Estimating Ten-Year Returns from Three-Year Return Data

Summary

The document asks how to construct a ten-year return when the available observations cover three-year periods. It highlights that simply compounding three such returns spans nine years, while combining a fourth full three-year return overshoots the target. One response suggests annualizing a three-year return and extrapolating it across ten years. Another proposes recovering monthly returns when the supplied series includes overlapping windows that begin before a full three-year period has elapsed, then calculating rolling ten-year returns from those monthly observations.

The answers depend on what the data actually represent. If only completed three-year returns are available, they generally do not reveal the intervening monthly path, so an exact ten-year rolling return cannot be reconstructed from them alone. Annualized extrapolation imposes a constant rate assumption and is not equivalent to observing ten years of compounded performance. The thread raises the key data-availability question but does not settle which method fits the asker’s series.

Key ideas

• Three consecutive three-year returns cover nine years, not ten.
• Annualizing a three-year return and extending it assumes a constant annualized rate.
• Overlapping partial-period returns may allow recovery of monthly returns if their construction is known.
• Completed three-year observations alone generally do not determine exact ten-year rolling returns.

Tags

# Compound 3-year returns to obtain 10-year returns: How to do?


# Compound 3-year returns to obtain 10-year returns: How to do?












I have 3-year returns at a monthly frequency, snippet below. How to compound the 3-year returns to obtain 10-year returns (since the cumulative product of 3 3-year return would be the 9-year return).

What is the best way to do it and why?

- Draw 4 3-year returns and just use first 10-year returns?

- Draw 3 3-year returns, and 1 1-year return

- Draw 3 3-year returns, and 1 "1-year" return but not over the full set of 1-year data points.

- Other ways?

Any help and intuition is appreciated.

## Answer by Ashish Garg (score 0, accepted)

https://quant.stackexchange.com/a/43315

You can annualize your 3 year returns and then calculate the 10 year returns as the simple linear extrapolation using the annualized returns.

## Answer by mperlow (score 0)

https://quant.stackexchange.com/a/42035

If 3 year returns start at t1 (i.e. the first "3 year return" is a one-month return), then you can back into the individual monthly returns. Once you have monthly returns, you should just be able to take 120 month rolling periods. This does not work if you are only provided 3 year returns once all 36 months are available.

Do you have 1 year returns as well?

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