Life is a game of probability, reward and risk.
Trading options has introduced me to the relationship between probabilities, reward and risk. But the more I think about it, the more I realize this is not just a trading concept or even just a financial concept, this is a guiding principle of life. Let’s take a look.
Reward / Risk is inversely proportional to probability.
What does that mean? Well, let’s look at a few examples to illustrate.
The lottery. When you buy a lottery ticket, the potential reward is extremely high, possibly millions of dollars. The risk is extremely low, only a few bucks for a ticket. High reward divided by low risk equals a very high ratio. Since the reward to risk ratio is inversely proportional to probability, we can assume that the probability of winning the reward is extremely low. Are we correct? Absolutely. The probability of winning the lottery is extremely small.
Trading options. If you wanted to, you could approach trading options just like playing the lottery. Buy a bunch of $0.05 options. Set your target price at $1, you just made 20 times your money. Want more, set your target at $2 for a 4000% gain. The higher you set your price target, the higher your reward to risk ratio goes. But at the same time, the higher your set your price target, the less likely you are to achieve that target. So, if risk stays the same, then as reward goes up, probability goes down.
Beyond trading and finance.
Now let’s think about the bigger picture. Isn’t all of life just a continual series of reward to risk scenarios? For example, a baby starts to learn to walk. He has in his little mind a reward (to walk). The reward in this case is a constant, and so the variables here are risk and probability. When the baby starts trying to walk, he will risk falling down. What if the baby wants to try and avoid this risk. Well, if he never tries to stand up then he never takes on the risk. But at the same time, what happens to his probability of success if he never tries to stand? That’s right. As risk goes down, probability of success also goes down.
Now the baby is a young child who wants to learn to ride a bike. Learning to ride means taking off the training wheels, but there is a risk involved in that. If the training wheels never come off, the risk is reduced dramatically and so is the probability of achieving the goal (reward).
Into the emotional.
Now the young boy is much older. He meets a girl. He likes the girl. He wants to develop a relationship with that girl, possibly even a life-long marriage relationship. But there’s a risk involved. It’s an emotional risk. That is, if he commits himself emotionally to the relationship, there is a risk that he will get hurt.
So, he decides to limit that risk. He decides to hold back his emotional commitment — to avoid engaging fully in the relationship. As he does this, his risk goes down but what happens to the probability of success? Most likely, if he’s not willing to commit emotionally to the relationship, it is more likely to fail.
But what happens if he changes the reward? Maybe instead of a marriage relationship, he changes the goal to simply having a casual friendship. The reward goes down and therefore the probability of success goes up. He can limit his emotional risk and still potentially have a friendship. Higher reward requires higher risk if you want to keep the probabilities the same.
The probability factor.
When I was growing up, I often heard that if you wanted to do something great, it required risk. In other words, I understood reward and risk to some degree. But the part I never heard about was probability and how it was related to reward and risk. To me this makes a big difference. I know this has been a pretty philosophical discussion, but there are a few practical conclusions we can draw from it.
- The reason get-rich-quick schemes don’t work is because they violate this concept. They try to tell you that you can achieve a great reward with very little risk. But we know that if reward is high and risk is low, the probability of success is low as well.
- We should learn to accept a reasonable amount of risk and also to aim for a realistic reward. Trying to eliminate risk or aiming for an extravagant reward will ensure failure time after time because of low probabilities.
- Have respect for the equation and realize that over time, coming out ahead, even by a little bit, is a great success.