Aleks sent me this. I have nothing to say on the substance here, but the grumpy-old-man quotes are amusing:
Mr. Buffett on complex calculations used to value purchases: “If you need to use a computer or a calculator to make the calculation, you shouldn’t buy it.”
Mr. Buffett on the use of higher-order math in finance: “The more symbols they could work into their writing the more they were revered.”
Mr. Buffett adds: “If you stand up in front of a business class and say a bird in the hand is worth two in the bush, you won’t get tenure…. Higher mathematics my be dangerous and lead you down pathways that are better left untrod.”
I imagine that you could get tenure if you say a bird in the hand is worth two in the bush . . . but I don’t think you’ll get tenure if that’s all you say. You’re supposed to do some research, too!
But this does remind me of something I’ve always wondered about, which is: who should be teaching college classes? For example, if I’m taking a class to learn how to read, write, and speak French, I’d much rather have an expert language teacher than someone who has done tenure-worthy research in French language and literature. If I’m an advanced student and want a deeper understanding, my preferences might go the other way. Similarly, in statistics, intro students might do best with a non-researcher who’s good at teaching.
What about business school? I can’t imagine someone teaching an entire course just saying “a bird in the hand is worth two in the bush” over and over again. At the very least, I’d think that it wouldn’t hurt to learn some basic mathematics and statistics, as well as some psychology, economics, and all the rest. On the other hand, I can sort of see Buffett’s point: if you learn how to solve some complicated optimization problem, I can see how you might focus on those details and lose the big picture.
For me, though, it goes the other way: knowledge of the mathematics gives me the confidence to think in larger concepts and not get snowed by irrelevant formulas. A lot of the weak statistical research–maybe, 50% of the stuff in the Annals of Statistics?–that I’ve seen has this problem, that the researcher is solving some technical problem without questioning the silly underlying assumptions that motivated the problem. You sometimes have to know a bit of mathematics, if you want to to be able to step back and solve the important problems.
"If you need to use a computer or a calculator to make the calculation, you shouldn't buy it."
Obvious hyperbole, but Munger is on to something when he says "Some of the worst business decisions I’ve ever seen are those with future projections and discounts back." Anyone who has ever done a life cycle cost calculation knows that with very small changes in the assumptions you can get any answer you want.
I personally prefer NN Taleb's newish piece in this vein: http://www.edge.org/3rd_culture/taleb08/taleb08_i…. He makes a very coherent argument (basically statistical decision theory for fat-tailed distributions, minus the formalisms of decision theory) and backs it up well with data. Seems much saner than Buffett…
I disagree that you can "get any answer you want" at least, if done right.
The point of a well formulated Bayesian decision model is that you model the uncertainty in the future, and then you discount it all back to present value, and you arrive at a probability distribution of present values. This probability model tells you not just what you think is most likely to to happen, but how much variability there could be.
If it's informed with data, and informative prior distributions that reflect economic understanding of how the past data might be different from the future data, then you've got basically the best decision method that I know of.
In fact, you might say that this is exactly what Buffett does. He has a combination of very informed priors, and relatively good understanding of fundamental economic rules of dynamics (so to speak).
This kind of thing is rarely done in business school on the other hand.
Typical business school Excel models are crap and based on someone's most likely projections with no uncertainty and give a false sense that you've "solved" the problem. That's where Buffet etc are right to ignore the calculations.
Typical academic models are probably based on extremely complicated stochastic calculus, using assumptions like time independent brownian forcing, or maybe if you're lucky levy forcing… these models are elegantly solvable by fancy mathematics, and probably also mostly crap since they make the kind of "silly underlying assumptions" that Andrew Refers to.
It's a case of missing the important DETERMINISTIC portion of the model and getting fancy with the probabilistic part. I've seen Andrew mention this fault in more than one occasion here on the blog.
The best models are those that use a combination of real data and economic insight into fundamentals, and they're mostly made by people like Barclay's Global Investors, and a few other big hedge funds and things. They're closely guarded, and based on a combination of engineering methods including time series signal processing, stochastic calculus, simple linear regressions, monte carlo simulations, and a whole host of things. For the most part, I don't think it's the Hedge funds that are hurting as badly right now, it's the banks who didn't have that kind of expertise.
(disclaimer, I used to work at Barra, and know some people at BGI and other hedge funds, as well as a well known finance professor, but I'm not in finance anymore and I've never been in business school. take this all with a large-ish grain of salt).
There is no doubt points to be taken from that discussion, but I agree that the discussion is too metaphorical and not precise enough to really evaluate rigorously — and thus everyone can take different things home from it.
This somewhat reminds me of the column a couple months ago about the blind faith in the copula modeling. The point is, the fancier the modeling, the easier it may be to forget it is just a model. Or perhaps better said, the easier it is to treat it as if it were more than just a model.
Considering that Buffett is still quite wealthy and is willing to spread that wealth I suspect I might trust his advice and intentions more than quite a few people.
He also has a very goofy sense of humor.
