Humans are a strain on GDP growth

In a previous post, I drew graphs which showed that an investment's "yield average" and "yield variance" are positively correlated. In plain English, this means that a high risk investment will have a better return on investment than low risk investments, even after fully accounting for the risks of delinquency and default. Why does this occur in practice?

There are two opposing forces which influence the "appetite for risk". From an individual's micro-economic perspective, losing all of his money creates more harm to him than the good that would result in doubling his bank roll. That's why it does not make any sense to go to the casino and wager all your assets on black at roulette (even if the green slots were removed, making the wager completely fair). The reason for this is that our appreciation of various products is not proportional to the price of the acquired good or service.

To illustrate this point, lets compare apples and oranges. An apple is worth 5$ of "pleasure" to me, and an orange is worth 9$ of pleasure (I obviously prefer oranges to apples). If the price of oranges is above 9$ and the price of apples is above 5$, I will buy neither. Say I have 16$ to spend, and the price of apples is 4$ and the price of oranges is 8$, I will definitely buy something. What will I buy? 16$ buys me 4 apples, which gives me 20$ of pleasure (I net 4$ of pleasure if I buy apples). 16$ buys me 2 oranges, which gives me 18$ of pleasure (I net 2$ of pleasure if I buy oranges). So despite the fact that I prefer oranges to apples on a 1:1 basis, at some price points I will buy apples rather than oranges.

Return on investment is usually measured in dollars invested against dollars paid back (put dollars in, then wait some amount of time and get dollars out). When consumer goods are purchased in retail sales, the return on investment must be measured as dollars in, then wait some amount of time (usually very short), and get pleasure out. For a transaction to be completed, the selling party has to own an asset which he values less than the buying party. As long as the price of the transaction is between the two valuations, both parties will gain from the trade. The fair price for the trade is the multiplicative middle. If a seller and buyer simultaneously value an item at 1$ and 4$ respectively, then the fair trade value would be 2$, so that each person gets a return on investment of 2:1 on the transaction; in practice there are multiple sellers and buyers of a given item, and the market price is set to the multiplicative average between the two closest prices, which are always very close in any liquid market.

At first glance, markets do not seem to obey the rule of trading at the multiplicative average of the valuations. Take water as an example: if I can't buy water on a daily basis, I will die. So the value of water is very high for me (at least 25$ dollars a day), much more than the 1$ I pay for a 2L bottle of water (good for 1 day's worth of water consumption). The ROI that I am getting on water is 2500% a day (10^508 % a year). So why isn't the price of water 24.997$ for a 2L bottle (at this rate, the yearly ROI is 5%)? If there was only one person that owned all the water in the world, he could set the price at 24.997$ and I would grudgingly buy it. But this person would probably not be respecting the fair price of trade stated in the previous paragraph. That's because an individual highly values 2L of water per day, but he has very little use of the 10^19 other litres of fresh water available on Earth. Thus water for him is worth very close to 0$ per litre. The multiplicative average of 0$ and 25$ is darn close to zero (the 1$ cost comes mostly from packaging, publicity, distribution and retailing; it is fair, so don't write a letter to your MP complaining about the "Big Water" lobby).

The average person has an extremely good return on investment in buying water and basic foods (these are cheap and keep you alive!). In decreasing order of priority, most people would then buy clothing and housing, better tasting food, transportation, and luxury goods. The return on investment for consumer spending is called utility. The utility of an extra dollar of income is always lower or equal to the utility of the last dollar spent (this means that you don't wait for your salary to have reached 30K$ a year before you start buying food!). The function is thus decreasing (or flat) by definition.

