Compounding Trade Returns Versus Portfolio Return on Investment

Summary

The document asks how to turn a sequence of per-trade percentage returns into a cumulative return. It proposes multiplying the gross returns, then subtracting one, which is the standard way to compound sequential returns when each return applies to the capital carried forward. The questioner finds that this cumulative series grows much faster than an overall ROI calculated as total profit and loss divided by average investment across trades.

These quantities use different denominators and answer different questions. Compounding assumes returns accrue sequentially on an evolving account value; dividing total profit and loss by average trade investment measures performance relative to that chosen capital base. The document contains no answer explaining the discrepancy, and it does not specify whether trade capital is reused, trades overlap, or returns are measured on account equity. Those details are necessary to make the measures comparable, so the stated formulas alone do not show that either calculation is erroneous.

Key ideas

• Sequential percentage returns compound by multiplying their gross-return factors and subtracting one.
• The compounded series measures growth on capital that evolves from trade to trade.
• Profit and loss divided by average investment uses a different capital denominator from a compounded return.
• Comparing the measures requires knowing whether capital is reused, trades overlap, and returns are based on account equity.

Tags

# Cumulative returns from ROI of individual trades


# Cumulative returns from ROI of individual trades












I've a series of ROIs: $R(n) = [r_1, r_2, ... r_n]$ generated from taking $n$ trades. Each ROI value is in percent $[0, 1]$. How do I generate cumulative return $C(n)$ from this data?

My understanding is that the cumulative return for $n^{th}$ trade will be $C(n) = -1 + \Pi_{i=1}^n (r_i + 1)$.

However, this leads to an exponential curve, where if I look at $C(n)$ for a large $n$ (~3500+), the C(N) value is drastically higher than overall return on investment.

I am computing overall ROI as total PNL after n trades divided by average investment of the N trades.

What am I doing wrong and how to rectify it?

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