The Markov Property is a feature of stochastic processes that plainly means what’s happening now is the only thing that will affect what happens next. It is also called the memoryless property. Mathematically, it’s written:
which means that the probability of the k-th value of the stochastic process X being i, given the previous value was j, and given all previous values, is the same as the probability of the k-th value of X being i, given that the previous value was j. The important thing here is all other previous values except the immediate past don’t matter. Also, from the point of view of one-step back (k-1), the probable value of X in the next step (k) depends only on the information contributed at that particular point in time.
There is also a strong version of this property, aptly titled the ‘Strong Markov property’. The difference is that for the strong version, the probability of the next value of X, and all future values, depends on the current value. Both imply memorylessness—you forget the past and you only care about now, and how it affects either the next step (Markov Property) or the future (Strong Markov Property).
Side note for the non-mathematical readers, a stochastic process is a random variable whose probability distribution changes all the time or at least a number of times. If a random variable’s probability distribution is exactly the same always, you wouldn’t need to care much about the time dimension, but if it changes with time then you get a stochastic process. Quants think of financial assets as stochastic processes. Most people think of financial assets as random variables so they model them as if they follow one particular distribution. That’s useful in many cases but not quite right. An assets probability distribution changes with time. That’s why you always need to think about the out-of-sample distribution no matter what you are modeling.
Life is a Stochastic Process
“The only constant in life is change” - Heraclitus
If trading has taught me one thing, it’s how to stomach variance. My trades usually last a few days and my winning trades often go as follows: either they don’t seem to be going anywhere for hours or days, and then they move all at once, or they go my way, go back under water, and remain there for eternity before eventually going my way again. Rarely do I put on a trade and it just goes my way from the start.
Since I’m a small trader and the results of my trading mean a difference in my quality of life and my fortune, in the early days, my psychology, specifically my mood and outlook on life, would change with my paper pnl. If a trade was doing well, or I had had a few good trades, I’d assume it meant good things for my future, and vice versa. But after trading for a few years now, I’ve experienced many winning trades going red after initially being in the black, and recovered from several bad streaks— all of which is just part of the normal variance of trading. So I don’t react so much to a particular trade or even a few trades. But admittedly, a long series of good or bad trades affects me in a significant way.
Dealing with this kind of variance changed how I deal with things in my life too. I no longer label events in my life as good or bad as they happen, even if I feel good of bad in the moment. I don’t just immediately think that bad things will follow a bad event, and vice versa for good events.
Part of what changed my attitude is the Chinese fable Brent Donnelly shared in Alpha Trader:
There was once a farmer in ancient China who owned a horse. “You are so lucky!” his neighbors told him, “to have a horse to pull the cart for you.”
“Maybe,” the farmer replied.
One day the farmer forgot to latch the gate and his horse bolted. “Oh no! This is terrible news!” his neighbors cried. “Such terrible misfortune!”
“Maybe,” the farmer replied.
A few days later the horse returned, bringing with it six wild horses. “How fantastic! You are so lucky,” his neighbors told him. “Now you are rich!”
“Maybe,” the farmer replied.
The next week, the farmer’s son was breaking in one of the wild horses when he fell off and broke his leg. “Oh no!” the neighbors cried, “such bad luck!”
“Maybe,” the farmer replied.
The next day soldiers came and took away all the young men to fight in the war. The farmer’s son was left behind due to his injury. “You are so lucky!” his neighbors cried.
“Maybe,” the farmer replied. - Brent Donnelly, Alpha Trader.
Think of life as a stochastic process; whatever is happening, the distribution of probabilities changes all the time. Look for what you can do in the present to make what unfolds next favorable. That’s the key—looking for opportunities in the present. What the Markov property teaches us is that the only way to play a role in what happens next, and perhaps what comes in the future, is to act in the present. And that’s a powerful way to think about life, especially during the hard times. In those times, bring your mind back to the present and focus on what you can do.
“The most important decision you will ever make in your life is what to do with the next 24 hours” - Jared Dillian, WGGTB: Never Enough
Forgive Fast, Forgive Often; and That Includes Yourself.
The first time our Probs professor in Uni introduced the Markov property, he told us that the secret to his happiness is how forgetful he was of his own mistakes and other people’s. That didn’t make much sense to me at the time. I had learnt by then that people generally didn’t change—if someone did something to upset me, I would assume it said something about who they were as a person. I ruminated, and had a hard time letting go of things when someone did me dirty. I also didn’t easily forgive myself. I would dwell on my mistakes for days. What I didn’t see back then is how much energy all of that took away from me.
