Monday, November 07, 2016

Evens-Equivalent Trades

Risk of Ruin (RoR) (Epstein 2009) provides an easily understood metric (probability of bankroll depletion before doubling it) with which to compare strategies. By way of illustration, let us assume that both you and your brother are recreational handicappers. You trade baseball, home-underdogs and he trades horse-racing, second-favorites, as follows:

Sport
Bankroll
Trades
Average.
Odds
Average.
Win.Rate
Average.
Stake
Evens.
Odds
Evens.
Win.Rate
Evens.
Stake
Expected.
Value
Standard.
Deviation
EV.SD
Edge
Ruin.
Risk
MLB
5,000
500
2.10
51.00%
250.00
2.00
53.37%
263.05
17.75
262.45
219
7.10%
7.11%
H-R  
2,500
1,000
3.50
31.00%
100.00
2.00
52.62%
162.10
8.50
161.87
363
8.50%
16.53%

In the classic treatment of ruin, there is a working assumption of even-money trades to make the calculations tractable. To that end, we must first transform our real-world trades into their even-money equivalents with the same edge and volatility, see Krigman (1999). Despite having a smaller edge and a larger stake, you have a lower probability of depletion than your brother principally because you are risking a lower percentage of your bankroll per trade. Ideally, your RoR should be below 5% and to achieve this you both would have to either increase your bankroll or decrease your stake, as follows. [(MLB: 5%, 218.20 or 5730); (H-R: 5%, 54.97 or 4,546)].



Note that Edge's impact only equates with that of Volatility after 219 trades for you and 363 trades for your brother. And it takes a minimum of 806 trades for you and 1336 trades for your brother before you can be at least 95% confident that the combined effects of positive edge and mixed-bag volatility work in your favor to guarantee positive bankroll growth. In other words, despite having potentially successful trading strategies, you both will be well into your second season of handicapping before you can be sure of beginning to reap the benefits!