# Good Debt, Bad Debt and Flawed Investment Return Data

August 18, 2008 by Mr. ToughMoneyLove

Filed under Debt and Credit, Investing

I can’t tell you how often I hear or read someone argue that they have “good debt.” This “good debt” argument is made to rationalize having a car loan, a HELOC or second mortgage balance, and even credit card debt. The argument goes something like this: “The money I have borrowed is being paid back at 6% interest. Instead of paying it back all at once, I have invested the money in the stock market which historically has an average annual rate of return of 12%. So I come out way ahead.” (Yes, 12% is the number I read most often.)

Apparently, this mythical number won’t die, despite recent and expected future market conditions.) There is one gentlemen using the screen name Phil on the MSN Money message boards who seems to have devoted his golden years to telling others how much money he has borrowed so he can invest and earn “12% average returns” in the stock market.

### The Arithmetic Average Rate of Investment Return Provides a Biased Outcome

This scenario reminds me of the this little parable: A man puts one hand on a hot stove and the other hand on a block of dry ice. A statistician approaches and after carefully observing and analyzing the temperature data, declares that on average, the man must be quite comfortable.

I am not suggesting that the average investor or debtor needs to be a statistician. However, before an “investor” defends his or her consumer debt based on historical average investment returns, he needs to develop a clearer understanding of his own argument.

The average annual rate of return is an arithmetic average calculated by summing the annual returns (growth rate) of an investment (such as a mutual fund) over a period of years (3 years for example), then dividing the total by the number of years. Thus, if a mutual fund has annual returns of 20%, -10%, and 10% over a three year period, the annual average return will be 6.67% ((20-10+10)/3.)

### You Should Use the Geometric Compound Annual Growth Rate

The problem is that an arithmetic average is an appropriate statistical measure only if the contribution of each of the data points to the performance outcome is independent of the other data points. In the case of investment return performance, using the arithmetic average produces an upwardly biased outcome. The correct statistical performance measurement for an investment is the “compound annual growth rate” (CAGR) based on a geometric average. A geometric average is an exponential calculation. In the example above, the CAGR is calculated as follows:

[(1 + .2) * (1 – .1) * (1 +.1^ 1/3 -1 = 5.91%

In the world of investment performance over a three year period, the difference between 6.67% and 5.91% is significant.

Let’s look at another example involving a longer period and a mutual fund with lots of variability in its annual returns. If your returns from the fund each year over a five year period were 90%, 10%, 20%, 30% and -90%, you would have an **arithmetic average return of 12%**. Awesome, you think. Now let us calculate the geometric mean return as follows: [(1.9 x 1.1 x 1.2 x 1.3 x 0.1) ^ 1/5] – 1. This gives equals** a geometric average annual return of -20.08%**. Ouch. This is quite a bit different than the arithmetic average we just calculated. In dollars and cents, the hard truth is that it is the correct number to use.

Lest we get too deep into the math domain, let me explain this another way. The arithmetic average annual rate of return that is frequently quoted does not take into account the order in which the investment returns occur and therefore can introduce error in the analysis. This can produce calculation errors for the overall plan. Assume that you start with a $1000 investment. Let us also assume that in the first year your growth rate (return) is -10%, leaving you with an account balance of $900 to begin the second year. During the second year, your return is +10%. Therefore, your arithmetic average annual rate of return is 0%. The “good debt” team would think this is OK because a 0% average return means you haven’t lost any money during the two years. But you have. The 10% return in the second year put only $90 of earnings back into your account (.10 x $900), meaning that you actually lost $10 over the two year period. That is because the second year results depend on what happened in that first year. This is a very elementary illustration that helps us understand why the geometric average rate of return is the correct metric to use. Your results will depend not just on what the average rate of return is over a period of time, but also the point at which you put your money into the market during that period.

In summary, when someone suggests that you invest instead of paying off “good debt”, please be sure that you examine the actual data, **correctly calculated**. Also do not forget to compare after tax returns, because paying off debt can provide an advantage in that department. Otherwise, the 12% return “rule of thumb” you use in your mind may end up being a rule of “dumb.”

While you are contemplating the concept of “good debt”, also consider this potential future tax benefit of paying off your mortage.

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So true…its important to remember that any negetive number is going to have a vastly bigger impact than a positive number. A while back I wrote about the the “10% myth” where if you have $1000, lose 10% then gain 11% you still have less than you started with.

Great article.

Unfortunately, I think only people who really go looking for this information are the people who tapped home equity, watch their initial capital decline in value, and go searching for answers later.

While I still agree with the “good debt” theory in principle, I think it’s foolish to tap home equity for the promise of higher returns. Your article on future tax benefit is one, but having peace of mind for the later years and passing on the home to heirs are just 2 possible others.

>>A statistician approaches and after carefully observing and analyzing the temperature data, declares that on average, the man must be quite comfortable.

LOL. You had me rolling on the floor with this one because you are so right.

I also believe that there is no such thing as good debt. No. Such. Thing.

Owing money is a disease in this country, right along with our lack of sustainability. We have all been trained to live so far beyond our means that it seems normal – when in fact, it’s a terrible life sucking problem.

For several years now my husband and I have refused to get a mortgage. Why? Because we’re in the process of saving enough money to buy our home outright, and not have a mortgage – ever.

You ought to see the look on people’s faces when we tell them that. They look at us renting a cheap home in a semi-questionable neighborhood, and they just don’t understand it.

As for me? I’m retiring at 50, and I will be sending my daughter to the best private schools available because we don’t live beyond our means.It took us a lot of years to figure that one out, and now that we have, we have a much brighter future.

Connie: Thanks for visiting and congrats on the no-mortgage plan. As Dave Ramsey would say, you are living like no other now so you can live like no other later. You should read my article on the future tax benefit of no-mortgage home ownership. You will feel even better about your plan.

Great job debunking the “average returns” myth.

I’m not sure what the situation is in the US, but in Canada debt generally isn’t tax deductible, but your investment returns are. Depending on whether it’s in the form of capital gain or dividends, a 12% (true) return is actually only worth 7-9% after tax, further reducing any benefit.

I believe that some debt can be “good debt” (or perhaps more accurately, “justifiable debt”), but “no debt” is even better. Just because a debt confers some sort of benefit doesn’t mean that I don’t want to pay it down quickly.

MoneyGrubber: Thanks for the visit and comment.

Matt and MoneyGrubber: I would be interested in hearing some examples of “good debt” that you referenced.

I view debt as good/justifiable if it makes me money. Debt incurred to start or grow a business or to purchase an investment property will usually fall in this category. I also tend to think of a principal residence mortgage and student loans as possibly falling in to this category, although this will vary depending on the circumstances.

Of course, it is far better to have no debt at all, and even “good debt” should be avoided or paid off if at all possible. But as far as debt goes, these types are better than most. It’s kind of like how a kick to the backside is “good” compared to a kick to the frontside…

Well written. I again agree.