We are bombarded by information all day, every day. It’s especially hard to process all the business, political, and technical information about the financial world if you don’t live it like I do. This is why I’m starting a new series ‘What you need to know about the financial world in just 2 minutes’. Okay, I’m still working on the title, but you get the idea. Here’s August’s edition!

-Through the end of July, the stock markets (other than the NASDAQ) are flat. 2013 and 2014 brought us an average S&P 500 return of 22%. Ha. Not happening again this year. You’re going to have settle for somewhere in the 8% 3-year average range.*****

-Gas prices are falling. Sub-$2/gallon gas is on the horizon. Be sure to pass the savings onto your financial priorities, such as debt-reduction and savings.

-Apple stock is taking it on the chin (that’s bad). Don’t be surprised if many of your mutual funds (likely inside your 401k) are down on your next statement. Apple is one of the most widely held stocks in the world. You’re likely to own it somewhere in your portfolio, whether you thought you owned it or not.

-It’s student loan season. If you get student loans, then you may also get what’s called a student loan refund check. It’s toxic. Don’t cash it. Don’t deposit it. Send it back. You don’t need it.

-Airlines tickets are super-cheap right now. If you need to buy tickets, don’t wait until September or later. I bought a multi-city ticket from Indy to Denver to Dallas and back to Indy again, the other day, for $220. That’s insane!

-Interest-only mortgages are back. THEY HELPED DESTROY THE ECONOMY IN 2008. Sorry for yelling. Don’t get one. If you need an interest-only loan to make the payment fit into your budget, you can’t afford it. You should almost always stick with a 15 year conventional mortgage.

*****I calculated this incorrectly. If the market ends flat, the market will have average 14% over the last three years.

Peter Dunn a.k.a. Pete the Planner® is an award-winning financial mind and a former comedian. He’s a USA TODAY columnist, author of ten books, and is the host of the popular radio show and podcast, *The Pete the Planner Show*. Pete is considered one of the foremost experts on financial wellness in the world, but he’s just as likely to talk your ear off about bass fishing.

Hi Pete,

Regarding your statement, “2013 and 2014 brought us an average S&P 500 return of 22%. Ha. Not happening again this year. You’re going to have settle for somewhere in the 8% 3-year average range.”

This is hopelessly wrong on purely mathematical grounds. As the term is commonly used in the investment industry, “average annual return” is a geometric average of individual return rates. (According to wikinvest, it’s “the de facto method for comparing the performance of investments with liquidity.”)

This means that in order for your claim to be true, this year’s market would have to go *down* by about 15%. (The math is pretty simple. Let x be the return for this year. Then we have (1.22)*(1.22)*x = (1.08)*(1.08)*(1.08), which gives x=0.85. Here I wrote a 22% gain as the number 1.22, and so on.) I doubt very much that this is what you are really predicting.

Maybe you were inadvertently using the simpler arithmetic average. But no! In that scenario this year’s market would have to be even more horrible, down by 20%. (Here’s the math: (22+22+x)/3 = 8, which gives x = -20. Here I’m using x to represent the percentage return.)

It’s difficult to guess what computation you did to arrive at the number 8%. Maybe you estimated this year’s return as 2% (fair enough) and then calculated x = (22%+2%)/3 (OMG) which indeed gives x = 8%.

Can you explain?

Steve,

Thanks for swinging-by the blog, and thanks for your comment. I used the geometric mean. Over the last two years the S&P 500 has done the following – 2013: about 30% 2014: about 14%.

In order to justify my “about 8% over three years” comment, the market would need to return about 1.25% in 2015.

The geometric mean of 30,14,1.25 is 8.06714

There’s the math.

I’m not “hopelessly wrong” this time around, but I usually am on most other topics.

Hi Pete,

Thanks for responding so quickly. I really appreciate it.

You’re right that the geometric mean of 30, 14, and 1.25 is about 8. However, that’s not the right way to compute the geometric mean of the percentage returns 30%, 14%, and 1.25%. First you have to convert the percentage returns R to (1+R/100) and only then take the geometric average of several years.

This can make an enormous difference, as two simple examples easily illustrate. Suppose this year’s market was actually flat, so that the return R was zero. If you repeated your calculation using zero instead of 1.25, you would obtain zero as the 3-year average. That’s obviously wrong. (If it’s not obvious then consider a more outlandish example. Suppose the market returned 25% every year for 30 years and then was flat in the final year. Your calculation would again give zero as the 30-year average. But a first-year investor would have nearly 1000 times as much money as she invested at the start of this incredible run!)

A second example: suppose the market actually went down this year, so that R is negative. Now your calculation runs into serious mathematical trouble, because you have to take the cube root of a negative number (the product of two positive numbers and one negative number).

Let’s return to the gloomy, although plausible prospect, that this year the market remains nearly flat and indeed returns only 1.25%. What is the correct 3-year average of years 2013 through 2015? The answer is easily obtained by typing the following into google: (1.3*1.14*1.0125)^(1/3). The answer is 1.14. Since this represents (1+R/100), we see that the 3-year average is actually 14%. Not bad at all!

You’re right. https://petetheplanner.com/i-was-wrong-steve-e-was-right/#sthash.gee9v96h.dpbs