Measuring Cumulative Returns When Trading Exposure Changes
Summary
The document asks how to calculate cumulative percentage performance for a strategy whose long and short notionals, and thus net exposure, change frequently. It defines daily return as daily dollar PnL divided by that day’s net exposure, using a long-short example, and then illustrates the difficulty of compounding these daily percentages when the denominator varies over time.
A three-day hypothetical table shows that multiplying daily returns produces a cumulative percentage that can be hard to interpret alongside dollar PnL, because later gains or losses are measured against a different exposure base. The text raises the measurement problem but does not propose or evaluate a solution. Any answer would depend on what “capital” is intended to represent, such as invested equity, margin, or a chosen risk budget, and on how external scaling flows are treated. The example is therefore a prompt about return definitions rather than evidence that one specific cumulative-return method is correct.
Key ideas
- Daily percentage PnL is calculated relative to a chosen exposure denominator.
- Changing net exposure makes compounded daily percentages difficult to interpret.
- The document illustrates the issue with a hypothetical long-short strategy over several days.
- A meaningful cumulative return requires a clearly defined capital base and treatment of scaling.
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Full text
# How to calculate cumulative percentage return on a changing base
# How to calculate cumulative percentage return on a changing base
I am evaluating the cumulative % return on a trading strategy that requires constant rebalance / scaling, but find it difficult to arrive at an intuitive and sensible method.
#### Daily PnL & % Return
This is easy to derive. Say there are two legs, one long and one short. Assume 100% margin on both legs and it makes sense to use the net notional exposure as our "capital deployed" or as the demonitor for % return (assume I receive SOFR on the short leg). Let's say on date 12-20-2024 the long leg notional is \$2,000,000 and short leg is \$1,000,000, and the dollar pnl for this date is \$10,000. Then the daily % pnl for this date should be $$ \text{daily pnl}=\frac{\text{daily \\\$ pnl}}{\text{net exposure}}=\frac{10,000}{2,000,000-1,000,000}=1\% $$
#### Cumulative % Return
This is where it gets tricky as I face two major challenges. One is that I would rebalance / scale the positions constantly, resulting in jumps in net exposure; another is the net exposure of two legs change constantly themselves. Below is one hypothetical example where I find it hard to calculate cumulative return on:
| Date | Net Exposure | Daily Dollar PnL | Daily % Return | Cumulative % Return |
| 12/1/2024 | \$1,000,000 | \$100,000 | 10.00% | 10.00% |
| 12/2/2024 | \$5,000,000 | -\$10,000 | -0.20% | 9.78% |
| 12/3/2024 | \$10,000,000 | -\$100,000 | -1.00% | 8.68% |
Obviously this method's cumulative % return doesn't make sense as on day 3 -- cumulative return is 8.68% while the \$ PnL is negative -\$10,000. This is because the same daily \$ PnL would affect differently on changing net exposure base.
Since this strategy's nature is to jump and scale up / down on net notional exposure (contrary to most other strategies where base notional stays more stable), is there any way to measure cumulative return properly?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.