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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?

  1. Draw 4 3-year returns and just use first 10-year returns?
  2. Draw 3 3-year returns, and 1 1-year return
  3. Draw 3 3-year returns, and 1 "1-year" return but not over the full set of 1-year data points.
  4. Other ways?

Any help and intuition is appreciated. enter image description here

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

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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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