## Monday, January 18, 2010

### Average Yearly Stock Return of 98% for 40 Years

Statistics can be very useful objective data to guide decisions. However, they can also be used to mislead. For example, did you know that the TSX Composite index of Canadian stocks has averaged a 98% return per year for the last 40 years?

One of the useful data sources that Canadian Capitalist pointed to is a spreadsheet of total returns of different asset classes maintained by Norbert Schlenker of Libra Investments. Using the total returns on TSX Composite stocks back to 1970, we find that \$1 at the start of 1970 grew to \$40.23 by the end of 2009. This a 3923% increase over 40 years, or 98.1% per year.

I can hear a chorus of “just a minute – that’s not how you calculate yearly returns.” Of course, I agree. We shouldn’t just take the total return and divide by the number of years. However, a motivated debater could probably find creative ways to justify this calculation and muddy the waters nicely. For example, 98.1% really is the correct percentage when TSX Composite returns are viewed in terms of simple interest rather than compound interest.

The most reasonable way to get the average yearly return is to find the percentage that compounds for 40 years to give the same total return. In this case, the answer is 9.68% per year. This is called the average compound return.

In this particular case it’s easy to see that the first calculation is misleading because the final answer is so ridiculous. A more subtle way to make returns look better than they are is to take all the yearly returns, add them up, and divide by 40. This gives an answer of 11.12% per year. However, if you started with one dollar and made this return every year, you’d end up with \$67.87, which is much more than the \$40.23 produced by the TSX Composite.

These different ways of calculating average returns aren’t necessarily right or wrong. It all depends on what you use them for. The problem is that people with a particular axe to grind will choose the calculation that helps support their argument rather than the one that makes most sense in the given context. This is how statistics can become misleading.

In most cases, the compound return method gives the most meaningful answer. Unfortunately, the calculations are a little more difficult for the less mathematically inclined.

#### 8 comments:

1. You must be one of those guys who answered the question

What is One A Plus One B ?

You'll never grow up to be a welder!

2. Thanks for the mention Michael. Other pet peeves are not using total returns typically by ignoring dividends from stocks or using the wrong benchmark (a small-cap portfolio being compared to the S&P 500). Happens often enough with people who have an axe to grind or a product to sell.

3. True Capitalist - gotta beware of the product to sell reports - their returns may be screwy.

4. CC: I suppose there is no limit to the number of ways to mislead with statistics.

5. Great minds must think alike. I just blogged about this about a week ago.

For those looking to do web searches the 9.68% I believe is called Compound Annual Growth Rate (CAGR) and the 11.12% is called the Arithmetic Mean.

6. Retirement Investing Today: You're right that when the compound return is calculated as an annual average (as I've done), then it is often called the CAGR. Another term for this is the geometric mean. Unfortunately, no term is safe from potential abuse. There is little to stop someone from computing returns in whatever way they like and then just calling it the CAGR or some synonym.

7. I find the same can be said with mortgages. I found a mortgage acceleration company that is marketing their product by saying that they can reduce the actual interest rate of the mortgage by making prepayments.

Far from accurate, but some people will buy into their way of thinking.

8. No Debt Guy: I guess that's like the car marketing where you either get 0% financing or cash back. The really isn't any such thing as 0% financing, but it makes for good marketing.