Standard Deviation is a deviation from reality

I, Baruch, have started reading  Naseem Taleb’s book, The Black Swan, for the second time, having just finished it. People like me will read it because they are interested in markets, but in reality it has as much to do with philosophy, ethics and epistemology. In this, it is relevant to Spinoza students; it joins the corpus that continues the great project of enlightenment: what is real, and what should we do about it?

This book confirms a number of my prior prejudices, and I love anything that does that. As you regular readers (all one of you) know, I run an equity fund. I get paid (not enough) based primarily on how much money I run (a few hundred million dollars) and on the relative performance of that fund against a benchmark (this has always been positive so far, though Taleb would say this might be pure luck). Recently however, I have also started to get paid partly on something called a Sharpe Ratio. This measures my annual performance against the “standard deviation” of my returns over some prescibed period (maybe monthly, daily, I don’t actually know). So if I make, say, 30% in a year, I should not be pleased with myself unless I added just a little bit of performance every day adding up to 30%. If that performance comes in great weekly gobs of 10%, 15%, 20%  or more, accompanied by periodic swingeing losses of 5-15%, then I am in fact, not a winner but a schmuck. You, my punter, get to pocket 30% and buy a yacht, but doing it in an interesting and exciting way is apparently worth less to you than doing it boringly. Presumably also the yacht you buy for exactly the same amount of money which I just made for you “feels” different, the one bought with profits that arose with less volatility being “better”. This was bitter sarcasm, by the way. No-one has yet told me how to make 15%-30% in a stock portfolio without taking risks in a way which leaves me open to big drawdowns. I am just told “keep your Sharpe Ratio up, the consultants love it.”

I have always felt in my bones that this approach was worthless and unfair, and after reading this I properly understand why. It’s based on a flawed understanding of the nature of risk. For whoever this knobcheese Sharpe is or was, risk is a static thing, it is fluctuation around a norm, a standard: it is, literally, a “standard deviation”. For Taleb, the nature of markets and life is that there are periods where this is true, but (a very big but indeed) what really defines reality are large events outlying the norm, game changers. These are “Black Swans” — all swans are white until you see a black one — events like the 1987 crash, the collapse of the Soviet Union and the ERM, the emergence of the internet, LTCM, Enron, 9/11,  etc. The common link is that these are events unforseen in their time (Taleb points out that we pretend that we did foresee them, in elaborately argued but largely fictional apologia, after the fact), and in fact largely unforseeable. The effects of these black swans make up, if not the bulk of historical returns, a hell of a lot of it; compounded, they are more statistically significant than variations within the standard deviation. Taleb makes the fairly shocking point that if you exclude the 10 largest daily moves in the S&P 500 in the past 50 years, the index would be more than 1000 points higher (higher!? scary); right now it’s at 1500. That’s a pretty big deviation, “and yet,” he writes, “conventional finance sees these jumps as mere anomalies.”

How could the “professionals” go so wrong? The narrative fallacy (we need a story, even if it’s fiction), confirmation bias (I knew they’d fly planes into buildings), the ludic fallacy (assume an efficient market), a need to scienticize, a desire for precision where none is possible: we suffer from all of these. We are not equipped to make sense of a world (he calls it “Extremistan”) ruled by the random and the extreme, where distributions are logarithmic and not arithmetic. The world follows power laws, winner takes all rules, much much more than we think it does, while, dangerously, the “experts” are people who believe we inhabit “Mediocristan” where conformity and predicable bell-curved, “Gaussian” distributions rule.

I am bastardizing a book with a lot more in it than this. And as I said, it is certainly not just about markets, though that aspect interests me the most. I wish I could get into it more here, but what can I do, this is a blog. Now, not all of the book is good. The style can grate, though I got used to it. Taleb is, shall we say, no stranger to self love. This confidence seems to have continued even though his hedge fund, Empirica, prominent in the press that surrounded his previous (and also excellent) book Fooled by Randomness, seems to have mysteriously stopped trading by this book’s publication. We are told Taleb has withdrawn “into pure ideas after the constraints of an active and transactional life.” I was told during an interview at a fund of fund house, who would know, in 2004 that Empirica had blown up. Now, apparently, it is largely restricted to consulting; I too went through a period of “consulting” inbetween the hedge fund I worked on blowing up (not my fault, I think, but Taleb expects me to say that), and getting a new full time job at my current beloved gnome-like employers. Taleb is wont to bang on about the need to remain “practical”, rather than concentrate on the theoretical. That his thesis may have failed in the real world would seem at least material to it. He admits to being responsible for Don Rumsfeld’s infamous “known unknowns” speech, too.

Net net, however, I don’t mind. The book is so chock full of good stuff I am, as I said, reading it again. I can also envisage a scenario in which Empirica (if it indeed failed) can claim to have been unlucky, investing as it did in (theoretically) mispriced long out of the money options positions, in a period in which volatility as an input in option pricing has been squeezed to unimaginably low levels, even as the world and its dog have been writing (selling) calls and puts on everything. According to the metaphor, world and dog have been picking up nickels in front of steamrollers; Taleb was betting they would get squashed once or twice, or at least lose a foot or something. Instead no one expected that the steamroller would in fact slow down — and, of course, this would validate the original thesis in a way that Taleb would never have foreseen. In itself, what else is this unprecedented shrinkage of volatility but a Black Swan! Taleb’s thesis, far from being falsified (like myself, he is a great fan of Popper), is strengthened! Truly, it is impossible to escape the Black Swan.

