## Saturday, April 16, 2011

### Intro to Economics for Physicists: Part 2: Rate of Return & Risk

This is a continuation of the Intro to Economics for Physicists Part 1, which was an introduction to some of the vocabulary used in the study of economics, but given in terms that may have more meaning for those people who consider themselves physicists at heart.

Highlights include: a) there is no reason why we can't use SI units in economics, such as measuring GDP in GW-hr / year. This means that we can get rid of the units of dollars or euros or yen from the study of economics. b) In order to make economics more like a science, we need to de-humanize it. We need to remove the un-quantifiable term "utility" and replace it with a quantity that can be measured, that incorporates our environment, and that should be optimized. That quantity is the "rate of production of entropy" due to all life forms.

This post is devoted to explaining the relationship between the rate of return on investment and risk. One way of calculating the rate of return on investment is to calculate the effective interest rate such that the net present value (NPV) is zero. This is also called the Internal Rate of Return. The IRR is inflation-adjusted and averaged over the lifetime of the project. While rate of return is fairly easy to calculate (given assumptions on capital costs and projected income), it is a lot more difficult to calculate the risk associated with a particular project.

What any financial adviser could explain to you is the fact that the rate of return on your investment is a function of the risk you are willing to accept. For example, high risk investments, such as Tech Stocks, will tend to have a higher average rate of return on investment than low risk investments, like a US Treasury bills, which tend to yield a lower average rate of return on investment. Below is a figure adapted from Brealey and Myers's textbook Principles of Corporate Finance.

This figure shows a general trend that the average rate of return on investment is associated with investment options that have a greater chance for fluctuation, hence the larger value of normalized standard deviation. A financial manager would tell you that if you are investing for the large term, these fluctuations don't matter, so chose the investment option with the historically greatest average rate of return. Though, if you are not investing for the long term, then you need to choose an investment option with less chance of a negative return on investment.

Risk is an important topic to discuss because different people have different types of responses to risk. Some people are risk averse: here we define risk aversion to mean that, even when accounting for the time value of money, people will chose the safer route compared with the riskier route (whose probability-weighted reward is higher than the probability-weighted reward of the less risky route.) Risk aversion shows up all of the time. The simplest case being that a person with risk aversion would choose to be given \$50 instead of a 75% chance of \$100 and a 25% of \$0. On the other hand, many people demonstrate the opposite of risk aversion: risk affection. This would be the case with gambling and the lottery. In this case, the probability-weighted reward is less than the cost of the ticket. (The probability-weighted reward is roughly \$2 for a \$5 ticket, though this depends from state to state. Roughly, speaking Las Vegas is forced by law to pay back 90% of the investments and state lotteries pay back on the order of 30%. In both cases, there is a probability-averaged negative return on investment.) Some people who show signs of risk affection (i.e. gambling) think that the only way to make money is by taking it from other people (i.e. that there is a set amount of money in the world, and the only way to get rich is to take it from other people.)

Personally speaking, I can show forms of both risk aversion and risk affection. I hate gambling and I've never bought a lottery ticket, but when it comes to my retirement Roth IRA, I consistently purchase the riskiest forms of investments, even when my financial adviser suggests for me to be less risky.

Note: part of the reason why I hate gambling and the lottery is that it's a form of Win-Lose. There are winners and there are losers. There is no net gain for society. It's simply moving money from one person to another. I think that this is a horrible waste of time and resources. We should be focusing on win-win situations. For example, when you build a profitable power-plant, you are creating a win-win situation. You are literally creating money (kW-hrs) out of nowhere. There is no such thing as a fixed pot of money in the world. We can create more money by investing in projects with positive, un-subsidized returns on investment. Such projects are win-win situations. (Think Dangy Taggert and Hank Rearden from Atlas Strugged. They created win-win situations in which the amount of wealth in society increased, measured in kW-hrs of available work.)

So, risk is all around us. Every choice we make is full of risk, though some choices might seem riskier than others. The questions are: Can we quantity risk? And if so, how do we make decisions based off of the risk? Or if not, how do we decide how to act if we can't quantity the risk associated with a certain investment?

There are arguments on both sides of the debate regarding whether risk can be quantified. There are people like the author of  Black Swan (Nassim Nicholas Taleb) who believe that our current methods of quantifying risk are unable to handle the large fluctuations seen in financial markets. This is an especially valid criticism because most risk is quantified assuming bell curves and standard deviations; however, real financial markets are scale-free, meaning that large fluctuations are more likely to occur than when predicted using a bell curve (i.e. gaussian) distribution. But I think that Taleb's criticism is not necessarily a criticism against trying to quantify risk, but rather is just a criticism of how we currently attempt to quantify risk. The mathematics of scale-free probability and scale-free networks has been known since at least the 1960's, and can be found in many textbooks on statistics and economics. (Also, check out Extreme Events by Malcolm Kemp.)

