Risk Management For Trading - Part I

Part I - Expected Value

Table of Contents

• Trading is too risky

• What is risk?

• Everything in life has risk

• How to quantify risk: Probability

• How to quantify risk: Risk vs. Reward

• How to quantify risk: Expected Value

• Variance - Your #1 worst enemy

• Verdict

• Trading risk vs other businesses

Trading is too risky

A common misconception around trading is its perceived similarity to gambling. Frequently, people express concerns that trading is "too risky" and is essentialy the same as throwing away your money. This statement usually stems from people who've heard horror storries of relatives or friends purchasing penny stocks and then loosing it all, or even have experienced it themselves.

And in that case I'd agree. This is way too risky and can lead to disaster pretty fast. However, I don't consider that to be trading.

This specific example is only one of multiple possible approaches to let money work for you. In my opinion, it's incorrect to label trading as "too risky" overall because of this one example.

I believe it would be far more helpful to think about this from another perspective. Instead of living in denial and projecting the fear of financial ruin onto others, it would be constructive to take responsibility for the situation and acknowledge that there may be another approach to this.

This challenge is widespread among humans because of our natural insticts. We're hardwired to succeed to survive and when we perceive someone else to be better than us, our brain goes into animal mode. It wants to be better than this person and belittling them is usually easier than putting in the work.

Consequently it is their belief that everybody must face financial ruin through trading and only the "lucky" ones are fortuante enough to make it. They couldn't have taken any measueres to prevent their downfall! It was destined all along and they just had bad luck!

Let's apply some critical thinking to this problem instead. At the heart of critical thinking lies the belief that we should use our own reasoning and abilities to do independent research to reach our own conclusion rather than simply accepting what everyone else is saying.

The influental chinese military strategist Sun Tzu teaches in The Art of War "to rely not on the likelihood of the enemy's not coming, but on our own readiness to receive him; not on the chance of his not attacking, but rather on the fact that we have made our position unassailable."

Let's become ready to embrace the risk of ruin!

What is risk?

My first big question when looking at something is always "what is it?" Before I can come to any conclusion I first need to understand what I'm thinking about.

The Cambridge dictionary describes risk in simple tearms as the possbility of something bad happening. It involves uncertainty about the consequences of an action in regards to something that people value.

Inherent in this statement is the idea that everyone has their own tolerance or appetite for risk. What one person values most is not necessarily the thing that another person values the same. Losing $10.000 might be too risky for one person but may not be the same risk for someone else.

An important thing to note here is that there is no absolute right or wrong! The nature of risk is dynamic and changes from individual to individual. Of course trading has risk, but what doesn't?

Everything in life has risk

Risk in itself is not bad! We take calculated risks where we percieve our chances to succeed to be higher than our chances of failure everyday. Driving in a car has risk, flying in a plane has risk, playing the lottery has risk, hell even just going outside has risk associated with it. As long as you're taking risk that is aligned with the direction of your goals, it's totally fine to calculate it and take it when the odds are in your favor.

A lot of people tend to only think about risk when it comes to money because of a phenomenon called loss aversion. And for the most part, they are right!

Consider the following example:

• you're offered a gamble on a coin flip.

• if it lands tails: You lose $100.

• if it lands heads: You win $110.

Even though the mathematical expected gain for every coinflip is $5 (see next section for the calulcation), most people are more likely to decline this bet. However, professional gamblers (read: professional risk takers) will take this bet every time! Why is it that professional gamblers are so confident in taking this bet? Because they rely on two concepts called Risk vs Reward (R:R) and Expected Value (EV) to make their decision instead of gut feeling!

How to quantify risk: Probability

Now that we understand that everything has risk, "not taking risk" doesn't suffice as argument anymore. We need to have some kind of metric to decide whether it's worth taking a risk or not. Luckily there are already ways to put any type of risk associated with betting into context and calculate it.

The first term we need to understand is probability. It is used to describe the number of times something will happen out of a total number of chances and is commonly written as a fraction. 1/2 is read alout 1 out of 2. The total number of possible outcomes is written at the bottom (2) and the target outcome is the top (1).

The probability of rolling a 5 on a die is 1/6 because there are 6 total outcomes for a roll and only one of those is our target (5).

Probabilites are also commonly expressed as percentages and converting fractions to percentages is fairly easy. You just need to divide the target (top) through the total number of outcomes (bottom) and then multiply the result by 100.

