Skip to content
All library documents

Calculating Simple Returns from a Total Return Index

Article Quant Q&A · Author: Carol.Kar
Read the original

Summary

The document clarifies how to compute a simple period return from consecutive values of a total return index. Divide the change in the index by its previous value: this expresses the increase or decrease relative to the starting level. The reply distinguishes this calculation from taking the ratio of the two index levels alone, which gives the growth factor rather than the return after subtracting the starting investment unit.

The question also mentions log returns, which are calculated from the natural logarithm of the index ratio. The answer provides only the simple-return formula and does not discuss compounding conventions, annualization, missing observations, or whether an index series already incorporates dividends and other distributions. Those details matter when comparing return series, but for the stated calculation, the change-over-prior-level formula gives the simple return for each period. The exchange offers a concise definition rather than numerical examples or empirical evidence.

Key ideas

  • A simple return is the change in the total return index divided by its prior value.
  • The ratio of consecutive index levels is a growth factor, not the simple return by itself.
  • Log return uses the logarithm of the consecutive-level ratio.
  • The answer does not address compounding, annualization, or data conventions.

Tags

EquitiesStatistics
Full text
# Calculate the total returns from the total return index


# Calculate the total returns from the total return index












I have the `Total Return Index(RI)` for several companies.

I know that I can calculate the log retunrs with $ln(RI_t/RI_{t-1})$. Therefore my first guess would be to calculate the total returns like that:

$RI_t/RI_{t-1}$

Is this true?

I appreciate your answer!

## Answer by brian (score 3, accepted)

https://quant.stackexchange.com/a/9834

No, it would be $$(RI_{t}-RI_{t-1})/RI_{t-1}$$

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.