Jamesian Philosophy Refreshed

The great Cuban chess player Jose Casablanca once said, "I can draw any game against any player in the world." It sounds like a fairly equivocal sort of boast. It is actually a profound observation about life. Casablanca was saying that if he played to draw, he could get a draw. Against anyone. Because he was THAT good.  But he was also admitting that he could lose, IF he played to win. The search for a win is what would create the risk of a loss. Deep.  But of course one might expect depth from the sour looking but well dressed fellow in the photo here.

The use of the words "risk" and "uncertainty" in vernacular English leaves the relationship between the words imprecise. That is, if I were to ask you, dear reader, what is the difference between risk and uncertainty, there would be no univocal "right" answer, though the words clearly are not synonyms. In general, we think of risk as a less-than-certain loss, so uncertainty figures into it, but uncertainty figures into a lot of other words too (such as "hope," which we think of as a less-than-certain gain). In finance, and in other areas as well, there has been some movement toward using the two words in a rigorously paired way, such that, to borrow a formulation from the George W. administration, "risk" represents the known unknowns of a situation, "uncertainty" represents the unknown unknowns. Here's a straightforward example: I know that a certain stock is interest-rate sensitive. I know that the Federal Reserv...

Risk aversion is a straightforward name for the psychological fact that humans are often willing to pay a premium for certainly, or at least for limiting the zone of uncertainty. Suppose you, dear reader, appear on a television game show. The master of ceremonies says to you, "I can give you a nice crisp $100 bill right now!" You say, "oh, goodie." "Or!" he continues with a dramatic flourish, "I can flip a coin. If the coin comes up tails, you'll get nothing. If the coin comes up heads, you'll get $200." Let us suppose there is no element of what finance types call "counter-party risk" here. Your counter-party is the emcee. We'll assume he is entirely trustworthy and that there is nothing tricky about the coin flip itself. The expected value of the coin flip, in simple arithmetical terms, is ($200 + 0) ÷ 2 = $100. The value of the payoff if you reject the coin flip is, again, $100. So you should o...

"Most traders think there are two types of trades: winning and losing. Actually, there are four types of trades: winning trades and losing plus good trades and bad trades. Don't confuse the concepts of winning and losing trades with good and bad trades. A good trade can lose money and a bad trade can make money. A good trade follows a process that will be profitable (at an acceptable risk) if repeated multiple times, although it can lose money on any individual trade." - Jack Schwager

  You’ll remember that in earlier posts I've discussed a hypothetical widget-making company, XYZ, and said that we could enter various reasonable assumptions about this company’s stock in a calculator available in any of several websites, and receive for our troubles the value of a proposed put or call. How does the calculator do that?   A skeptic may sneer at the whole idea and say, “only supply and demand determine the value of a financial instrument. The demand for an option on a particular stock may change from day to day – as may the supply, as new writers enter or leave the market – so surely no formula or algorithm can tell us in advance what the value is.” That’s a plausible response, but it is in error. The value of stock options can be defined mathematically in ways that the value of the underlying stocks cannot. After all, we know intuitively what the value of a stock option is on the expiration date. If it has expired worthless, we know the value i...

In our last post devoted to the mathematics of finance, we mentioned that the standard deviation of a bell curve showing the range of possible returns from an asset can be employed as a surrogate for its risk. I'd like to pursue that point a bit. It is the chanciest corporations,  the ones that do have significant risk, that have to bribe you into buying their bonds with a higher return than their safer brethren need offer: thus, a trade-off. One way of looking at the trade-off is this: suppose I come into your neighborhood and offer to play a simple game. You will roll a pair of dice I provide and I will give you $1,000 times the number shown on the dice when they come to rest. I require only that you pay me $1,000 before we begin. The lowest possible score is 2, so the lowest possible pay-out is twice what you’ll pay me up front. This, then, (if I am honest and actually have the money I’m offering to pay) is a can’t-lose proposition for you. The worst outcome is ...

One of the central elements in modern finance theory is that of a risk-return tradeoff. The idea is simply that investors are risk averse, and accordingly must be paid to incur risk. T here is, then, a constant trade-off in the investment world: safe investments carry low return, high-return investments aren’t so safe. Fortunately, this conforms with almost everyone’s intuitions. What exactly is risk, though? Yes, we have an intuitive idea. The guy jumping out of an airplane is taking a risk that the appreciative audience standing on firm ground below is not. Further, if he has neglected to    check his gear properly he is taking an extra, unwarranted, risk. But we can be a good deal more specific about what the word means in the world of investments. It means the size of the standard deviation of return. It means the width of that bell curve we've discussed in earlier posts.   Standard Deviation A standard deviation is the “average distance from ...