The probability of rolling a 5 is 1/6 * 100 = 0.167 * 100 = 16.67%.

All these numbers represent the same thing 1/6 = 0.167 = 16.67%

The next concept to understand is a ratio. It has two numbers with a colon in between. It looks like 5:1 and is read five to one. The first number describes how many times something does not happen, the second one how often you will hit your target. There are 6 numbers on a die in total, 5 of which are not a 5 (1, 2, 3, 4, 6) and only one number that is a 5 (our target). So the first number is a 5 and the second number a 1.

The odds against us rolling a 5 are 5:1.

We can convert these two back and forth using the formula: m/n = n/(m+n) where m:n is our ratio and n/m+n the probability of us hitting our target. Our probability to roll a 5 is 1/6 and the odds against us are 5:1. Notice that if you add the two numbers in the ratio together you get the bottom part of the probability.

You can play around with the idea here.

Code examples in python for the calculations can be found here.

How to quantify risk: Risk vs. Reward

Up until now we only talked about chance, something happening X amount out of Y times. But this does not yet represent risk. To model risk we have to put it into the context of winning and losing which we can do by weighing our expected losses to the reward we're expected to gain.

This is called the Risk to Reward Ratio (R:R). The amount of our expected losses equal the times we lose multiplied by the amount we lose and the amount of our expected wins equal the times we win multiplied by the amount we win. Let's take a closer look at our coin flip example.

We're winning $110 every time we hit heads and lose $100 every time it lands on tails. The probability of each of this scenarios is 1/2 or 0.5 or 50%. To have a quick first estimate if this might be a profitable bet, we can use the formula R:R = Risk/Reward.

It's a quick estimate because it only compares what you stand to gain against what you stand to lose, without considering the likelihood of either.

$100 / $110 = 0.91 or 0.91 : 1 which means that for every 0.91 units (dollars in this case) you risk, 1 unit is the potential reward. A ratio less than 1:1 means you stand to win more than you risk, which is generally seen as a favorable bet.

You can also use the concept of odds to solve for the win probability needed for this bet to be profitable using the formula n/(m+n) where n is your risk and m your reward: $100 / ($110 + $100) = 0.4762 and then convert it from a decimal into a percentage multiplying it by 100 = 47.62.

You need to win at least 47.62% to be breakeven on this Risk:Reward ratio. Mathematically everytime you're getting better odds or have a better winrate than this, it's worth taking the risk. Every time you lose will be offset by the times you win my multiples.

How to quantify risk: Expected Value

We already know that our coin flip bet might be profitable. But how profitable? The fundamental bedrock of profitable gambling (read: risk taking) is the calculate the expected value (EV) of our overall expected outcome. EV combines the two concepts of probability and risk:reward by summing up how much you lose multiplied by all the times you lose and the amount you win multiplied by all the times you win:

EV = win% * win - loss% * loss

Let's review the math for our bet and extend it with EV calculation:

The probability of the coin landing on heads is 1/2 or 0.5 because our target or win scenario is just heads (one side) but the coin has two sides in total. So the top number is 1 and the bottom number a 2.

The same is true for the probability of the coin landing on tails. As a shortcut to calculate the second probability you can just convert the fraction of the first probability to a percentage and then substract it from 1: in this case 1-0.5 = 0.5.

The odds against the coin landing on heads are 1:1. Solving 1/2 for n/(m+n) yields us 1/(1+1). So m:n is 1:1 which means for every time our target scenario does happen (land on heads) it also does not happen 1 time (lands on tails).

To calculate the expected value of this bet, we just fill in the variables with our actual values from the example:

EV = $110 * 0.5 - $100 * 0.5 = $5.0

Every time we win, we win $110. We win 1/2 or 50% of the time and every time we lose, we lose $100 which also happens 50% of the time. Note that we're not using the decimal representation (50%) of the percentage but its pure value (0.5) in the formula.

We're expected to win $5 on average every time we take this bet! This is the reason why every professional would take this bet every time. Because it literally prints money.

Calculating the expected value is done by
1: identifying each possible outcome and its probability and then
2: multiplying the probability of each outcome by its result and adding them all up.

But wait a minute.. didn't we say that most people are "probably right" to not take this bet due to their loss aversion?

