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Mathematically correct but psychologically wrong (johndcook.com)
99 points by fogus on Nov 2, 2010 | hide | past | favorite | 61 comments


Here's another strategy: break all your debts up into similar sized chunks. Draw a grid with all those chunks on a big sheet of paper, and post it up on the wall. Cross off the chunks as you pay them off (highest interest rate first). It's mathematically and psychologically correct!


Crossing off a chunk on your grid does not reduce the number of nasty letters and phone calls you get from creditors.


You only get those phone calls if you're not paying anything at all to the creditors and or/ignoring their phonecalls. If you talk to your creditors explain your situation and are making payments, the phone calls and letters stop.


If you've fully paid off a debt then even if you fail to make payments in future its not coming back to haunt you. Also even apart from psychological considerations there is how soon until a creditor is likely to institute proceedings against you - it's probably sooner for smaller debts.


I have a friend who used to use what he called "the hat system": when a creditor phoned to complain about his account, he'd explain that every month, he put the names of everyone he owed money to in a hat, and then draw names and pay them until his debt paying budget was used up -- and everyone who phones to complain doesn't go in the hat that month.


People in debt do strange things.


One sticky issue: you may not know what the interest rate actually is for the chunk you paid.

e.g.

    1. Charge $100 at the grocery store, 12% APR
    2. Pay off $10
    3. $200 Cash advance from ATM, 20% APR
    4. Pay off $10
Guess what, you have several $10 chunks to pay off, but at various interest rates. Most issuers pay down the lowest APR first, regardless of any chronological ordering. So if you know the policy, you should be able to figure it out, but if you continue to charge while you are paying down your debt, there could be a lot of chunk-juggling to maintain a sane view of what you owe.


> Most issuers pay down the lowest APR first

As of fairly recently, that's supposed to be illegal here in the US now (supposedly there are loopholes about "accidentally" giving people business instead of individual cards).


I think the real gem is at the end of the article:

"Many things that don’t look optimal are in fact optimal once you take the necessary constraints into account. For example, software that seems poorly designed may in fact have been brilliantly designed when you consider its economic and historical constraints. (This may even be the norm. Nobody complains about how badly obscure software was designed. We complain about software that has been successful enough to criticize.)"


i thought this was a great point too.


The thing is, to me (and the HN community), this seems blatantly wrong. Why do we need a psychological hack to motivate us, when we know what the optimal solution is?

However, the majority of people who are drowning in debt got there because they weren't looking for the optimal solutions to their cash flow problems. Seeing their debt snowball shrink (or grow, I guess) in measurable steps is what provides the motivation to proceed. And in reality, the difference between your highest and lowest interest rate is probably 15-20% or so. Not enough to make or break you (and if it is too much of a difference, you are probably on your way to bankruptcy anyways).

P.S. Think of the variable cost savings of stamps and bill paying time! </sarcasm>


Psychology is the science of the mind. I don't know about you, but I have a mind. Therefore psychology affects me.

I know, I know. My being a member of HN should make me above psychology. But apparently it affects every human being. Annoying isn't it?


Nobody is above psychology, although it affects people differently. However, as a member of HN I would expect that you would be above psychological hacks (as in, you can think beyond them, and make decisions based on your own reasoning, rather than relying on them as a crutch).


At least in terms of finance. People here may need tricks against procrastination, though.


Fortunately (in this example) the smallest debt usually has the highest interest rates. Usually people's smallest debt is their credit cards, the next smallest their car loans, their next smallest their student loans and their least smallest the home loan.


In the UK student loans probably have a smaller interest than a mortgage.


Except that most people I know of have multiple debts on most of these categories.

- 4 credit cards - 2 car loans - 2 student loans - 1 mortgage

Individual debts don't follow the same distribution as the categories.


In which case, just put them all on the mortgage (if you have equity). Usually the best interest rate.


Most people you know have 9 loans?


That was an example of a common distribution. Some of the debts are things like a $500 credit card balance.

Of course, I was thinking mostly young married couples, so it may not hold outside that demographic.


9 semesters of college on loans is 9 loans. Sometimes 18.


Ah, in the UK you just pick up a single student loan to cover all your tuition.

Thinking of most people I know whose finances I roughly know about... I'd say the average is one credit card (probably just $500-$1000 limit, not neccesarily maxed out, often paid off in full each month), no general loans, and a mortage and/or student loan depending on their need for them.


you can make the snowball strategy be the optimal strategy by simply picking the right cost function.

optimality entirely depends upon your cost function. so pick the right one and optimise. the author clearly has one in mind---paying out the least money to eliminate the debt. but this doesn't seem the right one to me.

for example, i would much rather pay off small debts to friends (which typically have 0% interest) over larger, higher interest rates to banks, simply because there's a social cost owing money to friends, whilst it's kind of the purpose of a bank.


Also getting phone calls and letters from your creditors are a psychological cost to most people. The snowball system minimizes the number of outstanding debts (and thus probably also the number of creditors) the fastest.


