A Simple Math Question for Bankers

Think back to your high-school math class, and reminisce about this question:

“Train A departs from Union Station at noon travelling eastward to Halifax at a speed of 80km/hr. Train B departs three hours later from the same station travelling in the same direction at a speed of 100 km/hr. When and where will they collide?”

We strained our minds, and most came up with the conclusion that 15 hours and 1,200 kms from where train A set off, the carefree conductors would face a rude awakening.

Most of us were just glad to be done with the question, and probably didn’t think of it much further. But consider what was going on at one minute past midnight in this imagined world.

There were two conductors each told that they could depart Union Station at a certain time and speed towards their destination. Both had done exactly what they were told, with the predictably disastrous results. There was probably a track-side argument, with each side blaming the other. Possibly the conflict spilled back to Union Station, with blame being attributed to whoever was in control of the train schedules that fateful day.

One way to look at this is that there was a conflict. Each conductor was told to do something, and when they did the disaster struck. Laying blame at the end is difficult, as neither side did anything wrong. As outsiders to this problem we can see that if blame does lie somewhere, it is with the Union Station scheduler.

Now take yourself out of your math class and consider reality. We have a similar train wreck brewing in our economy.

Depositors go to their banks and put aside some money. They are made a promise: the ability to withdraw their deposit at a moment’s notice (i.e., on demand), and be paid the proceeds at the same value as when they made the deposit (i.e., par value). In layman’s terms, you get back what you deposited, and you get it whenever you want.

Bankers receive these deposits, and the law gives them a different set of privileges. Bankers too may make use of this deposit, and they use it to fund investment and lending operations. For example, in the modern fractional-reserve banking system your banker uses a portion (or fraction) of your original deposit to lend to a potential homeowner as a mortgage.

The conflict depositors and bankers are subject to should be apparent. They both have a claim to the deposit, but there is only one deposit available to satisfy both claims.

This usually isn’t too big a problem, at least not for depositors, as not all of them ask to redeem their funds at the same time. Thus, even though there is an oversubscription of rights to the original deposit at all times, this oversubscription goes unnoticed until many depositors redeem their money at the same time.

When this mass redemption occurs the conflict is exposed. Depositors expect to get their money back as per the original terms of the deal – on demand and at par value. Bankers expect to be able to continue using the money to fund their lending operations, and thus the money is not in their possession to return to the original depositors.

This is the case of the common bank run. A bank run is really just a simple outcome that results from when too many people have claim to not enough goods. The ire and angst that is generated during a run, whereby depositors are genuinely upset that the bank is not able to return their deposits, signifies that there is a conflict between the two parties.

When a bank run occurs, the primal question is “who to blame?”

With our original math question still fresh in our minds, let’s answer the question. Two parties are given conflicting orders (or rights). Each did as they were told, and the predictably bad result occurred. It is pretty hard to blame either of these parties for the outcome. Depositors and bankers are just abiding by the law. They don’t make the law, and although both sides may have knowledge that the law is inconsistent and creates conflict, they have to play with the cards that they’re dealt.

If we want to assign blame to someone, why not look at the institution that sets the rules of the game. The initial conflict of the oversubscription of claims to the original deposits is created by legislation by Parliament, and enforced by the Bank of Canada. Just like the scheduler at Union Station is responsible when two trains collide which he instructed to embark, law makers should be held responsible for the ire, angst and lost money when banks go bankrupt or bank runs result.

If Parliament and the Bank of Canada wanted to be proactive about this conflict, they would act now. Changing banking laws to outlaw fractional reserves would not only erase this conflict, but would harmonise those laws controlling banking relations with the laws that enforce other contractual relations in the economy. Doing so might just avoid a train wreck in the future.

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2 Responses to “A Simple Math Question for Bankers”

  1. Patrick Barron says:

    Very well presented. This is a good way to think about the problem, especially when attempting to assign blame for the subprime housing bubble and subsequent bust. The banks did make many loans that turned out to be bad, but who really was the instigator? The Fed, of course!

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