Stop Using Arithmetic Returns!

Summary:

  • Arithmetic means ALWAYS overstate investment returns over time
  • Negative returns are actually fractions less than 1, not negative numbers
  • Avoiding drawdowns and reducing volatility can enhance your returns

Two people are each investing $10,000. Their returns over five years are detailed in the table below.

Year 1Year 2Year 3Year 4Year 5Average return
Investor A30%-25%-10%45%20%12%
Investor B15%-10%10%25%10%10%

Investor A makes great returns in 3 out of 5 years. Investor B never makes more than 25% in a given year, but has only one losing year of -10%. So who ends up with more money at the end of the five years?

Investor B! Have a look at the balance of their portfolio after each year.

End of Year 1Year 2Year 3Year 4Year 5CAGR
Investor A$13,000$9,750$8,775$12,723.75$15,268.508.83%
Investor B$11,500$10,350$11,385$14,231.25$15,654.379.38%

Investor B finishes with more money despite having a lower average return and trailing Investor A in 60% of years.

Taking the average of returns, often referred to as the arithmetic mean, always overstates the true performance of a portfolio. Addition gives equal weight to positive and negative numbers, meaning a 50% loss is canceled out by a 50% gain.

With a function like compound returns, the results of each year multiply together. And remember, we are multiplying fractions/decimals rather than positive or negative numbers. A 25% drawdown is the equivalent of multiplying your principal by 3/4. To cancel fractions (and get back to even on our investment), we need to multiply by the inverse of that fraction, in this case 4/3. That means earning 33% on our investment!

The rules of multiplying fractions gives a drawdown more weight than an equal advance in percentage terms. As investors, we would be wise to think in terms of multiplication rather than addition.

Thanks for reading! Comment below if you have anything to add!

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