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Kicking Tails


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Like many people, I find that poker strategy is a good analogy for risk-taking in investing. Poker strategy isn’t as much about what cards you are dealt as it is about how you play the cards you are dealt. As it is with markets, you can’t control the flop – but you can still correctly play the cards that are out there.[1] Now, in poker we sometimes discover that someone at the table has amassed a large pile of chips by just being lucky and not because they actually understand poker strategy. Those are good people to play against, because luck is fickle. The people who started trading stocks in the last nine years, and have amassed a pile of chips by simply buying every dip, are these people.

All of this is prologue to the observation I have made from time to time about the optimal sizing of investment ‘bets’ under conditions of uncertainty. I wrote a column about this back in 2010 (here I link to the abbreviated re-blog of that column) called “Tales of Tails,” which talks about the Kelly Criterion and the sizing of optimal bets given the current “edge” and “odds” faced by the bettor. I like the column and look back at it myself with some regularity, but here is the two-sentence summary: lower prices imply putting more chips on the table, while higher volatility implies taking chips off of the table. In most cases, the lower edge implied by higher volatility outweighs the better odds from lower prices, which means that it isn’t cowardly to scale back bets on a pullback but correct to do so.

When you hear about trading desks having to cut back bets because the risk control officers are taking into account the higher VAR, they are doing half of this. They’re not really taking into account the better odds associated with lower prices, but they do understand that higher volatility implies that bets should be smaller.

In the current circumstance, the question merely boils down to this. How much have your odds improved with the recent 10% decline in equity prices? Probably, only a little bit. In the chart below, which is a copy of the chart in the article linked to above, you are moving in the direction from brown-to-purple-to-blue, but not very far. But the probability of winning is moving left.

Note that in this picture, a Kelly bet that is less than zero implies taking the other side of the bet, or eschewing a bet if that isn’t possible. If you think the chance that the market will go up (edge) is less than 50-50 you need better payoffs on a rally than on a selloff (odds). If not, then you’ll want to be short. (In the context of recent sports bets: prior to the game, the Patriots were given a better chance of winning so to take the Eagles at a negative edge, you needed solid odds in your favor).

Now if, on the other hand, you think the market selloff has taken us to “good support levels” so that there is little downside risk – and you think you can get out if the market breaks those support levels – and much more upside risk, then you are getting good odds and a positive edge and probably want to bet aggressively. But that is to some extent ignoring the message of higher implied volatility, which says that a much wider range of outcomes is possible (and higher implied volatility moves the delta of an in-the-money option closer to 0.5).

This is why sizing bets well in the first place, and adjusting position sizes quickly with changes in market conditions, is very important. Prior to the selloff, the market’s level suggested quite poor odds such that even the low volatility permitted limited bets – probably a lot more limited than many investors had in place, after many years of seeing bad bets pay off.


[1] I suspect that Bridge might be as good an analogy, or even better, but I don’t know how to play Bridge. Someday I should learn.

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Categories: Analogy, Investing, Theory, Trading
  1. February 12, 2018 at 11:32 pm

    I play bridge. It is mainly about complex systems and information and using logic to decide what to do. Probability plays a secondary role, especially below the expert level.

    Poker is a better analogy here. But do learn bridge. It happens to be the best card game in the world!

    • February 13, 2018 at 10:56 am

      If it’s good enough for Gates and Buffett, it ought to be good enough for me!

  1. March 27, 2018 at 9:48 am
  2. March 28, 2018 at 12:03 am
  3. March 28, 2018 at 8:46 am

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