This is an Uncertainty Wednesday post on a Thursday. By going over the Wednesdays from the last couple of years you could try to quantify the probability that I will not write an Uncertainty Wednesday post at all, or that I will write one, but a day late. You could graph this historic probability and most likely would find it to be rising over the last few months. You could then use that to predict what the next few weeks will look like. What would that be useful for? For instance, for deciding whether it is worth checking Continuations on Wednesday to see if there is a new post. Or to make a 1 dollar bet with a friend as to whether I will post or not.
Now what about betting your life savings on that? Or not just your savings but you life? Clearly not something you would consider, at least not if you are sane. It could easily be ruinous or deadly. I definitely don’t recommend it. And yet nonetheless we do take some level of life risk all the time. For instance, every time you cross a street you take some risk of getting run over.
So how should we reconcile these two? Well the probability of my not writing a blog post on any given Wednesday is quite high. The risk of any road crossing is quite low. There is clearly a threshold that’s so low that we are willing to accept the risk of ruin or even death. Understanding this explains why the innovation in air travel has been focused on safety over advances in speed. Those who complain that we have gone backwards in air travel by pointing to the Concorde and today’s lack of supersonic options fail to see that we have grown the number of flights by several orders of magnitude while at the same time shrinking the number of fatalities. That is extraordinary progress and makes much of modern life possible (ask yourself how much air travel we would have if there were 1 in 10 chance of not arriving, 1 in 100? 1 in 1000?)
What about risky activities, such as back country skiing? Or horse back riding? Or scuba diving? Every person has to decide for themselves what kind of risks they want to take. But there is an important fallacy here that is worth dispelling. And that’s the idea that because an activity is really dangerous it is not worth trying to reduce risk. People will point to famous horse back riders being thrown off their horse or famous skiers being swept away by an avalanche. If it can happen to them, then why even bother with safety precautions?
To understand why, consider the following math. Suppose there is a 1:100 chance of something bad happening in a specific activity, i.e. a 0.01 probability of a bad accident (potentially fatal). You will do this activity 100 times and the risks are independent. What is the probability of you not having an accident? Well, that would be 0.99^100 = 0.366 which is really bad news. Because it means that the probability of you having an accident is 1 - 0.366 = 0.734 which is 73.4%. Or put differently roughly 3 out of 4 people who do this activity for 100 times will have an accident. Most people will conclude that’s not acceptable (although people do go wing suit flying nonetheless — btw, I should point out I don’t know the accident rate for wing suit flying but it is apparently quite high). But now suppose that safety precautions reduce the risk of accident to 1 : 1,000 or 0.001. Now we are looking at 0.999 ^ 100 = 0.905 and hence the probability of having an accident is no 1- 0.905 = 0.095 or put differently roughly 1 out of 10 people. That’s a lot better than 3 out of 4. What if we can eliminate even more risk and get to 1 : 10,000 or 0.0001. Well that gives us 0.9999 ^ 100 = 0.99, meaning on average 1 in 100 people will have an accident.
In summary then everyone needs to figure out for themselves what kind of activities they want to engage in and how much risk of ruin (or loss of life) they want to take. But for any given activity there is a huge benefit to risk reduction within that activity. In investing, historically one answer against the ruin problem has been diversification, but there are alternatives such as constructing a bar bell portfolio or hedging. I will write more about this in a future Uncertainty Wednesday.
