After reading Size Matters, I fired an email off to The Quant, who has been sleep-deprived since his new son’s arrival in late-December. Still, what he can do with one brain cell may certainly be much more than my entire brain, so here it is.

Teresa’s Question

Hope you’ve had some sleep lately! ;-) I have a quick question.

A friend called today after reading the attached and asked me about the standard practice of people plugging in the batting average of their trading system as “the edge”. Somehow, I think this is incorrect.

For example, Thorp’s edge was in identifying discrepancies between two types of securities - classic arbitrage - and being able to lock in/hedge the position from the start. The outcomes were quantifiable before putting on the trades. He was able to do this with number crunching when computers were not on every desktop. That was his edge, in my opinion, but traders who input their batting average aren’t really doing the same thing, are they?

I mean, in my tiny mind, one’s edge would be the defined as anything over random, so a trader with a 53% batting average is doing only a tiny bit better than the expected 50%. So to implement Kelly is problematic because “the edge” is not what it seems, and that’s why we are better off to focus on risking only a certain percent of equity a la the simple Trader Vic formula - bet a certain percent based on the account balance, so when you’re up you trade bigger. When down, trade less. Does this make sense?

The Quant’s Answer

Not much sleep, so my response might not be too clear…

You have to estimate the parameters of a trading system (win %, win/loss amounts) from past data. I think you can use more statistics to get confidence intervals around those numbers - so an idea of how stable over time. It would then be best to be conservative when plugging into the formula.

If you get very conservative you’ll end up with your conclusion: “better off to focus on risking a certain percent of equity a la the simple Trader Vic formula”.

EG: coin toss which is 50-50, but win 2 and lose 1

As in his paper, (page 3), edge = 0.50 and odds = 2. Gives optimal f = edge / odds = 0.50 / 2 = 25%. Risk 25% of bankroll.

Now reduce the success of the system. Win 1.1 and lose 1 (change assumptions to not be as confident in how much we win), still with 50-50 odds. Edge = 0.05, odds = 1.1. Optimal f = 4.54%. Risk 4 or 5% of bankroll. That’s a lot less.

Similarly, keep win:loss at 2:1 but reduce win % to 35%. Now, edge = 0.05, odds = 2. So edge / odds = 2.5%. Also a lot less

As we reduce the success parameters further (and probably towards realistic levels since winning systems are hard to come by) we start to see results telling us to risk 2-3% of bankroll as in the examples I have given.