But the important point is that quantifying risk is our way of trying to mold our model of the world over top of the actual world. Any model of the world is imperfect, but that doesn't mean that we should destroy all models of the world. For example, one of the main tenants of far-from-equilibrium thermodynamics is that there is no known best way for a system to go from out-of-equilibrium to equilibrium. (Disproving optimal routes in Far-From-Equilibrium Thermodynamics).  In physical terms, this is another way of saying that there is no variational principle for systems far-from-equilibrium. The real world will always be too complicated to model perfectly, even with near infinite computing power. Given that we live in a world far-from-equilibrium, the best we can do is to make approximations and formulate models of the world that are known to be imperfect. If the models are clearly not working, then we need to have debates and vote on whether to pick a new model or stick with the old model. And there is no option for us to not to have a model in which to predict the future.

In much of the financial world, the model of the world they have chosen to accept is the following: Man is the epitome of life on Earth and his collective happiness should be maximized, and money is the representation of human desires, needs and wants. The best way to maximize the greatest good for the greatest number of people is to maximize the rate of return on investment. Maximizing this figure of merit will create money (and hence happiness) out of thin air, and will maintain mankind's dominance here on Earth.

Note: While I am not necessarily an advocate of this model of the world, I do think that there is one valuable thing to take out of this model of the world: the rate of return on investment. I believe that the overall goal of life is to bring the world to equilibrium as fast as possible, and this can be accomplished by maximizing the rate of entropy generation. As mentioned above, there is no known best way to maximize the rate of entropy generation in systems far-from-equilibrium. But with that having been said, it seems like calculating the estimated rate of return on investment of various projects, and then choosing the option with the highest rate of return on investment will tend, over time, to generate the greatest rate of entropy generation.

The question remains: how do we choose between projects that have both different average rate of returns on investment and different values of risk? This amounts to asking the question: is there a way of converting a value of average rate of return with a given value of risk into a value of certain-equivalent rate of return with zero risk?

In theory, it's possible to remove uncertainty through the use of futures' contracts, derivatives or other financial options to convert the price of an uncertain item (such as natural gas or oil) into an average certain equivalent price over the life of a power plant. But as we saw in 2008, futures' contracts can be deemed worthless if a company goes bankrupt. There's no way to remove all uncertainty, and 'certainty equivalence' may only be a dream.

So, the answer to the question above is not straight forward, but it turns out to be:
"It depends on whether we as a society prefer risk aversion or risk affection." If we were neither risk averse or risk affectionate, then there would be a straight forward way of converting a given average rate of return into a certain-equivalent rate of return. However, there is nothing to tell us whether to be risk averse or risk affectionate. You can't derive the optimal amount of risk; you just have to use past experience to help guide you on whether to be risk averse or risk affectionate. [My own opinion is to optimize the average rate of return on investment using capital, labor and fuel costs in "certainty equivalent dollars" using at least three levels of security, so that the "certainty equivalent costs" including the price of buying futures contracts, derivatives or credit default swaps.]

So, while this post has been intended as "Intro to Rate of Return of Investment & Risk for Physicists", you can see that, even if we could argue on how to quantify risk, there is nothing in physics textbooks to tell you how to decide between two projects with different average rate of returns on investment and two different values of risk. While this lack of certainty might repulse some physicists who prefer to make calculations for systems with a known variational principle, I think that it's interesting that the laws of physics can provide us information about the meaning of life (increasing the rate of entropy generation), but leave us hanging as to how to best fulfill the meaning of life. I see this as a good thing!

Seen in a positive perspective...
Since there is no variational principle for life, there will never be a computer that can calculate the best way to live one's life. There never will be some authority who can predict the future. We are all stumbling in the dark. Some of us see the light at the end of tunnel (the universe at equilibrium), and are trying to get there, but have no way on knowing the best way to the end of the tunnel. The problem I see is not between people with competing ideas on how to get to the end of the tunnel (i.e. people with different ideas on how to grow society), but the problem I see is that there are people who are actively trying to go in the opposite direction (to prevent society from growing.) There are some people who believe in Robert Lindsay's version of the Thermodynamic Imperative and are trying to stop any production of entropy and any growth for society.

My hope is that teaching science, engineering & the version of economics discussed in these posts can be a way of bringing us together so we all can grow as a society. And since the figure of merit (rate of return) for this new version of economics (which only uses SI units) is the same figure of merit as in the old economics (though, it would include environmental damages and the rate of return for all life forms), it seems likely that people who don't necessarily believe in the new economics can still feel a sense of peace knowing that optimizing the rate of return on investment should do both of the following:  a) maximize the rate of entropy generation in the universe and b) perhaps ultimately yield the greatest good for the greater number of humans, even though this was not its intended goal.

What do you think?