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 1 | Year 2 | Year 3 | Year 4 | Year 5 | Average return | |
| Investor A | 30% | -25% | -10% | 45% | 20% | 12% |
| Investor B | 15% | -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 1 | Year 2 | Year 3 | Year 4 | Year 5 | CAGR | |
| Investor A | $13,000 | $9,750 | $8,775 | $12,723.75 | $15,268.50 | 8.83% |
| Investor B | $11,500 | $10,350 | $11,385 | $14,231.25 | $15,654.37 | 9.38% |
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.
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