"The theorist not having definite assumptions clearly in mind in working out the 'principles,' it is but natural that he, and still more the practical workers building upon his foundations, should forget that unreal assumptions were made, and should take the principles over bodily, apply them to concrete cases, and draw sweeping and wholly unwarranted conclusions from them. The clearly untenable and often vicious character of such deductions naturally works to discredit theory itself."
–F. H. Knight
"The combination of precise formulas with highly imprecise assumptions can be used to establish, or rather to justify, practically any value one wishes . . .Calculus . . . [gives] speculation the deceptive guise of investment."
–Benjamin Graham
"I found a flaw in the model that I perceived as the critical functioning structure that defines how the world works"
–Alan Greenspan
"The Price Is Wrong, Bob!"
–Happy Gilmore
THE NATURE OF KNIGHTIAN UNCERTAINTY:
There is no such thing as "value". To understand how I have reached this seemingly ridiculous conclusion I must walk you through my analysis. I apologize for the length of what will follow but it is necessary due to the imbeded assumptions which under pin economic theory (of which I am quite critical).
I would refer you, reader, to the works of F.H. Knight, Karl Popper, John Law, Benoît Mandelbrot, George Soros, Daniel Bernoulli and Ed Thorp as a counter point. I would suggest that you apply Popper's test of falsifiability to the underlying assumptions of both Keynsian and Austrian economics. The assumption of "rational" self interest is not testable and can always be asserted as an explanation for any behavior post hoc. It is from this poisonous tree that fruit of asset price appreciation is harvested. It is on the back of Bernoulli's theory of marginal utility that all economics bases its assumption for rational behavior. However, the implicit assumption is that individuals can predict their own utility function with certainty or with known maximum and minimum bounds(or that this utility function is stable though unknown to the actor). While this assumption holds when making decisions with respect to a discrete selection of alternatives on a finite time interval in reality there are an infinite combinations and permutations of alternatives. The binomial to normal approximation of the rational expectational decision tree does not work.
What George Soros calls reflexivity and Mandelbrot recursive self affinity is the process by which people make assumptions and as those assumptions hold people increase the size of their investment in those assumptions. Using normally distributed prices as their presumption people decrease their expectation of variance as observations of prices within an interval increase. They begin to borrow money to increase the rate of their return. The problem comes when variance exceeds the maximum expectation. Lenders lose confidence in their ability to collect their principal and raise the cost of capital accordingly sellers are forced to reduce leverage to meet this cost and are forced into sell assets in the process, the fall in prices created by delevering triggers lenders to become more concerned still; and they raise their cost of capital further and the cycle repeats itself. This is what is commonly known as the credit cycle. The net effect is that prices of assets are not, never were and never will be normally distributed they overact to the upside in good times and overact to the down side in bad times. Further, this process is scale invariant as well as recursive. It is precisely when one has made a consistent rate of return in an investment that they are often most at risk, because they begin reduce their expectation of the rate of the rate of change in prices, or the acceleration of price changes if you will. For this reason, because people usually make steady amounts of money over medium length time periods and then go broke very quickly, that one cannot asses the performance of an investor based on how much money they have made in the past. While they may be a "competent investor" They may also be exposed to instantaneous volatility and be bankrupt in two weeks, it is impossible to tell.
DECISION MAKING UNDER KNIGHTIAN UNCERTAINTY.
Let us return for a moment to Mr. Bernoulli. While it is possible that value does not exist at all, risk with respect investment is a matter definition, for surely there is risk in the world. However, I will argue that the only acceptable definition of expectation in investing should be deductive mathematical expectation. Qualitative measurement of expectations are notoriously unreliable and since only a few % points difference in returns determine whether an investment is acceptable or rejected the necessary confidence interval can never be achieved. Which is to say, the margin of error for qualitative analysis is greater than the difference in returns between which the analysis would presume to distinguish.
While this may seem impractical, in practice it merely means restricting investments to those which can be synthetically replicated (statically) using different instruments by taking long and short offsetting positions; in short (pun intended) arbitrage.
