calculation subtracts the short portfolio’s return from the long portfolio’s return, averages the monthly differences, and annualizes by multiplying by twelve.

For a longer period, the question considers compounding returns across months and two deployment schedules: opening a full-sized position every holding-period interval, or allocating a fraction of capital each month so overlapping positions remain within a capital limit. It also asks what further adjustments are needed. The document contains no answer or empirical evidence, so it does not resolve which schedule is appropriate. The choice depends on the intended portfolio exposure and capital constraint; annualization and return aggregation also require care when positions overlap.

Key ideas

• The document distinguishes one-month long-short returns from returns over longer holding periods.
• For a one-month period, it proposes subtracting short portfolio returns from long portfolio returns.
• It asks whether longer holding periods should use staggered full allocations or smaller overlapping allocations.
• The exchange provides no resolution or empirical comparison of the proposed schedules.

Tags

# Calculation of Long-Short-Portfolio returns for different holding periods


# Calculation of Long-Short-Portfolio returns for different holding periods












I have monthly stock returns I want to invest in according to my trading signals. Now I want to figure out the optimal holding period of the long-short-positions. (The same time for both positions).

I invest one unit long and one short. For a holding period of one month I just substract the returns from the short-portfolio of the ones from the long-portfolio and multiply the mean of all of them by 12 for the annual return.

My questions concern the longer holding periods, let's say it is two months. First I have to multiply the return of `t=0` with the return of `t=1`. Do I then invest the dollar every month or do I invest it only every other month so I never invest more than my initial one dollar at a time? (For a holding period of `x` then every `x-th` month.)

Or would I only invest 1/2 dollars every month so I don't exceed one dollar at a time? (`1/x` dollars for `x` months of holding.)

And do I have to consider anything else for the return calculation afterwards?

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