Wednesday, February 2, 2011

A Savings Account for Risk Lovers

If you've ever purchased a lottery ticket, enjoyed a trip to the casino, or taken part in a cash-prize March Madness pool, chances are that (like me) you are secretly a risk-lover. OK sure, you probably take great care in managing your investment portfolio, making sure not to take on too much risk for your age and income level, or perhaps you have hired someone who you trust will do this for you. Deep down though, you love risk - maybe not all risk, but at least risk that involves a relatively small upfront cost and a small, but positive, probability of a relatively large payout.

An Economist named Maurice Allais documented this phenomenon when he mailed out a survey to his economist collegues asking them to choose between two lotteries under two different circumstances.

First, you must tell me (without thinking, or trying to figure out the "right" answer) which of the following lotteries you would prefer.

A: I will give you (straight up) 1 million dollars.
B: I will give you
$1 million with a probability of 89%
$0 with a probability of 1%
$5 million with a probability of 10%

Have you made your choice?

Good. Now I have another, somewhat less generous proposition for you. Which of the following lotteries would you prefer?

A: You get zip, zero, nada with a probability of 89%
I will give you $1 million with a probability of 11%
B: You get nothing with a probability of 90%
I will give you $5 million with a probability of 10%

Got it?

OK. Now if you picked the same letter of lottery both times (A and A) or (B and B), you are what economists refer to as a "rational" person. You have preferences that are consistent. Economists (except for those funny Behavioral ones) always assume that all people are "rational". It is a basic principle of economics that I teach my students on the first day of Econ 1. For those of you who preferred lotteries with different letters (usually first A and then B), you just proved all of those economists wrong.

See theoretically, these two sets of lotteries are identical. In both sets of lotteries the same outcome happens 89% of the time. Really you are supposed to be choosing between differences in what happens the remaining 11% of the time. In both sets of lotteries you are given the same choice.

A: Take $1 million with a probability of 11%
B: Take $0 with a probability of 1%
Get $5 million with a probability of 10%

Theoretically, the baseline 89% doesn't matter because you have the same outcome in both options. Now, those of you A/B people are probably saying "Wait! of course the baseline matters! In one situation you're giving me $1 million dollars, and that's awesome. I don't want to risk losing that for a small probability of getting $5 million. In the second situation I've got nothing, and the chance to get $5 million 10% of the time seems much better than getting $1 million 11% of the time." Until now there were no financial instruments designed to suite the "irrational" preferences of us A/B people. Now there is one.

In order to encourage savings among the poor, many of whom spend large sums on lottery tickets each year, the "save to win" concept was born. First implemented in South Africa, and now all the rage in Michigan, "save to win" accounts do not pay you interest, but instead distribute interest in random, lump-sum payments each month. If you have $1,000 in the bank, you won't get your 0.15% (generous these days), or $1.50 per year, but you will have a small probability of getting everyone's interest payment, a much larger amount, each month. Sounds good right? - Especially considering that the average american family spends $500 on lottery tickets every year. Why not get the same thrill by putting that money in the bank?

The only downside is that these accounts are illegal in every state except Michigan. State governments make big bucks by exploiting our preferences, profiting on state lotto players and the fees they charge to casinos. This is widely recognized as one of the most regressive ways to raise revenue, but nearly every state does it, and they don't want to give up their monopoly on lottery play. Perhaps its more politically feasible than raising taxes, but does that mean that we should continue to encourage the poor to pay for our roads and schools instead of saving for a rainy day?

Come on fellow Americans, let's man up, pay slightly higher taxes, and stop exploiting people with gambling addictions, or maybe a need to have some hope that their financial situation could change overnight. "Save and win" accounts may not fix all of our problems, but it would encourage a higher savings rate, and give the people who need it a chance at a more secure future - at least in the short-term.

If you are interested in learning more about the history of the "save to win" idea, check out the Freakonomics podcast called "Is America Ready for a No-Lose Lottery?" - available free on iTunes.