The Mistakes We Make

We will go a little Nassim Taleb on this one. This thread is about tail risks. Grab that cup of tea. This is interesting.

But first, this: Two events are said to be independent if the chances of occurrence of one is independent of the chance of occurrence of other. The chances of me getting my car damaged/totaled are different from your car’s chances of the same. It depends on the kind of drivers we are and also on the traffic situation. However, the events are said to be correlated if the chances of our cars getting totaled are same/dependent – take the example of a hurricane damaging both our cars equally

Imagine you open a new car insurance business, ‘Khareedlo’, and by commenting for better reach on LinkedIn, you finally have 100 customers – all from, say, Uttarakhand

At the start of every year, you charge your customers an annual premium for a simple agreement in which you pay them ₹1 lakhs if their car gets damaged. However, if nothing happens, you pay them nothing. You get your premium for that year though. Real world may have other scenarios too, but why complicate the same here

Now, you took some help from your front-bencher friend, ‘Debu’ and figured out that the chances of a car getting totaled is 14.5%. So, what’s the expected loss in a year, you asked Debu? He quickly referenced the EV thread on whatgaurav and figured out that the amount would be ₹14,500 [1,00,000 x 14.5% + 0 x 85.5%].

Given this, you jumped in joy and set the price of the premium to ₹16,000, adding 1500 as convenience fees on top of those 14.5k. With this your annual revenues are 16k x 100 = INR 16 lakhs. But this means, that you can pay for a maximum of 16 cars in a year, anything more than that and you’d be at loss.

You went to Debu and asked him, what would be the chances of you making a loss in a year (more than 16 cars getting damaged)? Only 28% in a year, he said. And if you stay in business for 20 years, it goes to 2%. Pretty swell, right?

Nope. This is where those tail risks come in. Let’s consider that there’s a hurricane in Uttarakhand and all the cars you gave insurance for are totaled. In this case you’d have to pay out a sum of ₹1 cr (1 lakh x 100). Remember you’ve been making a profit of only 1.5 lakhs per year, so if the hurricane comes sooner than later, you’d go bankrupt. Debu tells you that the chances of a hurricane coming in is only 5%, but that one event is bad enough. These are tail risks – those tails in your normal distribution – and they so happened because the events (cars getting totaled) were correlated. Do note that in normal scenarios you damaging your car is an ‘independent event’

So, I’ll keep the nerdy stuff aside and tell you that the chances of an independent event (cars getting damaged) in this case are only 10% and for correlated events it is 5%. Together, the math would give you 14.5% and more often than not, people get fooled by this 14.5% figure. But those 5% inherent events are the most dangerous

Consider more such examples of tail risks – 

1.     COVID hitting your investment portfolio

2.     Bitcoin gains going for a toss if RBI bans them

3.     Even darker, your relationship with XYZ if they cease to exist

In our example, if we really want our chances of accumulating losses to go to those 2% that we were happy about before, the premium has to go 50% higher to 24k

Moral: Tail risks need to be accounted for. There are often bad events in our lives that take away everything we had before like in the case above. The only way to avoid them is to increase our premiums today. Diversify investments, plan for contingencies and give a little bit more to those relationships so that them future fights aren’t that damaging and live life to the fullest – today 

So, that’s all for the Sunday. Hope you have no tail risks in future! Bye.

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