Couple of days back I was randomly chatting with some people on one of the very few whatsap groups that I am part of. Suddenly someone’s comment caught my attention and I was absolutely amazed at what I read. The guy was recommending buying stocks with money funded by his credit card. I almost jumped off my seat and engaged in a long conversation with him, which started on an unpleasant note. I must admit that I was so worked up by his this ’extremely risky’ suggestion that I was quite mean to him. I surely should not have targetted the person with certain comments that I did….however frustrated I might have been at his refusal to appreciate the obvious risks of his suggestion.

Understanding probability to understand risk

It dawned on me that lot of people underestimate ‘Risk’ simply because they are unable to comprehend ‘probability’ properly. This hypothesis was proven just a few minutes later when someone else started debating about the probability of tossing 100 Heads in a row. He seemed to think that the probability is 0.5 as each toss is independent. I almost gave up trying to explain to him in different ways that the probabiity of tossing 1 single head (H) in one toss cannot be same as that of tossing 100 heads consecutively in 100 tosses: HHHHHHHH…….100 times.

Hence I decided to write this post to discuss how ‘a very low probability of something bad happening’ can be misleading.
Note: To keep the example simple, I am keeping the discussion on ‘expectation’ out for the moment. Will do a detailed post on that later… 
We often subject ourselves to certain events / exposures which can have a good outcome or a bad outcome….let’s say the good outcome is only a status quo or a small benefit…where as the bad outcome is something majorly bad.  Example: trying to run and cross a low traffic (empty & narrow) road blind-folded….here the positive outcome is just reaching the other side which is no big deal…kind of a status quo…where as the negative outcome is being hit by a speeding vehicle and possibly losing one’s life.
Let’s say in any given hour….you see only 1 car passing by on that empty road….without getting too much into physics and relative velocity etc,  let’s assume that it takes you approximately 5 seconds to cross the road and it takes an average car 1 second to drive past you. This means in any particular second, there is a 1/(60X60) chance of a car passing …..which means if you are trying to cross the road blindfolded once, in that span of 5 seconds the chances of you getting hit is only 5/(60X60) = 1/720 = 0.14% chance of being hit….sounds pretty safe right?

 

Let’s do the math. The chances of being hit is 0.14%, means the chances of crossing safely is 99.86% (looks like a very very  safe activity). The problem happens if you try and do it again and again…..if you do this 2 times, then the chances of crossing safely become (99.86%)X(99.86%), as for you to stay safe, it is necessary that you are able to cross both the times safely ….if you do it a 100 times, then the chances of staying safe (after all the 100 attempts) becomes (99.86%) ^ 100 = 86.93%…..but if you do this a 1000 times, then your chances of not getting hit ever, becomes (99.86%)^1000 = 24.64% only…..how about doing this every single day for over 8 years (~ 3,000 times)?… Here staying safe after 8 years is equivalent to not ever getting hit, which is equivalent to crossing safely each of the 3000 times. The chance of not being hit ‘ever’ reduces to only (99.86%)^3000 = ~1.5% leaving us with a 98.5% chance of getting hit at least once and possibly getting killed. Drawing from the confusion of my earlier coin-tosser friend, the probability of getting hit on the 3000th attempt is however still exactly the low 0.14%….as it is in any of the independent individual attempts. The problem is in the probability of hitting a cumulative track record of : [(safe) X (safe) X (safe) X ……3000 times]

 

So you see how the probability gets turned on it’s head when you do something silly long enough. An otherwise 99.86% safe independent activity becomes a 98.5% extremely unsafe ‘series of activities’. Here the fact that each crossing is very safe, is no more relevant. This is exactly how risk works…..so next time you are over-leveraging yourself, or trying to buy stocks with loan from your credit card, thinking that the chances of a negative outcome is very very low…remember that the low probability of getting caught on the wrong foot becomes an extremely high probability when you try it long enough.

 

The exact same thing is applicable when someone is selling a naked PUT option, without the cash available for a ‘very low probability’ option assignment. You might end up enjoying the cash flow for a long time, but eventually you will run out of luck and will almost certainly get wiped out.