The utility function that I use for myself has three steps: the first 10K$ covers my essential living needs (pleasure ROI > 100%), the next 20K$ covers my discretionary living needs (pleasure ROI > 25%), and I have yet to find a use for the 30K$ and above money, so I barely care about it at all (pleasure ROI 0+%). Say I stumble upon a winning lottery ticket tomorrow morning, and I suddenly receive 10M$. I'm lazy, so I decide to never work again, and I have 50 years left to live. How do I invest the money? I can't afford to be short of pleasure at either 100% or 25% interest rates, which means that I pretty much have to guarantee an income of 30K$ a year for 50 years. So I will set aside 1.5M$ in AAA government bonds (their effective yield after inflation and taxes in Canada is 0%!). And since my utility function is flat for the rest of my money, I'll invest the 8.5M$ remaining in the highest average yield and highest variance instrument that I can find. I'm using an extreme example to illustrate how a non-flat utility function necessarily leads to a "balanced" portfolio requiring different investment instruments which bear different variance and average yield. To balance your portfolio, you must choose investments with risks and yields that maximize the dollar value of pleasure that you will consume in your life. Note that at 100% ROI, being short of essential living pleasure at any time is horribly expensive.

That's force number one: the utility function of humans is not flat. Might we have a flat utility function (if happiness was linearly proportional to income), variance would not affect our investment decisions at all. Everyone would invest in the highest average yield assets, which means the riskiest investments. This would greatly increase GDP output.

Force number two is in the opposite direction: it encourages us to take risks. In a financial system that only allows collateralized loans, the worst that can happen to you is that you lose everything (all your assets). That is not so bad in occidental countries, since the state guarantees about 20K$ a year of cash and services, which supplies us with the first 10K$ of essential living needs (it prevents us from dying of thirst, or otherwise loaning ourselves essential living needs at a usurious rate of 100% a year!).

Better yet, in a financial system that gives us loans without collateral, the worst that can happen to you is still that you lose everything (all your assets), because bankruptcy prevents your total net worth from going too far in the negatives (it is actually based on cash flow, not on net worth, but the result is very similar). Yet borrowing without collateral allows you to leverage your investments, reaping much larger rewards than would be achievable might you only be allowed to invest your hard earned assets. How does this make any sense?!? Why would someone loan you money to invest (either on the markets or in your own pleasure) that you may not payback? Obviously you are getting a better yield than the loaning party offered you, otherwise you would not have accepted the loan. Why shouldn't they invest the money themselves directly instead? For one thing, they can't benefit from your pleasure. So if the lender has a ROI of 5% on his pleasure, and you have an ROI of 10% on yours, by all means he should lend you his money. The same applies to traditional investments also (stocks especially). When the bank loans you at 6%, and you invest in the stock market and get 10%, you are either more risk tolerant or smarter than your banker (probably both!). You and your banker are getting a good deal out of the loan.

So the social safety net and bankruptcy laws encourage us to take risks on the one hand (increasing GDP growth), and our utility function for consumer spending pushes us to hedge our portfolio, rather than betting everything on the statistically fastest horse (decreasing GDP growth). William Poundstone should have read this paragraph before going ballistic on Kelly's criterion.

La conclusion de l'histoire: if humans had a flat utility function (or if the social safety net was 30K$ a year and everyone's utility function matched mine), the average yield of all investments would be exactly matched with GDP growth, making the previous post's graphs one dimensional, and making the deflation problem's solution trivial. Lady GDP puts it this way: "Humans: can't live with them, can't live without them!"

Before all you socio-communists reading this blog suggest dishing out 30K$ a year in social safety nets to increase the appetite for risky investments (thus GDP), keep in mind that the utility function that I use for myself is not universal. Most people actually know what to do with their 30K+ income tranche: that's how Porsche stays in business. Those that don't care about the 30K+ income tranche won't put any effort in producing this income. I'm a workaholic exception, so the pleasure of working and investing money brings my ROI above 30K$ from 0% to 0+%, which makes a huge difference. If I was the only human alive, I would produce 2000 Kg of bananas a year, even though I only consume 1000 Kg, just for the fun of producing more bananas. Thankfully, I live on a planet inhabited by lazy monkeys.