Sympathetic Research
Vol #206: December 12th, 2024
It’s not just humans that have a bias for the status quo.
There’s a very slight statistical edge to the “same side” in a coin flip - it lands back upright roughly 50.8% of the time. With a proper flipping machine, a casino could turn this into a game with a better edge than blackjack, but slightly worse than roulette.
A coin toss is easy to model in our heads, with only two possible outcomes, and a fixed percentage success rate. As we apply this to other scenarios, we can adjust the win rates, or and build games of chance with various different pay outs.
Aspiring players will spend the flight to Vegas reading Beat the Dealer, and attempt some amateur counting and basic strategy to try and get their odds as close as possible to even. “And I’m getting free drinks!” the justification goes.
What is incredibly difficult to grasp, is the streakiness of any random variable. Just like equity charts don’t grind up 8% a year at 3bps a day, even a basic coin flip exhibits some serious streakiness.
Across one million flips, a simulation of a perfectly 50/50 coin shows maximum streaks of 18-20 flips every time you run it. The chances of getting 20 flips in a row is the simple exponent (.50)^20, or 1 in 1,048,576. Half that if you are willing to have either a heads or a tails streak.
But the chances of any run of 20 in a row at any point in the million flip series is much higher. It’s a complicated statistical puzzle called the “Birthday Problem”, and is the same logic that provides the fun fact about how it only takes 23 people in a room for there to be a 50% chance of sharing a birthday.
If you’ve ever considered a martingale strategy, this should be a blazing red warning. One in a million might not hit the VAR calculation, but if you size your bet at $1, you’ll need a bankroll of a million bucks to sustain that 20th bet.
Doubling your bet every time is not a good strategy - that’s financial advice. But even if we’re not scaling, the realities of streakiness bleed into every trading strategy. Chopping those million trades up into 1000 instances of 1000, the average of the longest streak in each dataset is just over 9. Flip a coin every trading day for four years, and at some point you’re going to hit 9 in a row - either direction.
Most trading strategies hope to do a little better than this. Either the win rate needs to go up on an even money bet, or the payout needs to be lopsided.
A 70% win rate feels invincible. You regularly hit 5, 6, 7, 8 correct trades in a row. Run a couple million flips and there are instances of 35, 40 wins in a row. But 5 or more bad trades can still happen in a row about ~1% of the time. Two and half times a year. More often than you go to the dentist.
Bring that down to a humble 55% win rate, and you’re going to be doubting your edge regularly.
Even worse, if your win rate is high but the payout isn’t appropriate, you’ll be deluded by success until the walls come crashing down. Collecting $1, 9 times in a row seems like a great strategy until you miscalibrate and have to pay out $10.
Kris over at moontower says it fantastically here:
“Unlike rolling dice or flipping coins, it’s hard to learn anything about the distribution of prices from direct experience. Historicals help but you only have to look at acute incidents in markets over the past 5 years alone to appreciate the challenge of calibrating what’s improbable.”
When you’re building a trading strategy, you need to be aware of both the hit rate and the expected value. It’s just as important to right size that 1 in 10 payout, as it is to be prepared for 5 losses in a row on a 70% win rate.
This becomes even more devilish as psychology enters the trading game. Trade a daily coin flip at 70% win rate and all of the sudden for five straight nights you’re going to bed doubting yourself. What’s changed? Did someone swap the coin? Am I accepting too little for these short positions or paying up too much for longs? Should I be hedging with UltraShorts and VIX teenies?
While the theoretical informs the practice, there is a distinct gap. Transaction costs or slippage explain part of the messiness of the real world, but the human element is uniquely important. Not only are the benchmarks of expected value constantly moving, but counterparties are also adjusting as the market mechanism grinds towards efficiency.
Mathematical simulations only know price and count, options in the real world require additional indicators or perspective to know whether they’re right to trade. The same $2.50, 30 delta put spread is a buy in some environments and a sell in others.
The payouts are relatively easy to calibrate. They’re what the market gives you at any given day. Most of the time they’re efficient, but they do get kinked and bent out of shape as participants express their biases.
What to do next looks conveniently like the scientific method. First there’s a problem definition, and some observations. Let’s be honest, you’re only going through this rigor because you know what it’s like to lose money, in the near or distant past. Much fiction is created in Excel and Python, so be wary of how to collect and analyze the data.
But even in this quantitative research lies a profoundly human element. Celebrating Max Planck’s sixtieth birthday, Albert Einstein gave a speech about the Principles of Research. He might as well have been talking about finance. (Replacing trader with physicist and cosmos for market).
“The supreme task of the {trader} is to arrive at those universal elementary laws from which the {market} can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them.”
The highlights are mine, because they are distinctly at odds with the way we typically think about sterile labs and white coated researchers. Yet they align perfectly with my model for successful traders.
There are dozens of times a day where illogical things happen in the market. It will look like dealers trying to pin a stock, or predictable market action. But it’s really just a big RIA in Dallas unloading some equities on a hunch. Or the arbitrary hedging action that comes from flipping tails four times in a row. To apply an unsympathetic and narrowly rational lens to these behaviors will lead you astray.
Intuition comes through experience. And while you can’t intuit the chances of flipping tails 25 times in a row, you can effectively parse competing hypotheses. Over the past two months the (liquid) security that would most significantly reduce one of my newer strategies volatility would have been long BABA stock. Thanks to ChatGPT and some quick hacking I know that, but my experience tells me that’s not really practical or useful.
Trading is a continuous process of research and adaptation. We need to leverage all the modeling we can to frame expectations and come as close as possible to some independent truth. Yet because human managers are capable of adaptation - their survival depends on it.
The cheese is on the move, and a 55% win rate is fuzzy at best. Finding edges in the market place requires one foot planted firmly in the realities of number theory and position sizing, with a head in the clouds experiencing and intuiting from the ebb and flow of daily price movements. Both of those forces have to be comfortable with a position.