Converting Returns into a Compounded Performance Index

Summary

The document explains how to turn a sequence of periodic returns into a continuous index or equity curve starting from a base value. It distinguishes adding return increments from compounding them and gives the accepted answer: multiply the index by one plus each period’s return, cumulatively. This corresponds to the cumulative product of gross returns.

A numerical illustration shows why the distinction matters: an index at 0.7 followed by a daily loss of 10% becomes 0.63 after compounding, rather than 0.6 as a simple additive treatment would imply. The example makes the update rule concrete, though the post does not discuss cash flows, fees, or how to handle missing observations. The method applies when returns are expressed as periodic simple returns and the goal is to track compounded performance over time.

Key ideas

• A performance index is updated by multiplying its prior value by one plus the period return.
• Cumulative products of gross returns produce a compounded equity curve.
• Adding return amounts does not reflect the effect of sequential gains and losses on capital.
• The example illustrates that a loss applies to the index value at the start of that period.

Tags

# Convert returns into an index?


# Convert returns into an index?












What's the right way to take a series of returns and convert it into a continuous index? Let's say I want to show the performance of a strategy starting from 1, and adding on returns so that I get an equity curve, should I be using `cumsum(1 + returns)` or `cumprod(1 + returns)`?

## Answer by Owe Jessen (score 4, accepted)

https://quant.stackexchange.com/a/829

It should be cumprod. Say you have an index of 0.7, and a daily return of -10%. The new index should be 0.63, not 0.6.

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