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# Average Rate of Return & Actual Returns

There can be a lot of confusion when it comes to understanding how our investments make money in the securities market. Actual returns are all that matter but we often hear about average rate of returns.

If I look at a stock chart then I might see that stock XYZ started out at \$30/share in 2007 and now, in 2017, is at \$90/share. It’s not only important where the new end-point of this stock is but what it went through to get there.

If I bought 100 shares then I would have spent \$3,000 in 2007 to buy that stock. How that stock behaves year to year is called sequence of returns and the average of each year’s percentage is called average rate of return.

## Example 1: 6% Average Rate Of Return

We hear the term “average rate of return” quite a bit in the securities lingo. This is basically saying that over the lifetime of a particular investment (or an index), through all its ups and downs, the average return was 6% – as in this example.

So stock XYZ could have behaved in the following manner over those 10 years:

Yr 1 → +6%
Yr 2 → -3%
Yr 3 → +12%
Yr 4 → +10%
Yr 5 → +5%
Yr 6 → +9%
Yr 7 → +5%
Yr 8 → -8%
Yr 9 → +10%
Yr 10 → +14%

The average rate of return would be 6%. It refers to how much the stock grew on average each year, namely +6% a year on average.

So if I plug in 6% a year into a compound interest calculator using a starting balance of \$3,000, would I get the same result regardless of the actual returns of the market?

#### Using A Dollars Example For Actual Returns

Sticking to the above example, let’s see how that initial \$3,000 would have behaved in those 10 years.

Yr 1 → \$3,180
Yr 2 → \$3,085
Yr 3 → \$3,455
Yr 4 → \$3,800
Yr 5 → \$3,990
Yr 6 → \$4,348
Yr 7 → \$4,567
Yr 8 → \$4,201
Yr 9 → \$4,621
Yr 10 → \$5,269

So my initial investment of \$3,000 ended up with actual returns of \$5,269 after 10 years with the above mix of market ups and downs.

Even though there were some negative market years, I never dipped below \$3,000.

If I plug the initial \$3,000 into a compound interest calculator with a 6% interest rate and a 10 year duration then I would get \$5,458 as the final number.

So the way stock XYZ behaved in real life was off by 3.5% in the final account value. This may not seem like a big deal especially since we had an overall 75% gain over the 10 years.

## Example 2: 6% Average Rate Of Return

In this example I’m still using the 6% average rate of return but using different actual annual returns.

Yr 1 → +11%
Yr 2 → +10%
Yr 3 → -32%
Yr 4 → +2%
Yr 5 → +3%
Yr 6 → +15%
Yr 7 → +28%
Yr 8 → +13%
Yr 9 → -6%
Yr 10 → +16%

Using the compound interest calculator I would get the same result as in the first example, \$5,458. After all, the average annual rate of return is still 6%.

So could I guess that \$3,000 with an average 6% rate of return should end up at around \$5,458?

Yr 1 → \$3,330
Yr 2 → \$3,663
Yr 3 → \$2,491
Yr 4 → \$2,541
Yr 5 → \$2,617
Yr 6 → \$3,009
Yr 7 → \$3,852
Yr 8 → \$4,353
Yr 9 → \$4,092
Yr 10 → \$4,746

Years 3, 4, and 5 I had a loss in my account value where I dipped below my initial \$3,000 investment.

What’s interesting here is that the final account value is only \$4,746. Even though the averages of each year’s rate of return comes out to 6%. The final value of the portfolio doesn’t reflect this.

We still had an overall gain of 58% over the 10 years (not bad) but the compound interest rate method of predicting the future account value was off by 13%.

## So What Does It All Mean?

The point is that when you are using a compound interest calculation to estimate what your final value will be in the future, it might be helpful to be more conservative.

That said, I can also create a scenario where the final account value will be higher that what the compound interest calculator would result.

In the 2nd example the average rate of return was 6%. But if I were to plug in 4.6% into the compound interest calculator then I would get the final sum of \$4,746. That’s a difference of 1.4% or a difference of +/-25%.

Since these fairly representative examples that I gave, I think it would be safe to give yourself a wiggle room of 25% when calculating a potential average annual rate of return.

## Factors Unaccounted For

I didn’t account for tax-loss harvesting where you write off some losses every year on your taxes.

I didn’t account for any taxes owed on dividend income or sales of appreciated stocks.

We didn’t factor in inflation which could be beneficial some years. Though it’s almost always deleterious.

We didn’t factor in whether you’d continue to invest. If you continued investing in both examples through dollar cost averaging, then you would have performed more favorably since you would have bought the same stock at a discount during the years it was depreciated.

## Don’t Get Fooled

The final thing I want to say about securities investments in general is that they are great for false advertising.

It would be perfectly legit to advertise to you that a specific investment has an average annual rate of return of 6%. The assumption then would be that on average the investment returned 6% a year.

When in fact it matters how volatile the investment really was. This discussion is called your sequence of return.

I found a wonderful example how someone can go through great lengths to try to trick you even by going to the trouble of giving the same explanation I gave above.

If you look at the data set it’s simply repeated values in sets of 5. Here, they are comparing 3 different individuals and saying that they will all end up with the same final value of \$5.4 million when investing \$1 million.

But what investment can you think of that behaves in this cyclical manner every 5 years? It’s nonsense and it’s a sales tactic. Don’t get fooled.

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