This is why I remain under Taleb’s spell. I have never written an option, and hope I will not do so anytime soon. I am going to find out as much as I can about Benoit Mandelbrot. I am also going to make damn sure I pay no attention to my Sharpe Ratio, and will absolutely refuse to sign any annual goals document which wants to pay me on the basis of it. Unless they threaten to fire me, of course.

Later on, I am going to deal with another very important part Taleb’s work, on the problem of induction; here, I fret, he directly opposes Spinoza.  But it is so large a problem, and needs so much more input from other writers (such as Popper), that you will just have to wait until I have the guts and the time to take it on. In the meantime, another troubling thought has crossed my mind. Bento, if you ever read this site any more, do you have any idea what I am going on about in this post? Do you think anyone will?


9 thoughts on “Standard Deviation is a deviation from reality”

  1. Not to worry Baruch, your words are read and appreciated — every single one, and in groups too.

    Re Spinoza’s affinity for inference: It is not how modern science works, but it is how mathematics works, on a whole (if you look at it from a logistician’s perspective). And Spinoza was trying to give “the world out there” a similar indisputable footing as that of the platonic world of mathematics. Curiously, the very deepest cosmologists and particle physicists are now also toying with purely mathematical ideas for describing the very basic structure of the universe — so Spinoza’s project may in the end prove to have been a good first effort, intuitionally.

  2. Thanks for that. But I worry my pearls are not understood. Do you understand why shrinking volatility could lower option prices?

    Spinoza may at some point in the Ethics use inductive reasoning. I am checking now. I understand and accept the point you make, however, it is a good one.

  3. Duh, of course I know the link between option prices and volatility — back in 2002 I wrote a database program that calculated historical implied volatility for equity based on options prices.

  4. Well to paraphrase A Fish Called Wanda, a chimpanzee could write a database program that calculated historical implied volatility for equity based on options prices; but it doesn’t mean he understands it.

  5. Moreover, do you realise on reading about the myth of standard deviation why your database program that calculated historical implied volatility for equity based on options prices was almost certainly wrong?

  6. No, actually the concept of historical implied volatility is quite specific, and the value can be calculated quite accurately. Whether the value is meaningless is another question, but accurate it certainly was.

    A chimp might eventually write something like it, but not on the first try.

  7. the K ratio has the same issue although it measures variance in the slope of the return. The flaws I think are inherent in using single success criteria for multiple forms of exposure. Taleb’s deep out of the money options approach might have a drastically different volatility than writing options, but either method may be more successful although my bet would be with Taleb.

  8. Baruch, if you find Taleb and Mandelbort interesting, you should check out Didier Sornette of the Crisis Observatory at ETH Zurich. While Mandelbrot (and Taleb with him) tends to propose that fractal distributions somewhat accurately capture risk, Sornette argues that conditional autocorrelation surfacing during extreme events make it impossible to accurately fit returns data to any statistical distribution, even a fractal one. Of course, Taleb would probably agree with him and say that this is what he was saying all along, which may be true. At any rate. Sornette is definitively worth a read.

    Historical implied volatility is indeed very specific and can be calculated accurately, but its relevance is wholly dependent on the validity of the underlying model, usually some version of Black-Scholes-Merton. That is, when calculating implied volatility one is merely asking “if this model is correct, then what must volatility be in order for prices to be what they are”. The answer to this question may or may not be relevant – though obviously, the model is never ever “correct”.

    I find it very interesting, though, that volatility – implied or actual – only exists in the past and (hypothetically) in the future. Empirically speaking, it never exists “now”, as it is intrinsically a related to changes over time. Now, this means that when we use historical volatility as measured in one of many possible ways to say something about options prices, we are not only extrapolating into the future, we are also extrapolating into the “now”.

    Then again, while this is especially evident (and consequential) with regards to volatility, one could perhaps argue that it is the case to some extent with most or all financial data. Given non-infinite liquidity, a “current” stock price, for instance, is nothing but an extrapolation from the past (the last transaction that was made, that is) to the now – except in the instant you make a trade yourself. At any other time, mark-to-market prices are but inferred estimates of one’s actual worth (this applies to cash as well, it may be worthless by the time you reach the deli because of the apocalypse that will be upon us a few moments from now). So, your mark-to-market value and definitively your VaR numbers will not just probably be wrong tomorrow, they are almost certainly wrong “now”.

    Of course, in the case of models like CAPM, we are not only extrapolating from the past into the now, and from the now into the future, but from the past to the future and then back from the future into the now (and then back to the future?). I fear, though, that I am no longer in neither mediocristan nor extremistan, but that I might be getting lost in the nebulous abstractistan.

    Attempting to return to reality, bank balance sheets are interesting examples of how extrapolation to the now can mess us up. Who knows how Lehman Brothers would have fared if we extrapolated into the now differently.

    All the best,


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