From an economics point of view, it's basically another way of saying that wealth maximization is different from utility maximization. While the two are frequently correlated, it's not necessarily so.

The snowball strategy could be perfectly rational for people who gain more utility from the small but frequent accomplishments of paying off debt earlier than they do from maximizing their overall lifetime wealth.

It's not what I would do, but as they say, there's no accounting for taste.


I've had this argument with my parents on saving for retirement vs paying off loans.

It would seem like one would prioritize savings, but due to the variance in interest, the net gain is in favor of paying off high interest loans vs building low interest savings.


It is better mathematically to pay off debt than to save (since debt is usually costing you more than the opportunity cost of not saving).

Still, from a practical standpoint, you shouldn't put ALL of your disposable income towards debt, as you will want some sort of emergency fund to keep you afloat when your car breaks down. Otherwise, you go rely on more debt. Spending saved money is cheaper than spending borrowed money.


Assuming you have a credit card, you should pay off all debts worse than credit card debt, and all credit card debt, saving no money. If your car breaks down, charge it. It's only if you have a source of debt that's more pleasant than credit card debt, and which you can't easily get back in case of a car-breakdown-forcing-credit-card-use that you'd want to save some debt to keep cash around for emergencies. And even then you'd want to look at the extra interest you're paying compared with the risk of emergency and the difference between the interest rates of that debt and your credit card, and a lot of the time it'll be like (IF i have a car breakdown, which is 5% likely, then I'll end up paying 5% higher interest on the repair money for a few months ... this is NOT worth failing to repay some debt immediately which will cost in interest a lot more than the expected loss of that incident)


Absolutely, I try and keep about a 2k float, but aim on building that higher.

And my car did just break down hard enough for it to be junked.


At a very general level, accumulating savings while carrying debt only makes sense if you can get a greater (risk-adjusted) return on your savings than the interest rate you need to pay on your debt. So if your return on your savings is lower than the interest on the debt, paying off your loan with your savings is like getting the difference between the return and the interest rate for free -- i.e. you should definitely pay off your debt.

Of course, there are lots of complications to this general rule in the real world. The US, at least, taxes the returns on your savings (capital gains and dividends) and gives you tax benefits for your debt. When saving in a 401k, employers often match your contribution, which amounts to a guaranteed 100% return on your investment for the portion that's matched.

Liquidity is also a concern. For example, if you have a 30-year mortgage on your house at 5%, you probably wouldn't want to put all of your savings into paying down that mortgage since you can't get it out again until you sell your house. If you have a sudden need to raise cash, you'd need to get a home equity loan, which can be tricky if your house value has plummeted or if interest rates are high.

Thus the full answer is that, well, it depends on a lot of life factors, and although paying off your debts is generally good advice, especially for very high interest loans like credit cards, there are many factors to consider other than the spread between the return on your savings and the interest rate on your debt.


It would seem like one would prioritize savings, but due to the variance in interest, the net gain is in favor of paying off high interest loans vs building low interest savings.

Sorry, but you're wrong. Your retirement savings should go into relatively high risk investments with good long term average returns, such as the stock market. At this point the average return on investment for retirement savings exceeds the interest rates on your loans, and therefore the net gain is for preparing for retirement. (Unless, of course, you're facing a short term cash crunch where long term returns become irrelevant to your utility.)


Am I only one who was surprised to see not one reference to any research or proof of his claim? That is, anything that shows a situation where people in, say, equal debt situations, 1/2 were given snowball, half given pay big ones first, then measure debt reduction, satisfaction, perception of accomplishment, etc? Or even just a survey? Anything?

I've heard snowball as a great approach... but without some proof, I wonder if it truly is "...a problem with an obvious but naive solution". Behavioral Economics theorizing aside, even one example from a simple survey or academic study would do much to support his overall point.

Otherwise, his "Many things that don’t look optimal are in fact optimal" comes into question, and I don't want my silly need for proof to get in the way of that essential point, which, come to think of it, I firmly believe even without much proof. But still...


I can't offer technical proof, but the snowball method saved me. Psychologically, getting rid of the easier debts wasn't the biggest factor though. The increased cash flow from the lack of those payments allowed me to make payments on larger debts that actually felt like they were making a dent. That was an awesome feeling.


The mathematically (but not morally) correct way to deal with big debts is to figure out how many cents on the dollar they can get back from you with a debt collection agency and offer them slightly more than that.


If we're ruling out ethics, the optimal approach would be to simply not pay the debt back.


I always find it fascinating how poorly the brain conceptualises various problem spaces, specifically in math related fields. The Monty Hall problem is an excellent illustration and just shows how irrationally our minds operate.


And the lottery. We misestimate probabilities, particularly when they are extreme (near-certainty and near-impossibility). That gap between how likely an event 'seems' and its real probability explains the lottery, not wearing seatbelts, smoking, witchcraft, the monty hall problem...


Possibly but then you must also consider the psychological effect of consciously making an illogical decision... which results in habitually justifying irrational behavior


I think the people giving this advice know enough psychology to know it works (defined as: likely to get people out of debt), and enough mathematics to know it's not optimal.

