# 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.

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.

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.