February 12, 2020

Volatility and Risk Aversion

12:24 PM

It’s been a very hectic couple of weeks. A lot of midterms and assignments means I don’t have time to focus on what I want to do, so I’m once again forced to put those tasks off until a future unspecified date. Next week, maybe. Probably. Hopefully.

I’m making myself write this one out without stopping or getting distracted or worrying about the quality and/or success of the result because it has honestly been a while since I’ve been able to actually finish one of these. I think things have been happening so fast and so frequently that I’m rarely able to get all of my thoughts down in one sitting. I’m always thinking about what’s going to happen within the next hour, within the next day, what I should be doing, when this task will end, etc. As with everything, my desire to analyze and control the trajectory of my life has interfered with my ability to actually do things in reality.

I often say that it would be naive to not think about the consequences of my actions. To have made a mistake and failed is the opportunity to not make the same mistake again. To have failed and not learned my lesson is foolish and generates pain that would otherwise be avoidable. Don’t take risks. Don’t gamble with your time. And so on, and so forth. Any other course of action would simply be reckless.

I’ve been trading a bit of options lately, ever since I was introduced to them in my Mathematical Finance class. Something interesting about options trading is that they can be strategically purchased or sold to create a variety of positions, each with their own strengths and weaknesses. The same position can be created multiple different ways with the same potential profit and cost, because options are priced perfectly fair, down to the cent. There’s no cheaper or more expensive way to create a position, and there are no free benefits. If you want protection against losing money, you pay for it with an initial premium. If you want a cheaper strategy, you pay for it because the strategy is riskier.

Risk aversion has been my default life strategy for a long time now. I avoid the volatile because it minimizes my loss, but I pay for it by forgoing the things I could gain. Shying away from pursuing a new relationship prevents me from getting into uncomfortable situations or potentially messing with the status quo of social circles, but it also leaves me wondering what I might have missed out on by not giving it a chance. Not practicing my skills saves me the frustration of a lack of improvement, but it doesn’t let me get any better, either.

I thought I was only acting in the ways I thought was most rational, but it turns out that the most logical strategy is not always the best. Sure, there are many, many occasions where that statement is true, but there is a reason that a large portion of mathematics and statistics remains theoretical, and that is because of the concept of randomness. And perhaps it may be all designed perfectly on a grand scale, but to us it is random and unpredictable. Only time will tell us for certainty whether something occurs or does not occur, and by then it is far too late for any logic or rationality to affect that situation, because it has already happened. To attempt to “game the system” and analyze the probabilities and possible outcomes of every action will simply lead to a predictable and repetitive life. Not predictable because it leads to where one wants to go, but in fact the opposite, as things never truly go according to plan. Most logical people would take a 90% probability of a smaller reward versus a 40% probability of a large reward, because choosing the latter would more likely result in zero gain. Over the course of 10,000 simulations, statistics will tell you that your expected reward will be higher when you choose the 90%.

But we don’t usually have 10,000 attempts at something. More often than not, it’s only one. Two if you’re lucky. But nowhere near enough to tell you for certain which is the better option. Choosing the safe option over the riskier one will always be more logical in the realm of thought, but it will always give you that which is predictable and consistent. And because the options are fair, that which is less risky will always have a less impressive return.

The Monty Hall problem is a very famous mathematical brain teaser that involves three doors on a game show. The player is told that a new car lies behind one of the doors, while the other two will have goats. The player selects door 1 and the host opens door 3 to reveal that there is a goat behind it. The player is then offered the choice to stay with door 1 or switch to door 2. It turns out that mathematically speaking, switching doors is more likely to reward the player with the car. Switching to door 2 is then supposedly the correct answer, as you may have been told by a very academically astute and slightly annoying friend before.

But suppose you are on that game show now, and you are presented with the same choice. You know that switching is statistically a better option: the math tells you that it gives you a 66.67% chance, while not switching leaves you with 33.33%. But you’re just living out one of 10,000 simulations. No matter which choice you select, whether you actually win or not is, at best, just a guess.

I’m not advocating for you to blow all your money on slot machines. I’m majoring in statistics and I’m fully aware of the power of probability and mathematics in influencing real-world events. I’m just telling you this now as someone who spent the last few years picking the safe option that it’s not all it’s cracked up to be. It is for the most part a very dull and unsatisfying life, with neither pleasant surprises or tall obstacles. It’s just nothing.

Perhaps the trick to living out this journey is not to try and predict where it will take you but to embrace some sort of naivety, living and making decisions for the moment, for your desires, without focusing too much on what the future could or could not hold (obviously, this does not apply to everything; please take reasonable steps to invest for your future and do not ruin your life). As C.S. Lewis wrote, “You cannot go on seeing through things forever. To see through all things is the same as not to see”.

Dealing with failure is still something that I struggle with, and I know most people can probably say the same. But to dwell on the possibility of failing is to forego yourself of success, which is in this case not just money or objects but true, meaningful life experiences, the worth of which is not quantifiable by numbers and dollar signs. To desire success must come with the open invitation of failure, as you simply cannot have one without the other.

And that, I suppose, is only fair.

- Sam