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.