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Math vs. Psychology

Personal finance is one of those fields in which our human brains seem tailor-made to fail.

Often, the best approach is to recognize our psychological shortcomings and make concessions to deal with them. For example, if Investment Approach A is mathematically superior to Investment Approach B, but we don’t have the psychological traits necessary to carry out A successfully, it might be better to go with B.

A few examples:

Asset Location

Mathematically, it makes more sense to put all of your fixed income investments in your tax sheltered accounts before putting any equity investments in them.

Yet it’s much easier to simply use the same asset allocation for each account. (For example, if you intend to have a 60/40 stock/bond allocation in your entire portfolio, use a 60/40 allocation in your 401k, in your IRA, and in your taxable accounts.)

Also, using the same allocation in each account eliminates a situation in which one account is extremely volatile (and therefore worry-inducing) because it has all of your stock investments in it. One single mistake–like bailing out of the market after a downturn–would eliminate any gains derived from tax-sheltering your bonds instead of stocks.

Debt Snowball

Mathematically, there’s no question that the best approach is to pay off debt in order of interest rate, regardless of balance. So, typically, that means consumer debt, followed by mortgage debt, followed by subsidized college loan debt.

Yet Dave Ramsey’s “Debt Snowball” method of paying off debt encourages people to pay off debts in order of size (smallest first), and it’s possibly the most successful debt repayment method ever devised. It takes advantage of the fact that frequent victories early in the process tend to motivate people to keep at it.

Invest First, Or Pay Off Debt?

Mathematically, you should invest prior to paying off debt anytime you expect to earn a rate of return that’s greater than the interest rate of the debt you’d be paying off.

Yet, as Matt reminded us yesterday, many people derive a real psychological benefit to being completely debt free. To value that mental benefit at zero seems to be a mistake.

How do you resolve it?

Do you find yourself running into these same math vs. psychology conflicts (or others that I didn’t mention)? If so, how do you attempt to resolve them?

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  1. Rick Francis says

    For the asset allocation- you could only view the combined portfolio. This would work best if you have a program like quicken that can download account information without you having to see the individual account balances.

    As for the debt problem- the division debt between creditors is a fairly arbitrary division. The division doesn’t change your total debt, only the different interest rates really matter. Why not create your own divisions, say units of $100. You could get a bunch of candy to represent the debt and then each time you pay off the debt you get to eat one of them. This division would give you small victories continually- and likely faster than the debt snowball and you could pay the highest interest first.

    -Rick Francis

  2. I recently wrote about the Debt snowball cost.
    It certainly depends on the mix of balances, the difference from high rate to low, as well as the dollar totals, but the cost of Dave’s method can be calculated. With the right combination of debt, he can cost you thousands. Some motivator.

  3. This is such an important topic.

    The most interesting aspect of it for me is how math and psychology inter-relate. I believe that the reason why math exercises are so popular in the investing field is that we are all scared to death to put our money at risk and so we turn to math to comfort ourselves. It’s psychology that is the dominant influence. We reduce things to numbers (even when that is not appropriate) to keep our fears at bay.

    And the fears of course influence how the math is done. People think of math as objective. But the construction of studies is highly subjective. It’s possible to design a study to say just about anything you want it to say. The idea with most investing “research” is to figure out a way to slant the numbers so that they say the things that our psychological fears demand that they say.


  4. There is no question in my mind that psychological comforts have value. The question to me is more about what figuring out to what that value actually equates. I think it is difficult for people to accurately prioritize psychological comforts vs. math unless they really know what the comfort will cost them, and it’s not always easy to put in terms of dollars and cents.

    For example, what is the potential cost of paying off your mortgage before investing? We can’t know the actual cost in advance, because we don’t know what future investment returns will be. There is even a chance it might ultimately cost less. But we can estimate the likely impact on other goals. Perhaps delaying savings now so you make extra mortgage payments and then saving more in the future translates to a reasonable likelihood you will have to work an extra year before you can retire.

    Based on that information, it’s easier to make an informed decision on the value of the psychological comfort of having your mortgage paid off early. Maybe you’d rater carry the mortgage longer if it means you could potentially retire a year sooner, or maybe an extra year in the workforce seems like a small price to pay to have the mortgage paid off quicker.

    A big psychological benefit that may have costs is asset allocation. If the stock market totally freaks you out, you can still retire without investing in it. You will likely have to save a lot more and/or save for a longer period of time. If you calculate out how much more you may need to save, you’ll have a better sense of the value of the psychological benefit of no stock market exposure. In other words, you can make an informed decision as to which is the greater sacrifice, having to divert a greater portion of your income toward savings or having to ride out more stock market ups and downs.

    On the debt snowball issue, there is another often ignored financial benefit to hitting the smaller balances first. You may be able to shrink your total minimum payment liability faster, which can be beneficial in case of financial emergencies, especially when you likely won’t have a substantial emergency fund in place because you’re focusing on debt reduction.

  5. Agreeing with Dylan, there is a definite advantage to being comfortable – and that means psychology matters.

    In my (option trading) business, there are certain strategies that have a track record of out-performance. But, no method out-performs all the time. If any individual investor cannot tolerate doing less well on occasion, I recommend that he/she avoid this strategy.

    Sure it’s better to adopt this method in the long run, but avoiding the short-term agony is worth something.

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