The Risk of Not Arbitraging

Comments are more than welcome – please take a moment to comment.

While I was traveling on business recently, my wife called one morning to tell me we had lost electricity in the house, and at the end of our discussion I reminded her to call the power company to report the outage. “Oh, the whole neighborhood has been out of power for hours – I’m sure someone has called by now” was her reasonable answer. But on second thought, I wondered “what if the reason that you’ve been out of power so long is precisely because everyone assumes that someone else has called, so no one has actually called?” I figured that given that it doesn’t cost too much time to call the electric company (but perhaps lots of frustration), it’s probably worth giving them a call so I repeated the suggestion. A few minutes afterward, I got this text from my son: “You were right, no one has reported an outage…Mom asked me to text you.” Even though everybody on the block had a vested interest in calling and ending the power outage, it took my wife’s call hours later to let them know that there was a problem [why they don’t have sensors to monitor this sort of thing is the topic for some other blog]. But most people, quite clearly, didn’t call, presumably because they also thought someone already had. The same psychological phenomenon – expecting someone else to do the deed – has been shown to prevent people in a busy city from helping someone who is laying on the sidewalk, possibly suffering a medical emergency, even in broad daylight. Psychologists tell us that if you ever find yourself losing consciousness on a busy city street, the best things you can do to save your own life is to get someone’s attention – anyone’s – and look them in the eye and tell them “get me help.” The combination of eye contact – to make it personal – and an authoritative tone might just save your life. Otherwise, you could lay there dying as hundreds or thousands of passersby assume that someone else has or will stop to help you.

Applying this to risk is pretty straightforward – through the notion of arbitrage. One of the rules of unbehavioral economics (my new term for traditional economics) is that there is “no arbitrage.” The idea is simple – prices of goods have to be related in a way that no one can make an instant and riskless profit. For example, if apples are selling for $1 a bag in NYC and it costs 10¢ to transport them to Philly (which otherwise has no apples), then the price of apples in Philly (ignoring taxes and other factors) has to be $1.10. Unbehavioral economics maintains that if the price is anything higher, then an enterprising person can “arbitrage” this market – making an instant riskless profit by buying them in NY for $1.00, paying the 10¢ to get them to Philly, and selling them there for $1.10. Makes sense. But someone had to actually make that riskless profit – by shipping them from NY – in order for the price in Philly to go down to $1.10!

The reason that the arbitrage argument works is that in many cases, somebody actually will do what it requires to take advantage of the opportunity, and the result is that prices move towards that “no more arbitrage available” point. Maybe that’s a better term for economists to use: instead of “no arbitrage” it should be “no more arbitrage.” Why? Because there had to be someone taking advantage of the arbitrage in order to get the prices to where they “should be.” If nobody did, then there’s no reason to expect the price in Philly to be $1.10.

The risk is that we all behave as if someone else has already make the riskless profit – has already arbitraged the riskless profit away. In other words, the risk is that we behave as if arbitrage opportunities don’t exist (because someone else has already taken advantage of it). But reality is that some human had to do it. Why shouldn’t it be you who gets that riskless profit? I’ll wager that it’s the same reason you didn’t call the electric company the last time you had a blackout.

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