Bracketology and Trading: Probabilities of Streaks
By Tommy O’Brien / TFNN.com
The NCAA® tourney is always a fun time of the year for sports fans. Did you happen to fill out a bracket this year? It starts with 64 teams each year (aside from the 4 play-in games) with a dream of winning 6 consecutive games to become National Champion. Because the NCAA basketball post season is a single elimination tournament that means that each team must win 6 consecutive games, which requires a lot of skill and at least a little bit of luck on their side. If you’ve ever watched the tournament before then you are well aware of the vast amount of upsets that are unavoidable. Even when there is a high probability of success you must be aware that losses will be incurred, and this is a valuable lesson that applies to trading as well. As traders, we are always looking for trading set ups and analyzing probabilities of success to improve any edge in strategy.
What if I told you that last year’s National Champion Villanova, which happens to be my alma mater (solid hidden brag), had an 89% chance of winning each game they played in this year’s tourney. What would you say their chances would be of repeating as national champions with an 89% chance of winning each game?
Let’s ignore for a moment that we already know they didn’t even make the sweet 16! Well, surprisingly, even if Villanova had an 89% chance of winning each game they actually would have been an underdog to repeat with only a 49.70% chance of success of 6 consecutive wins.
0.89*0.89*0.89*0.89*0.89*0.89 = 49.70%
This number usually catches people off guard as they instinctively assume that any team entering the tourney with an 89% chance of success in each of their 6 games would surely be a good bet to win the championship more often than not. Sometimes it’s not intuitive to realize how probabilities shift when looking at consecutive events.
When trading binary options you are constantly forced to analyze the risk vs. reward of a trade compared to the perceived probability of success. If you are risking $80 to make $20 then you should believe there is at least an 80% chance that your binary option expires in the money if you plan to hold it until expiration. Let’s examine some probabilities of possible trades, and then how those probabilities shift when looking at possible winning and losing streaks.
Here is a chart of the Nadex US 500 June Index, which is based on CME® E-mini S&P 500 Index® Futures, as of 4pm on March 27th. Along the right axis are some of the weekly binary option strikes available that expire at 4:15 p.m. ET Friday, leaving just over 4 full days until expiration. Circled in red is the strike price that we’ll be discussing for a theoretical trade example.
If you bought the >2,316.5 binary option strike for $80 then you would be risking that $80 for a maximum profit of $20 if the contract expired in-the-money on Friday afternoon for the full settlement value payout of $100 per contract. In this theoretical trade, essentially you are putting up $4 of risk for every $1 of potential profit due to the fact that the current market is at 2,338.75, which is more than 22 points above your chosen strike price. With this initial trade advantage, as long as the Nadex expiration value of the underlying market closes anywhere above 2,316 as of 4:15 p.m. ET Friday then you receive the full value of $100 for a payout.
What if you planned on making 6 identical trades every day, with each trade having a theoretical 80% chance of success? What would the probability be on any given day that you are profitable on all 6 trades?
The answer is 26.21%. (0.80*0.80*0.80*0.80*0.80*0.80=26.21%).
This applies to longs and shorts, regardless of your market expectation. If you’re a trader that plans on making higher probability trades like our earlier example where you’re risking $4 for every $1 of potential profit then you should be aware of the very real possibility that trade losses will be incurred on a regular basis, just as upsets are all but guaranteed in the NCAA tourney. Only about 1 out of every 4 days will you likely be profitable on all 6 trades per day, even if you have an 80% chance of success of each trade being profitable. If you’re a trader that likes high probability and high risk vs. reward trade set ups then you should be aware of the probabilities of consecutive profitable and losing trades you could likely face throughout the year.
Let’s now look at the other end of the risk vs. reward spectrum. What if you’re a trader that likes risking small amounts on low probability events for high reward payouts? Here is a chart of the Wall Street 30 June Index, which is based on the CBOT® E-mini Dow® Futures, as of about 3:35 p.m. ET on Monday March 27th. Along the right hand axis of this chart are a list of some of the daily binary option strikes on the NADEX exchange, which expire at 4:15 p.m. ET, leaving just over 40 minutes until expiration.
If you bought the >20,530 binary option strike for $15 then you would be risking that $15 for a maximum profit of $85 if it expired in the money. Essentially you would be risking $1 for every $5.67 of potential profit. The reason for this risk vs. reward set-up is quite the opposite of the previous example as the underlying market currently sits more than 30 points out-of-the-money with only about 40 minutes remaining until expiration.
If you planned on making 6 trades each day, and each of those trades having an identical 15% chance of success, what is the probability on any given day that you could lose all those trades? To figure this out you calculate the probability of 6 consecutive losses (If you have a 15% chance of winning then you have an 85% chance of losing).
(0.85*0.85*0.85*0.85*0.85*0.85) = .3771, which = 37.71%
What this illustrates is that you have more than a 37% chance of losing all 6 trades you make on any given day, if they each have a 15% chance of success. This means that more than 1 out of 3 days you will lose everything you risk for the day when making those 6 theoretical trades. Are you equipped to handle that on a regular basis? At first glance this statistic is surprising to most, yet it demonstrates the swings that you will go through as a trader when facing consecutive outcomes. If about 1 out of 3 days you lose all 6 trades you make with a 15% probability of success, then you should be seriously considering the possibility of multiple consecutive days of all losses.
Let’s say you go 0 for 6 on Monday with all losses to start the week. When you wake up Tuesday morning there is still about a 1 out of 3 chance that you will then proceed to lose all 6 trades on the 2nd day of the week. If you win a coin toss 10 times in a row, the odds of the 11th flip are still 50/50 even though it would represent 11 consecutive coin flips won. Streaks are a part of trading much like they are a part of the NCAA tournament, and understanding the probabilities of those events occurring can allow you to make better decisions. Planning for the expected swings in trading, and bankroll management are two crucial factors to any profitable strategy.
This year we have a #7 seed South Carolina in the Final Four, while last year’s National Champion and the overall #1 seed Villanova didn’t even make Sweet 16. Anything can happen in the NCAA basketball tournament, just as anything can happen in trading. Preparing for all possible outcomes, and having a keen understanding of the probabilities of those events occurring, can help any trader be more successful.
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