As to the people in debt: if they always consciously made (suboptimal) decisions, most of them wouldn't be in debt.


So the way to overcome conscious suboptimal decisions is to keep making more conscious suboptimal decisions? That is what I have been doing wrong... stupid me for trying to change.

Jokes aside, you are probably correct, I have always been torn between trying and failing to be perfectly rational versus doing suboptimal emotional things.


No, the way to overcome suboptimal decisions is to make better decisions, even if they aren't fully optimal.


But it an optimal decision is even better than a "better decision that isn't optimal"


I had three student loans, and I am doing it the mathematically correct way. I paid off the second-largest with the highest interest rate before it came out of deferment, and am currently working on 2 and 3, putting all the spare cash into the one with the biggest interest rate.

It's really not psychologically difficult at all, except it's slightly more effort to pay two bills each month instead of one (since I could have afforded to pay off the smaller but lower interest rate one already had I not put that money into the higher interest rate one.)


Can't you instruct your bank to automate the paying?


Yes, but I'm usually paying more than the payment amount on the high interest one. How much has to be done manually, since my income fluctuates.


It would be nice to tell the bank to just pay anything in your account above a certain balance.


This is a matter of semantics, but if the "mathematically right" answer is also the wrong answer, than your math is wrong. Either you messed up the calculations, or (as is the case here) you started off with invalid assumptions. In this case, the invalid assumption is that you're psychologically able to do whatever will pay off your debts in the most money-maximizing way.


The main conclusion is definitely right. You need to take the constraints into considerations.

However, imo the optimal strategy to pay off debt is to reduce the total amount of payments whenever you have money to pay after the necessities of life are taken care of.

Simple :)


I believe this principle is central to any successful attempt to lose weight. The physiologically optimal approach to losing weight will fail for most where a seemingly less effective approach might succeed.


Could you elaborate?


>Clearly the optimal strategy is to pay off the debt with the highest interest rate first.

Clearly? This is plainly wrong. Let's say we have two debts: $1000 with 0.7% interest rate and $40 with 0.8% interest rate (these rates are daily). Assuming our daily salary is $19, having payed off $40 debt first, we will never be able to pay off the $1000, as the interest exceeds our salary. The other way around, we pay off $1000 (then $2546.5) debt after 135 days, and then a week later we pay off $40 (then $128) debt.

It is not the sole interest rate, but the ratio between interest rate and debt that matters.


Huh?

    Start: $40 @ 0.8% ($0.32 daily) + $1000 @ 0.07% ($7 daily)
    day 1: pay $19 on the small debt; $21.32 remain (and $1007 on the other)
    day 2: pay $19 on the small debt; $2.49 remain (and $1014.05 on the other)
    day 3: pay off the small debt ($2.51) and pay $16.49 on the remaining one ($1004.66 remain)
    day 4..n: pay $19 on the remaining debt
       balance goes as X=X*1.007 - 19; paid off in 67 more days
Perhaps it would help instead to think of them as investment opportunities: opportunity A pays 0.8% and has a limit of $40 invested, opportunity B pays 0.7% and has a limit of $1000 invested. First you max out opportunity A, then you start putting money into opportunity B. Ignoring opportunity A means you miss out on up to $0.04/day.


Your math is wrong, and I don't think it's possible to fix it and get the conclusion you want (because you should think about your total debt, and how much it goes up each day, when figuring out if you can keep up or not).

The daily interest on $1000 with 0.7% interest is around $7. Waiting a few days to pay of the smaller debt will not make it exceed $19.

Edit: Were you banning partial repayments? Most debt (I think) is not like that, but maybe it makes your math work


>Were you banning partial repayments?

Yes, I were. If partial repayments are allowed, it is indeed the best approach.

>The daily interest on $1000 with 0.7% interest is around $7. Waiting a few days to pay of the smaller debt will not make it exceed $19.

Of course not, but they will exceed $19 before you will be able to pay it off as a whole -- it will take more than 130 days.

Maybe I should make my statements clearer, so that next time I do not get downvoted for being misunderstood.


> Edit: Were you banning partial repayments? Most debt (I think) is not like that, but maybe it makes your math work

It does make it work assuming that partial repayments are not allowed, and interest is added to the principal (and paid off at the end) instead of being paid as it comes due. I don't think either of these is realistic, especially the second one. Also if I assume a savings account paying even 0.1%, it goes back to being payable in either order.


You skipped the Zero-th step:

Step 0: pay your minimum on all debts.

That prevents your principle amounts from increasing


Letting the principal on low interest debt increase in favour of paying off a high interest bearing one earlier, is actually a good idea financewise.


presuming, of course that you can do so without penalty, yes. But there are very few source of credit which will let you get away with deferring payments penalty-free.


That's an interesting boundary case, but you are arguing the proper way to pay off a debt for someone who is clearly in a bankrupt situation.


When dealing with people mathematical accuracy requires psychological ignorance.


I get more psychological assurance by paying less overall, thus I feel better paying off the higher interest loan.




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