"I imagine that you could get tenure if you say a bird in the hand is worth two in the bush . . . but I don't think you'll get tenure if that's all you say."
I think this misses the point, which is that mathematical finance, while going to great lengths to account for and model quantifiable risks, ignores non-quantifiable risks – the (in)famous rumsfeldian "unknown unknowns", Taleb's "black swan", etc… If I throw a *perfect* die, I don't know which number will come out, but I can state with *full confidence* (by definition) that one out of every six throws will yield a 1 (and I can get as many 1's as I want with as high a probability as I want if I throw it a sufficient number of times etc… etc…). However, in the "real world", where the die is not "perfect", not only do I not know which number will come out, but there are no probabilistic statements like the ones above that I can state with full confidence. It is this "mortal jump" from the "things of logic to the logic of things", as Marx might have put it, that enables banks to present value financial assets which under certain conditions may pay $1 at 50 cents. Take two such assets, and you have $2 in the bush valued at $1 in the hand.
The more practical point Buffett is trying to make, and which often gets lost on people who have devoted a lot of time and effort acquiring hammers like "time series signal processing, stochastic calculus, simple linear regressions, monte carlo simulations, and a whole host of things. ", and are now hell bent on finding some nails, is that in business, *easy does it*. It is much like dating. It probably won't hurt to say that the number of attractive females coming into my local bar this evening follows a poisson distribution, but if your pickup strategy involves "closely guarded formulas" based on a combination of geometric algebra, hierarchical bayesian models, and little known psychological insights into the female psyche, you are heading for trouble. Even if you succeed in getting the girl's number using such methods, it's probably best to refrain from calling her. And if you don't get a number, which is the most likely scenario, the answer is not to discard the relatively "silly assumptions" in your model and start over with some more realistic, state of the art statistical techniques, as well as perhaps some powerful aphrodisiac scent designed by a former tenured professor at Harvard (exact chemical composition: closely guarded). Simply find an attractive lady, catch her eye, smile, hopefully she'll smile back, go over and say "Hi, I'm Joe. I study stats here at columbia, but don't let that put you off". If she laughs, things are going well. And *the same goes for business*. Easy does it. This is how banks used to court their clients – find a customer with attractive economic prospects, have them come over, smile, and if you deem them trustworthy, lend them some money.
Higher mathematics is simply not the right tool for these jobs. The problem is is not so much that it distracts you from learning other skills or cause you to "lose the big picture", but rather that it leads you into adopting a mindset which is *entirely inadequate* to approach these problems.
Disclaimer: I used to try and pick up chicks over brunch in the west village, and I know some guys that go to San Diego as well as a french dude who gets lucky every other weekend with a different model – I myself was never really any good at it and I hardly ever go out anymore.
"Don't buy something you don't understand." — Is that from Buffet, Peter Lynch, Ben Graham? It's good investing advice regardless of whoever said it first or most loudly.
Similarly, if you have a pile of data, you can get into trouble if you apply methods you don't understand. Lots of trouble.
This attitude fits into the "models are to blame" school of thought. Their proponents do not understand that modeling is a tool to capture systematically ideas from the human brain, and to explore their logical implications. Models/math are created by people, and they are no better or worse than their creators. Since models cannot "talk back", they're just easy targets but really excuses.
On the other hand, Buffett may be espousing the well-worn statistical principle of parsimony. The use of complex, black-box models with almost no reliable data to justify the massive degrees of freedom is a failure to follow sound practice.
On Andrew's point, I believe research and practice are separate enterprises. Research rightfully emphasizes new methodology but applied science should all be about results. One must not be tempted by the means and miss the ends. In fact, most of the time, because of time constraint or risk aversion, applied science and new methods are incompatible.
Miguel: I get the point about unknown unknowns, and it's great that Taleb is popularizing it. By definition, those things are unknown whether we use models or simple rules of thumb. Even for long-tail risk for which we have some knowledge, one has to make a judgment as to whether we should ignore the risk or not. If we never ignore such risk, then we are always basing decisions on worst cases. We would never be willing to walk out of our own home since a car might hit ya.
Another point I don't hear enough about is that these models provide a lot of efficiency most of the time. Banks lost a lot of money, but money is really just some electrons in an accounting system and some paper in some people's wallets. The efficiency of having these models means stuff gets produced and stuff is much much much more important than money. (I include services with "stuff" here)
In the last 70 years we have increased the average person's REAL wealth what, 7 or 10 times? (in the USA) If we had continued to do business on a handshake and a smile with only our local friends we would probably be extremely poor in real terms. As Thomas Sowell said in one of his basic books on economics, "profit is the cost we pay to get efficiency" well perhaps "occasional large monetary instability" is another cost.
When Taleb and others talk about banks losing more than all banks ever made etc they should remember that they lost more *money*, but they didn't destroy more wealth than was ever made… WWI destroyed wealth like never before, this financial crisis is the economic equivalent of a sneeze to the ebola that WWI and WWII brought to the 20th century.
