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I am looking at a company's financial report and there is a table in it that lists returns over different annualized periods. It ranges from 1 year to 20 years. Would a 2 year return in this table be defined as the average return you would get in two years based off previous returns, or is it the average return based only on the last two years of data?

Also, how is this calculated? Annualized returns are raised to the 1/n power, where n is the number of years, so would a 2 year return just be 2/n power?

Thank you.

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In your question you do not provide any reference. I believe that we are in front of two possibilities: annualized linear returns and Compound Annual Growth Rate (CAGR). If compounding is not mentioned, I would assume annualized linear returns.

$n$-years Annualized linear returns

$n$ = number of years

$ n * r_A = r_* $, where $r_*$ is the return over the $n$ years time span.

n-years CAGR

$ (1 + r_{CAGR})^n = (1 + r_*) $, where $r_*$ is the return over the $n$ years time span.

A few additional notes:

  • With "small" returns, linear returns approximate CAGR. In $ (1 + r) * (1 + r) = (1 + 2*r + r^2) $, if $r$ is "small", $r^2$ may be negligible
  • Fractions of years may be tricky: for example 1 year and six months leads to $n = 1.5$
  • A third type of returns exists: continuous compounding. I list continuous compounding here for completeness sake but I do not think, based on my experience, that it is used in practice to present results in a financial report. It is interesting to look at their relationship with logarithmic returns
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