Sunday, September 29, 2013

Twists and Turns via Hyperbolic/Exponential Discounting

The law of diminishing returns can be summarized easily: too much of a good thing can make you sick; in some cases more sick than in others. Increases in total outcomes are not necessarily linked to increases in individual factors of production

There is so much pizza you can eat before it makes you sick and there are so many Master Degrees (if any) a person can obtain before student loans and other costs outweigh the benefits (increased salaries and such). 

To ground the idea with a more Economics-based example: there is a limited number of livestock, seed and workers that can be slaughtered, planted and employed in a farm, field and factory before output starts tapering off and marginal output starts contracting.

The quest for returns has made firms recognize this law and auto-correct if they dare break it.

But when considering a different set of laws, ones regarding investments - firms, individuals and governments rarely behave optimally...or rationally.

Theory states that agents/players utilize exponential discounting to determine their utilities. This method provides a clean-cut, time-consistent process that determines an investment's utility over time. Hyperbolic discounting, however, discounts short term gains at a higher rate than long term ones. Some empirical studies argue that people do in fact discount the short term more heavily than years ahead, proving that in practice, preferences change over time. 

The interesting problem comes when players under-discount future risks and losses and therefore make investments in the present that may not be the most favorable for them in the future. Social implications therefore abound: arbitrarily choosing to binge on vanilla ice cream today can manifest health risk factors in the future. Smokers regularly discount future risks hyperbolically; Bertrand Russell, a long time smoker and occasional philosopher (small joke), lucked out and died at 97, but most would agree that smoking is a slow countdown to death. And as such, should be heavily discounted.

Money today, it has been said, is worth more than money tomorrow. But money in 10 years, most believe, is worth practically the same as a bit of more money on the 11th year. As one approaches the 10th year though, money on the 10th year is once again valued above money on the 11th. And this is how preferences have been shown to change, resulting in agent's behavior aligning more with hyperbolic discounting than exponential discounting.

After having watched two post-apocalyptic films this weekend (Oblivion and Elysium), where the short-term actions of a whole civilization resulted in long-term damage, I realized the importance of discounting wisely:

In Politics: 
Short term gains as delivered by politician's campaign promises to constituents can and will backfire. Politicians are known to take the public's crap, and still ask for more, so much so, that in the end, all they do is try and please. Who is watching out for whom is anyone's guess. In the end, the people get the government they deserve; which shows how the public's predilection for instant gratification and mass hysteria when promises aren't kept constantly get in the way of investing in the future.

In Economics, Social Development and Order:
Developed economies are growing their GDP at 1% to 2% a year. Accumulating debt at an exponential rate is only viable if growth is increasing at the same rate. Cheap resources are becoming scarce and the economy cannot grow fast enough to make up for that fact. The search for yield has led to cheap money to land elsewhere (emerging markets, or local high risk investments). Social implications take the form of lost opportunities, greater income disparity between social classes and serious overall soul-searching.

In Education:
Rising education costs. Re-framing the MBA: are Finance jobs done, and are Entrepreneurial careers in? I'm all for it: I would rather create value through new companies than engage in astute money plays.

And then?

Example: A couple of years ago I was thinking of which MBA to go to, and I asked Seth Godin for his opinion. Seth is a generous person and is great at answering emails. His answer was (paraphrased): Why don't you take that money and start a company instead?

I thought about that long and hard, but decided not to. In my case, I applied Hyperbolic Discounting in my decision. I under-discounted the future risk in having to pay for graduate school in return for two years of unparalleled education. 

And it paid off. My current situation is a product of what I learned and did during those formative years. Drop-outs, Non-MBA's and successful prodigies can disagree, but in the end, it all depends.

What's perplexing is that Hyperbolic Discounting benefited me, when it probably, through particular circumstances, could have very well harmed someone else. 

What is clear though, is that, while there is no proverbial crystal ball, and predicting investment risk through well thought out discount rates is somewhat non-scientific, the theory behind discount rates is sound enough to help in making informed and conscious decisions regarding what could or might be.

The decisions agents "can live with" are suboptimal and myopic - aspiring to make the right decisions in spite of what an investor can live with could and can make a difference.