One of the things that Economists do that is the most valuable part of having Economists around is that they look past the money. I just don't see enough of that happening in this situation, unfortunately I don't see it in what the economists are saying in popular news either.
Lest you forget, Buffet finances many of his aquisitions through his ownership of an insurance company (General Re). I do believe that there is a small amount of mathematical modeling and higher mathematics going on there, and that they might have a computer or two.
This sounds more like his "aw shucks, I'm just a farm boy from Nebraska" routine where he is playing to the people than a serious comment.
– Another country boy from Nebraska.
Charlie Munger (Buffet's cohort) on Models sounds awfully Bayesian to me, actually:
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You've got to have models in your head. And you've got to array your experience ‑ both vicarious and direct ‑ on this latticework of models. You may have noticed students who just try to remember and pound back what is remembered. Well, they fail in school and in life. You've got to hang experience on a latticework of models in your head.
What are the models? Well, the first rule is that you've got to have multiple models ‑ because if you just have one or two that you're using, the nature of human psychology is such that you'll torture reality so that it fits your models, or at least you'll think it does. You become the equivalent of a chiropractor who, of course, is the great boob in medicine.
It's like the old saying, "To the man with only a hammer, every problem looks like a nail." And of course, that's the way the chiropractor goes about practicing medicine. But that's a perfectly disastrous way to think and a perfectly disastrous way to operate in the world. So you've got to have multiple models.
And the models have to come from multiple disciplines ‑ because all the wisdom of the world is not to be found in one little academic department. That's why poetry professors, by and large, are so unwise in a worldly sense. They don't have enough models in their heads. So you've got to have models across a fair array of disciplines.
You may say, "My God, this is already getting way too tough." But, fortunately, it isn't that tough ‑ because 80 or 90 important models will carry about 90% of the freight in making you a worldly ‑ wise person. And, of those, only a mere handful really carry very heavy freight.
So let's briefly review what kind of models and techniques constitute this basic knowledge that everybody has to have before they proceed to being really good at a narrow art like stock picking.
First there's mathematics. Obviously, you've got to be able to handle numbers and quantities ‑ basic arithmetic. And the great useful model, after compound interest, is the elementary math of permutations and combinations. And that was taught in my day in the sophomore year in high school. I suppose by now in great private schools, it's probably down to the eighth grade or so.
It's very simple algebra. It was all worked out in the course of about one year between Pascal and Fermat. They worked it out casually in a series of letters.
It's not that hard to learn. What is hard is to get so you use it routinely almost everyday of your life. The Fermat/Pascal system is dramatically consonant with the way that the world works. And it's fundamental truth. So you simply have to have the technique.
Many educational institutions ‑ although not nearly enough ‑ have realized this. At Harvard Business School, the great quantitative thing that bonds the first ‑ year class together is what they call decision tree theory. All they do is take high school algebra and apply it to real life problems. And the students love it. They're amazed to find that high school algebra works in life….
By and large, as it works out, people can't naturally and automatically do this. If you understand elementary psychology, the reason they can't is really quite simple: The basic neural network of the brain is there through broad genetic and cultural evolution. And it's not Fermat/Pascal. It uses a very crude, shortcut ‑ type of approximation. It's got elements of Fermat/Pascal in it. However, it's not good.
So you have to learn in a very usable way this very elementary math and use it routinely in life ‑ just the way if you want to become a golfer, you can't use the natural swing that broad evolution gave you. You have to learn to have a certain grip and swing in a different way to realize your full potential as a golfer.
If you don't get this elementary, but mildly unnatural, mathematics of elementary probability into your repertoire, then you go through a long life like a one‑legged man in an ass‑kicking contest. You're giving a huge advantage to everybody else.
One of the advantages of a fellow like Buffett, whom I've worked with all these years, is that he automatically thinks in terms of decision trees and the elementary math of permutations and combinations…."
Model Selection, rationality and the removal of bias, and even (if you read further down in this quote from his speech at USC) a Jaynesian approach to distributions:
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Which models are the most reliable? Well, obviously, the models that come from hard science and engineering are the most reliable models on this Earth. And engineering quality control ‑ at least the guts of it that matters to you and me and people who are not professional engineers ‑ is very much based on the elementary mathematics of Fermat and Pascal:
It costs so much and you get so much less likelihood of it breaking if you spend this much. It's all elementary high school mathematics. And an elaboration of that is what Deming brought to Japan for all of that quality control stuff.
I don't think it's necessary for most people to be terribly facile in statistics. For example, I'm not sure that I can even pronounce the Poisson distribution. But I know what a Gaussian or normal distribution looks like and I know that events and huge aspects of reality end up distributed that way. So I can do a rough calculation.
But if you ask me to work out something involving a Gaussian distribution to ten decimal points, I can't sit down and do the math. I'm like a poker player who's learned to play pretty well without mastering Pascal.
And by the way, that works well enough. But you have to understand that bell‑shaped curve at least roughly as well as I do."
Where Munger seems to get a little confused is in nature-state vs. knowledge-state. But that's forgivable. I'm just tired of people taking their position out of context.