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  • Roulette, Risk and Investing

    Posted by Jonathan on November 11th, 2003 (All posts by )

    Karsten’s post from the latest Carnival of the Capitalists is worth reading.

    Options are always undervalued. The difficult thing is to know which ones.

     

    9 Responses to “Roulette, Risk and Investing”

    1. Lex Says:

      I particularly liked his focus on the distinction between risk and uncertainty — and the useful analogy to a game of chance which has quantifiable risk. Markets are not like that. Basing current decisions on past performance is probably better than throwing darts at a board, but as you have noted, “perfect storms” come along and work havoc with the model, and even change the shape of the shoreline. The distinction was made by Frank Knight of the U of C back in the ’30s (see our masthead, above), noting that the role of entrepreneurs was to act in the face of uncertainty. Anyway, the guy is on the ball.

    2. Jonathan Says:

      “Basing current decisions on past performance is probably better than throwing darts at a board. . .”

      Much better, if you know how to do it. (This includes knowing which side of the distribution to bet on so that uncertainty works your way. This is what that much-ridiculed aphorism, “the trend is your friend” means.)

    3. Karsten Says:

      Thank you very much for your kind words re the post on my blog. Investing is somewhat like betting on horses – you don’t have success (for long) by picking winners. Making money in the long term depends on your being able to identify a horse on which the odds are skewed in your favour (read this: http://www.horseswild.com/drf_1c.shtml).

      By the way: by sure to blogroll me if you liked my little piece.

    4. Alexander Crawford Says:

      The fact to keep in mind is that the market is not a game of chance – we’re not playing roulette. In gambling you’re talking risk, in investing you’re talking uncertainty. A roulette wheel is a generator of a statistical distribution which can be represented very nicely by a model. If you assume that the wheel hasn’t been manipulated you can figure out your odds pretty quickly. If you compare this with the markets you’ll see that you never get a chance to understand the process (“the wheel”) by which the returns (“the numbers”) are created. But we still attempt to model the stochastic process (think VaR!).

      If you apply this thinking to options you’ll see that there are very many people out there, who think that they know the “real value” of an option. They base their price on an underlying statistical model which is probably going fail at some time in the future because the underlying generator of returns (the market) does something unexpected. This will then lead to some option buyers making a killing and others – naked sellers blowing up”

      Karsten,

      You should re-examine the roulette wheel analogy. The “Vig” or vigorish of a roulette wheel with a single ‘zero’ and a roulette wheel with BOTH a single ‘zero’ AND second “double zero” differs according to the differing statistical designs of each.

      Perhaps I am misunderstanding your case, and if so I apologize. But compare one wheel with a single zero versus another with two zeros. Because each spin on the two wheels is a unique statistical event, there is the possibility that over a million spins on each, that the wheel with only one ‘zero’ will actually produce less profit for the House than the wheel with two ‘zeros’. Yet this would be a statistical abberation. In the vast, vast majority of cases the person who identifies the greater statistical advantage to the House using a double zero roulette wheel over another House using a single zero roulette wheel would be wise to bet on that House that is LIKELY to enjoy a higher profit due to using the double zero roulette wheel.

      My point is that even a system with a predictable statistical model, when averaged across innumerable ‘events’ that are unique in and of themselves within that model, possesses a nasty surprise or three that are unavoidable if a handful of outcomes of those ‘events’ are what one is risking upon. (Personally I like craps as a gambling analogy better than roulette). To the House, roulette isn’t considered a “game of chance” (it doesn’t pay ‘true’ odds!). Every casino “gambling” game has a designed in Vig that the House depends on to evaluate it’s long term profitability. Even in Craps, which (with behind the line odds) allows an individual player to come closest to ‘true odds’ with the House, there is STILL enough of a Vig to make it worth the House’s effort to run Craps tables.

      Whether a particular roulette wheel ‘loses’ more than it ‘wins’ for a casino over the short term isn’t really a consideration, as unless there’s some specific design flaw the casino knows this is a abberation, and that as ALL it’s roulette wheels generate more and more individual ‘events’ towards infinity, the House will continue on average to profit via the vigorish.

    5. Jonathan Says:

      Alexander,

      I think that the main points are that 1) the statistical distribution of roulette outcomes is well enough understood that casinos rarely go out of business and 2) the statistical distribution of market price moves is poorly enough understood that traders, even very smart ones, often go out of business.

    6. Karsten Says:

      The roulette wheel just serves as an example of a generator (of random numbers). I was not contrasting the possible p&l in a casino to an investors p&l.

      The main difference between markets and gambling is that we can calculate the odds in gambling. The house can then adjust payoffs to the probabilities – it is understood that the house has a lot of money so it can stay the duration.

      There is no orderly returns-generator behind finacial markets. Imagine playing roulette in a casino where the table is in one room and the wheel is in another (locked) room. The croupier then goes in the locked room and comes back with a number.

      This is what happens in markets. We have no idea if he actually uses the wheel or if the wheel is fair if he does use it. The casino could at times spin the wheel and make up numbers at other times.

      As we human beings are orderly, we look at the past – say – 10.000 numbers and say “wow, this looks like such-and-such a distribution”. This assumption holds up until the guys in the locked room start getting frisky and come up with numbers that are not even on the roulette table. We then add the numbers to the table and incorporate this event (think “fat tails”) into our model.

      My point is that it is a fallacy to compare a decision under risk (gambling with a fair wheel – i.e. known odds) with a decision under uncertainty (life and markets).

    7. Jonathan Says:

      Well stated, Karsten.

    8. Bill Stepp Says:

      Lex,

      Frank Knight’s distinction between risk and uncertainty goes back to his book _Risk, Uncertainty and Profit_, which was published in 1921, not the ’30s.
      And since when are options always undervalued?
      I doubt any option trader would agree.

    9. Lex Says:

      Thanks, Bill. I just shot from the hip on the date of the Knight book. I had not recalled that he was active so early. I read Risk, Uncertainty and Profit many years ago, and it mostly went over my head at the time, though I did manage to carry away the core idea.