Yes! Let's take a closer look at what might happen when we start engaging in this game of dice.

Variance - Your #1 worst enemy

In simple terms, variance describes the distribution of outcomes around the average of a probability scenario.

The 50% probability of heads and tails in our example are just an average and there are no set rules in which sequence they can happen. Probability doesn't work like that. It has no memory and also no imagination about the future. It simply states that if you were to run this scenario forever, your heads and tails hits would average out at 50% or 1:1. If you flip a coin 10 times it could land on tails 10 times in a row before then landing on heads 10 times. The distribution of outcomes is purely random and follows no exact rule other than averaging out at 50%.

For that averaging out to happen, you actually need the chance to play more than one time! If you only have $100 to play and the first result is tails, you lost all your money and can't realize your theoretical gain of $5 a flip anymore because you can't continue to play.

If we run a monte carlo simulation for this game, simulating 20 different players with a bankroll of $100 each, we can see that around ~25% of players actually go bust early. Their game results in a final account equity of $0. They hit a losing streak and never had the chance to overcome the bad variance against them and realize their true EV. Each line represents one players equity account.

If we increase their bankroll to $10.000 instead, no player even comes close to $0. They have enough capital to withstand the drawdown on their account until they finally overcome that bad luck.

PROTECTING YOUR BANKROLL IS THE NUMBER ONE PRIORITY!

And just like that we created empirical evidence for the assumption that taking on too much risk is indeed 'too risky' and will lead to financial ruin. Taking on too much risk in this case was a too small bankroll to play with.

So most people are right when they say "it's too risky" because they can't actually afford to take this bet mathematically. They would be risking too much and can actually go broke betting in this game.

However, "going broke" is relative. If you earn $10.000 a month and only have $5.000 of expenses, you'd have plenty of leeway before facing financial ruin by betting $100. If we set the bankroll of each player to $10.000, not one player is going broke.

Verdict

We've established a very solid foundation about risk and how to decide if it's worth taking it or not in the context of betting money. We've learned that controlling your risk is crucial to mitigate the risk of ruin and in most simple terms can be done by literally not risking too much. There's actually a lot more you can do to manage risk effectively, which will talk about in detail in later issues.

One thing I want to reiterate is how big of importance the concept of risk is when it comes to betting money.

If you still have any questions, feel free to contact us at contact@katanaquant.com or our social media channels and we're happy to help.

Before we say farewell for this week, I actually got a little bonus for you. Up until now we only looked at risk in the context of betting money as activity. Let's have a quick look at other common types of risk that are important in the context of trading.

Trading risk vs other businesses

If we take a closer look at a trading business, it's actually a lot more similar to starting any other business than you might think. Starting small mitigates a catastrophical risk of early financial ruin.

That's good advice for any business you want to start! Start small and limit your investment before you've gained some experince and become profitable. And only then start scaling up gradually.

Over the course of the next weekly issues we will learn that trading also does differ a lot from other businesses. What first comes to mind is the possbility to automate everything in quantitative trading while most small businesses require a lot of your time, at least initially.

To grow your trading business, you generally need to do some research and backtest new strategies, which can be done at any time of the day from anywhere you like. That makes for very flexible and mobile working hours.

Marketing is not needed which lets you focus solely on the operational side of things, namely your strategies and software.

The startup is a lot quicker than other businesses. You might need 1-3 months for your first profitable and sustainable strategy whereas starting a software firm takes about 3-5 times more investment, and 20 times longer only to find out that the business model actually doesn't work and is not profitable.

Another very important distinction is the fact that a trading business is highly liquid. In most cases you already have everything you need to get started: a computer and an internet conncetion. There is no need to invest more money into physical assets, properties, plants or other materials that all depreciate in value and require maintenance which results in extra costs over time eating away at the little appreciation they get through the demand & supply of their markets. It's also not really possible to just sell 1/256 of your office you just bought because you need that amount of money right now.

In my opinion a lot of arguments could be made that trading as a business is actually not as risky as most small businesses.

- Hōrōshi バガボンド

Disclaimer: The content and information provided by Vagabond Research, including all other materials, are for educational and informational purposes only and should not be considered financial advice or a recommendation to buy or sell any type of security or investment. Always conduct your own research and consult with a licensed financial professional before making investment decisions. Trading and investing can involve significant risk, and you should understand these risks before making any financial decisions.