I don’t know who this saying is by, but it goes: ‘A strong man is hard on himself and easy on others, a weak man is easy on himself and hard on others.’
It’s great to be hard on yourself, but don’t beat yourself up when you make mistakes. Forgive yourself and forgive others too—quickly and often. Not for any moral reasons, but because it will be advantageous to you.
***
I’m a recent F1 convert and one of the things that astounded me about when I first started following it is how forgiving everyone is. A driver would swear like a sailor and scream obscenities at their engineer and it would be instantly forgotten. Another driver would total the car and no one would bat an eye. I found that quite amazing. I played basketball in high school and maybe there is some sample bias there but I found that when a team lost, teammates would point fingers. I also noticed that some teams were more forgiving. Anyone could shoot a three pointer and everyone else would go for the rebound or mark the opponents without complaining if the ball didn’t go in. Those teams tended to do quite well.
The level of forgiveness in F1 really impressed me. I think it says something about the value of being memoryless. F1 drivers need a lot of concentration. If you want your driver to succeed, you can’t put the emotional baggage of the past on them. It is in everyone’s best interest that mistakes are quickly forgiven and forgotten, however bad. It’s about edge. Reflecting on this has made it a lot easier for me to let go of things much quicker nowadays.
***
Jared Dillian once wrote about how being memoryless is a necessity for traders.
As a trader you must also have a very short memory—the memory of a goldfish. You fuck something up, you clean up the mess, and move onto the next trade. There is always another trade. This is something they teach professional athletes. Forget about the last pitch. Forget about the last at-bat. Forget about the last shot, no matter what the outcome. If you’ve struck out 54 times in a row, none of it matters. It was said that Derek Jeter was the best at doing this—he did not dwell in the past. He had absolutely no memory, and was out there hacking at his next time up at the plate. - Jared Dillian, WGGTB: Once a Trader, Always a Trader.
Of course any trader of merit will tell you how important it is to reset oneself each new day. That’s crucial, especially after a bad day. The first step is to forgive yourself for any mistakes you made, then clear your mind. Some traders meditate but I find that really hard. Instead, I clear my mind by doing specific things. The morning shower, the first sip of coffee, reading the news, journaling, to name a few. By the time I get to looking at charts I will have reset myself. Sometimes not 100% but at least 70%.
Don’t Fight the Last Battle
What most often weighs you down and brings you misery is the past, in the form of unnecessary attachments, repetitions of tired formulas, and the memory of old victories and defeats. You must consciously wage war against the past and force yourself to react to the present moment. Be ruthless on yourself; do not repeat the same tired methods. Sometimes you must force yourself to strike out in new directions, even if they involve risk. What you may lose in comfort and security, you will gain in surprise, making it harder for your enemies to tell what you will do. Wage guerrilla war on your mind, allowing no static lines of defense, no exposed citadels—make everything fluid and mobile. - Robert Greene, The 33 Strategies of War
I’m fascinated by the Japanese samurai, Miyamoto Musashi. It is said that he never lost a duel. That’s crazy to imagine. Robert Greene in his book The 33 Strategies of War claims that Musashi won each time because he would change his approach entirely to suit the current opp and the circumstances surrounding the duel. Every damn time.
Musashi wrote a famous treatise on swordsmanship called ‘The Book of Five Rings’ and if you read it you will see that his philosophy for life was about being more focused on the present. His principles include: don’t have preferences; don’t hoard weapons you don’t need; and, don’t base your actions on customary beliefs. He was quite an extreme guy who even detested any form of attachment including love and marriage; all that to be able to completely focus on the present in life and especially in a battle.
One thing I’ve noticed about people (and companies), especially when it comes to making money, is that they rely on the same strategies they have used before in life. In trading people rely on the same old strategies they’ve come to love, but I mean in other areas of life too. People rotate around a small set of actions, changing some minor details but not the core idea. Sometimes they come back to a strategy they used in their youth much later in life. This is one area where people can benefit from doing away with all their past beliefs and bring a fresh mind being memoryless.
Almost done with the RARCH side quest. I think I’ll take a break from the VIX studies and work on something new for the next post. It will be a surprise.
Madeon is my favorite EDM artist and DJ. He released this song on my Birthday in 2019 and seeing as it was a meh day, this was kind of a treat.
Until next time,
Brian
Hey Brian, thanks for all the work you put out for us traders, love the content and please keep it coming! Got distracted for a moment and saw the excerpt from Alpha Trader by Donnelly, and knew I needed to finish reading this article. Haven’t heard of Jared Dillian, but will be adding him to the list - once I get through the pile of books I already have 🥴