Would you accept an average guaranteed return of 10% annually provided the guarantor got to set the actual annual returns? Most people would and they would be committing a serious error, one that people make every day. For example, you could make 70% one year, then lose 50% the next, then repeat for 5 cycles. Sounds great, doesn’t it? Well, here’s the outcome:
| year | return | total % returns | rolling balance |
| $1,000 | |||
| 1 | 70% | $1,700 | |
| 2 | -50% | $850 | |
| 3 | 70% | $1,445 | |
| 4 | -50% | $723 | |
| 5 | 70% | $1,228 | |
| 6 | -50% | $614 | |
| 7 | 70% | $1,044 | |
| 8 | -50% | $522 | |
| 9 | 70% | $887 | |
| 10 | -50% | $444 | |
| average return | 10.00% | ||
| real return | -5.56% |
Average stock market returns are touted by fund managers. This is essentially fraudulent. That’s because average returns are not real returns. Why? It’s a trick of the math – or maths, for our Brits. Average returns are calculated from the start time. Therefore, if the stock price goes up, the start price is lower and the return is positive. If the price goes down, the start price is higher and the return is negative.
Example: xyz at $100, drops 50% to $50. While abc at $100, rises $50. 50% return in both cases, one being a negative return. The problem is over several periods. For XYZ, the new price requires a 100% increase just to get back to the start point. Let’s say that happens. You then have returns of -50% + 100% = 50% positive returns. Over 2 years, it’s 25% average return. But wait – we’re back where we started! Real returns are zero.
In fact, if you’re interested I’d be happy to sell you a 10 year fund with guaranteed average returns of 100% annually. Here’s how I’d win: the funds would be locked up for 10 years. For the first 9 years, you’d enjoy watching your balance grow at 111% annually. It would feel great! Ah, but year 10 you would suffer a 100% loss.
| year | return | total % returns |
| 1 | 122% | |
| 2 | 122% | |
| 3 | 122% | |
| 4 | 122% | |
| 5 | 122% | |
| 6 | 122% | |
| 7 | 122% | |
| 8 | 123% | |
| 9 | 123% | |
| 10 | -100% | |
| average return | 100% | |
| Actual Return | -100% |
This is how most funds trick you. Obviously, this is an extreme case for illustrative purposes, but here is a more legitimate example.
| year | return | total % returns | rolling balance |
| $1,000 | |||
| 1 | 20% | $1,200 | |
| 2 | 19% | $1,428 | |
| 3 | 17% | $1,671 | |
| 4 | -40% | $1,002 | |
| 5 | 6% | $1,063 | |
| 6 | 33% | $1,413 | |
| 7 | 12% | $1,583 | |
| 8 | 11% | $1,757 | |
| 9 | 10% | $1,933 | |
| 10 | -25% | $1,449 | |
| average return | 6.30% | ||
| actual return | 4.49% |
It’s a typical statement that the stock market returns 10% or so annually, long-term, discounting inflation. But that’s not really true. The math deception shown here demonstrates why this is a deceptive practice. Keep that in mind when reading mutual fund prospectuses. And don’t EVER buy mutual funds. They almost always lose to vanilla index funds because of fees.
The distortions happen most aggressively with whipsawing and larger downswings. Obviously, a 100% downswing is definitive and irrecoverable, at least in terms of account balance. Possibly, there could be mitigation in the form of assets worth zero, still owned, which could conceivably return to positive territory.
Now, to be fair, an actual rate of return is a tricky formula to work out. The distortions of multi-year tracking combined with the distortions of downside percentages being different than upside may render the very idea meaningless. You could calculate year X – year 1, then divide by X, but that’s a total return divided by the number of years. It doesn’t account for compounding. I’ve not been able to find anything that does this function, but a strong financial math whiz probably could.
Conclusion
Average rate of return is a faulty metric, but it is used by the financial industry to make stock market returns appear higher than they actually are. Averaging the move in percent terms makes no sense ultimately. A 50% decline is equal to a 100% rise and it works in both directions.
