# Use Math To Alleviate Fear Of Stock Market Volatility

Over the last ten years, the S&P 500 had returns of 26%, -37%, 5%, 16%, 5%, 11%, 29%, -22%, -12%, and -9%.

After seeing this volatility, you might just think twice about putting your hard-earned money in the stock market. Or if you already have money in the market, looking at these fluctuations might cause you to lose sleep at night!

### A Different View

Fortunately, if you were able to think about these returns in a different way, you’ll probably feel better about them and be more willing to take on the risks of the stock market.

Specifically, if you could average out these returns over time, you’d come up with a single percentage over the same period.

Before we get into the details, I must admit that I’m a nerd, and I like to crunch numbers! So in this post, you’ll see how to calculate the annualized return of the S&P 500 over any period of time. Don’t worry, it’s not rocket science. It’s pretty simple actually.

And since I believe we should be investing for the future, we should have a long-term view. So in this example, we’ll look at the returns of the S&P 500 from the last 30 years. Take a look below.

[table id=1 /]If this table doesn’t look too pretty to you, take these following steps to average out the annual returns.

### 6 Steps To Calculating Annualized Returns

- First, convert the percentages into decimal form by moving over the decimal two digits to the left.
**(26% = 0.2646, -37% = -0.37, etc.)** - Add 1 to each number.
**(26% = 1.2646, -37% = 0.63, etc.)** - Multiply all the numbers together.
**(1.2646 X 0.63 X . . .) In this example we get 24.39** - Take the Nth root of this number, where N is the number of years you’re averaging. You can do this by raising the number to the power of (1/N). We’re averaging 30 years in this case.
**[24.39^(1/30) = 1.1123]**

- Subtract the result by 1.
**Get 0.1123** - Move the decimal two digits to the right to get the percentage.
**Get 11.23%**

### So over the past 30 years, the S&P 500 returned an average of over 11% each year.

Of course, past performance is no guarantee of future results. But if you stick with the investment for the long haul, you’ll more than likely achieve a good return – a return that’s higher than those achieved with bonds and CD’s.

Now, picture the table above this way.

[table id=2 /]

Thinking about it this way doesn’t seem as random, does it? Doesn’t this table look more pretty?

Hopefully, knowing how to calculate the annualized return will give you more confidence when you’re investing over the long term. Now you’ll be able to withstand the swings in the stock market that can be severe at times.

### The Power of Dollar Cost Averaging and Compound Interest

In this case, if you started investing in 1980 with just $100 a month every month for 30 years, you’d end up with **over $295,000 at the end of 2009!** Even though you only invested $36,000, through all the market ups and downs, **you still earn over $259,000 on your money.**

This demonstrates how simple successful investing can be. The important points are to invest early, invest consistently, and developing the discipline to stick with it through the market ups and downs.

**Now that you know how annualized returns are calculated, does this make you more willing to invest in the stock market? Does it help ease your concerns about stock market volatility?**

This article was included in the Carnival of Personal Finance during the week of May 31, 2010. Check out A Gai Shan Life’s blog for a variety of great articles!

Darren,

I am enough of a math nerd to be intrigued by the process of calculating annualized returns, but not enough of a math nerd to understand why the math works. Still, it is very helpful to see those averages over a 30 year period. Like you said, we can’t predict the future based on the past, but seeing this math makes me want to continue to invest regularly over a long period of time. Good stuff.

Joe – Thanks. I’m not sure WHY the math works, but are you asking HOW it works? I can send you the excel file that I used to calculate the numbers, or perhaps a screenshot if you’d like to see it. Rather than the normal arithmetic average of adding up the returns and dividing by the years, it’s a geometric return that has a few more steps to it.

Regardless, investing over the long-term as you said is the key.

Darren,

Thanks for offering to send me the excel file you used to calculate these numbers. I will gracefully decline. Part of me wants to study it (the math nerd) but the practical part of me tells me I can just accept the results and leave it at that. Still, I had never seen those calcs before and really appreciate this post showing how to do it.

Dave Ramsey has been saying for years that the stock market has averaged 12% return over the past many (75?) years. Based on the math of this post, I can see how he is probably right.

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Nice presentation on something every investor should know.

Thanks DIY Investor. I agree, knowing this will help them for the long term.

Thanks for doing the work. I noticed there’s only been one period where the Dow fell 3 straight years. It finished 2000 at 91% of its 1999 value, finished 2001 at 88% of its 2000 value, and finished 2002 at 78% of its 2001 value. Multiply it all together and it’s only a percentage point or so removed from how much the Dow fell in 2008 alone.

Greg, thanks for stopping by. I haven’t researched the performance of the Dow, but my guess is that over time the annualized returns are above average too.

Thanks for pointing out those stats, and good luck with the new book!