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I was recently looking at a syndicated Real Estate investment that did some math to show what future returns might look like. The bottom line was that a $1,000 would turn into $2,360 after 10 years. They compute the cumulative annualized return therefore, as 136/10 = 13.6% on your investment. This seems correct to me, since annualized returns on investments that do not reinvest earnings is computed as the arithmetic mean of the gain in each year.

But how should I compare this to a mutual fund where dividends and capital gains are reinvested? Since compounding applies with such a mutual fund instrument, wouldn't I compute the real estate returns as (2.36)^0.1-1 = 9%?

In other words, if I want to compare this real estate opportunity to a mutual fund, shouldn't I view it as returning 9% and not the 13.6% that the brochure is telling me?

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    It’s an 8.966% CAGR. Average return in this case is nonsense. If you double your money in 10 years, it’s about 7.2%/yr, not 10%. Yes, for apples to apples, use 9%. – JoeTaxpayer Oct 14 '18 at 22:17
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Even though real estate returns (by this I assume you're meaning rent or lease income) don't technically "compound" like equity investments, there should still be some semblance of growth. Rent rates should increase due to inflation and market growth, so your return as a percentage of the value of the asset should be relatively stable. So using a CAGR of 9% would be appropriate. Bonds are treated similarly. Instead of using a flat rate of return, the yield is calculated as if the bond compounded, which is not the case in reality.

My guess is that this is some sort of sales material or seminar trying to get you to invest in something, and from a sales standpoint 13% sounds a lot better than 9%.

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Measures calculated for comparison purposes are only useful if they are consistent from basket to basket. So if you want to use ‘arithmetic mean’ as a measure to compare your various investments, you’d calculate them using the same approach regardless of their returns profile.

You can calculate different measures based on compounding, on mark-to-market returns each year, or on separate cash flow + capital gain, etc. But if you apply one measure to real estate and another to mutual funds, you might get a more realistic picture of the individual return profiles, but you’d lose the simple side-by-side comparison of the different products.

The following was added to address the change to the question.

If you’re looking for a measure based on compounding to compare with a mutual fund that reports performance with a compounding measure, here’s one. Given principal P and final amount A with annual simple interest rate R compounded over T years:

  • R = 10^{[log_10 (A/P)]/T} - 1

With your numbers, R works out to about 9%.

The bottom line is that to compare the performance of two funds, you need to use the same measure.

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