I have been meaning to read Ed Thorp’s new book A Man for All Markets. Short on time in recent weeks, I settled instead for a succinct interview with Thorp in Jack Schwager’s book Hedge Fund Market Wizards. Below are highlights in which Thorp shares his thoughts on position sizing and risk management. Key takeaways: (1) public markets are zero-sum redistribution tools, and (2) always determine your edge before risking capital!
When To Sell, Mistakes, Psychology
“JS: At what drawdown point would your position be reduced to zero?
ET: Twenty percent.
JS: How far down did you get?
ET: Our maximum drawdown was about 14 percent to 15 percent, by which point we were trading only about one-third of our normal base position size.
JS: How would you get restarted if the drawdown reached 20 percent?
ET: You wouldn’t. You have to decide ahead of time how much of a drawdown would imply that the system is not as good as you thought it was, and therefore shouldn’t be traded.
JS: In hindsight, do you think reducing your exposure on drawdowns was a good idea?
ET: It all depends on how confident you are about your edge. If you have a really strong conviction about your edge, then the best thing to do is sit there and take your lumps. If, however, you believe there is a reasonable chance that you might not have an edge, then you better have a safety mechanism that constrains your losses on drawdowns. My view on trend following was that I could never be sure that I had an edge, so I wanted a safety mechanism. Whereas for a strategy like convertible arbitrage, I had a high degree of confidence as to the payoff probabilities, so reducing exposure on drawdowns was unnecessary.”
Utilizing quantitative stop loss triggers or predetermined criteria for position termination could help eliminate bad decisions associated with psychological glitching when an investment moves against you. The stop loss makes the decision for you based on a framework that was created under neutral psychological circumstances, before any money was lost. For many qualitative investors operating without stop loss triggers, termination of a losing position requires overcoming significant psychological barriers such as loss aversion, anchoring, etc.
Expected Return, Sizing
“…a lesson about managing money that stuck with me forever after. Don’t bet more than you are comfortable with.”
“I learned about the Kelly Criterion from Claude Shannon back at MIT. Shannon had worked with Kelly at Bell Labs…The Kelly Criterion of what fraction of your capital to bet seemed like the best strategy over the long run. When I say long run, a week playing blackjack in Vegas might not sound very long. But long run refers to the number of bets that are placed, and I would be placing thousands of bets in a week. I would get to the long run pretty fast in a casino. In the stock market, it’s not the same thing. A year of placing trades in the stock market will not be a long run. But there are situations in the stock market where you get to the long run pretty fast—for example, statistical arbitrage. In statistical arbitrage, you would place tens or hundreds of thousands of trades in a year. The Kelly criterion is the bet size that will produce the greatest expected growth rate in the long term. If you can calculate the probability of winning on each bet or trade and the ratio of the average win to average loss, then the Kelly criterion will give you the optimal fraction to bet so that your long-term growth rate is maximized…
Say I am playing casino blackjack, and I know what the odds are. Do I bet full Kelly? Probably not quite. Why? Because sometimes the dealer will cheat me. So the probabilities are a little different from what I calculated because there may be something else going on in the game that is outside my calculations. Now go to Wall Street. We are not able to calculate exact probabilities in the first place. In addition, there are things that are going on that are not part of one’s knowledge at the time that affect the probabilities. So you need to scale back to a certain extent because overbetting is really punishing—you get both a lower growth rate and much higher variability. Therefore, something like half Kelly is probably a prudent starting point. Then you might increase from there if you are more certain about the probabilities and decrease if you are less sure about the probabilities.”
Investor using the Kelly Criterion in qualitative strategies (vs. blackjack / quantitative trading) ultimately encounter the “garbage in, garbage out” problem. Probabilities and expected returns in, for example, value investing are inherently subjective, therefore would impact the effectiveness of formulaic sizing frameworks like the Kelly Criterion. There is often noise around determination of probabilities & expected return as influenced by human psychology on any given day or hour. Any potential judgment inconsistencies would be detrimental to a “long-run” formulaic sizing framework.
Capital Preservation, Risk
“…there are no zero-risk trades…There was some remote possibility that we overlooked something. There is always the possibility that there is some unknown factor.”
“We had to be very careful with any possessions we had because it was all hard to come by. We had very little money and were just barely getting along. So nothing was wasted; everything was conserved…As far as risk goes, it made me think very carefully about planning for the future and trying to make sure that I had the downside covered so that I wouldn’t be caught in some awful economic circumstance where I wouldn’t have enough to get by on. It didn’t so much worry me, as it was something that I thought about.”
I wonder, could having lived through financial adversity make someone better at managing investment risk?
Sourcing
“…historically ideas don’t just appear in one place; they tend to appear in several places at almost the same time.”
“…the question wasn’t ‘Is the market efficient?’ but rather the appropriate questions were ‘How inefficient is the market?’ and ‘How can we exploit the inefficiencies?’ The claim of market efficiency, which implies that no market edge is possible, is a hollow statement because you can’t prove a negative. But you can disprove market efficiency if there are people who have a demonstrable edge. There is a market inefficiency if there is a participant who can generate excess risk-adjusted returns that can be logically explained in a way that is difficult to rebut. Convertible arbitrage is a good example. You can lay out exactly how it works, why it works, and approximately how much return you expect to get.
… I think inefficiencies are there for the finding, but they are fairly hard to find…It has gotten harder for me, but that may only be because I am older and less interested, and have more money, which makes me less motivated.”