Here we may incorporate Bernoulli's idea of marginal return to maximize the geometric mean rate of return for our investments. You must never invest in situation where the maximum loss and minimum payout are not calculable, with certainty. The expected payout must always be twice chance of winning. In practice this means that the waited average payout of all of your investment must be greater than zero from the moment you enter into the investment.
The answer to what causes losses to be more than expected is as discussed earlier. The change in expectation vs. your assumption when you entered into your investment. When I invest, I invest assuming only that the market price is wrong. I assume I have no idea what stocks are worth, as with Lehman Brothers, they could go to zero or they could go to 1infinity, I have no idea AND I want to make money either way. That is my only assumption that the market price is wrong. But rather than simply pulling out of the market, I want to make money on my knowledge that the market price is wrong.
To solve how to invest under these very restrictive conditions I will employ a bit of information theory. The impulse response of the an investment portfolio price or the change in the rate of change of an instruments price is its "convexity" which can be seen as a distortion of the linearity of its change with respect to its underlying (be they cash flows with a bond or stock with an option or what have you). This distortion from linearity can be modeled using the dirac delta function. Further, by identifying the inflection point of the price the "distortion" can be eliminated by the purchase of instruments with offsetting characteristics. Then the new portfolio can be analyzed in the same manner until the distortion is eliminated. This can all be done in one signal construction, statically rather than "dynamically" as the binomial process discussed earlier would suggest. Any time this process can be completed including total transaction costs and achieve a 2:1 pay off then an investment can be considered sufficiently profitable.
TO SUM UP
My basic assumptions are as follows.
Prices have infinite variance due to recursive self affinity in the behavior of market participants. As Mandelbrot demonstrated in 1962, prices are Levy distributed. The market fails to price in infinite instantaneous volatility and therefore volatility is always two cheap. Therefore I am a buyer volatility, through the use of synthetic volatility swaps on the companies that have the most difficult business to understand.
1) DOWN is UP
2) UP is DOWN
3 )The Market is a Ponzi Scheme, so is the dollar, so is gold.
4) Take as little risk with as much pay off as possible and only when the risk can be defined deductively rather than from statistical inference.
"Thus the professional investor is forced to concern himself with the anticipation of impending changes, in the news or in the atmosphere, of the kind by which experience shows that the mass psychology of the market is most influenced. This is the inevitable result of investment markets organised with a view to so-called “liquidity”. Of the maxims of orthodox finance none, surely, is more anti-social than the fetish of liquidity, the doctrine that it is a positive virtue on the part of investment institutions to concentrate their resources upon the holding of “liquid” securities. It forgets that there is no such thing as liquidity of investment for the community as a whole. The social object of skilled investment should be to defeat the dark forces of time and ignorance which envelop our future. The actual, private object of the most skilled investment to-day is “to beat the gun”, as the Americans so well express it, to outwit the crowd, and to pass the bad, or depreciating, half-crown to the other fellow.
This battle of wits to anticipate the basis of conventional valuation a few months hence, rather than the prospective yield of an investment over a long term of years, does not even require gulls amongst the public to feed the maws of the professional; — it can be played by professionals amongst themselves. Nor is it necessary that anyone should keep his simple faith in the conventional basis of valuation having any genuine long-term validity. For it is, so to speak, a game of Snap, of Old Maid, of Musical Chairs — a pastime in which he is victor who says Snap neither too soon nor too late, who passes the Old Maid to his neighbour before the game is over, who secures a chair for himself when the music stops. These games can be played with zest and enjoyment, though all the players know that it is the Old Maid which is circulating, or that when the music stops some of the players will find themselves unseated.
Or, to change the metaphor slightly, professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practise the fourth, fifth and higher degrees."
- J.M. Keynes, The General Theory of Employment, Interest, and Money 1936
"Double, double toil and trouble; Fire burn and cauldron bubble. Cool it with a baboon's blood, Then the charm is firm and good. O well done! I commend your pains; And every one shall share i' the gains; And now about the cauldron sing, Live elves and fairies in a ring Enchanting all that you put in. By the pricking of my thumbs, Something wicked this way comes."
From the Matrix:
