Interestingly, the concept of convexity isn’t foreign to most of us – we just do not see it in terms of asymmetric outcomes. Consider these aphorisms that are often delivered as grandmotherly wisdom; “Short term pain, long term gain”, and “Penny wise pound foolish”.

Both of these sayings reference gains that outweigh costs. In the former, one is encouraged to put up with short term discomfort in order to reap longer term rewards. For example, to endure the short term unpleasantness of exercise in order to reap the benefits of a stronger and more healthy body (and mind) in the future. In other words, small changes that lead to a big effect.

The latter is slightly different, in that it infers, rather than directly references a time frame for costs and payoffs. The saying is often directed at those who look to save small amounts of money on some purchases, then going on to splurge on others. A good example of this is someone who always looks to save a few dollars (or even cents) on the food they buy, but often splurges on luxury items.

There is no way that the tiny amounts saved from scrimping on food add up to the price of even one such luxury item; which is the point of the aphorism. Saving small amounts will not help one’s future financial security if one spends irresponsibly. If a person really wants to secure their financial future via saving, then saving on big ticket items matters more than scrimping on small ones.

But how does this relate to convexity? By telling us to focus on the gains that matter (not splurging large amounts unnecessarily), and not the small savings that don’t.

Another way to think about convexity in life is in terms of paying or not paying a small fee. Someone who pays the small fee is long convexity. Others who choose to not pay the small fee are short convexity.

Take flossing one’s teeth for example. The payment here is the couple of minutes a night it takes to perform the teeth cleaning exercise. People who floss are paying this couple of minutes, and people who do not floss are receiving this couple of minutes (they get 2 more minutes to do something else).

But, what is the payment for? Prevention of cavities, and other tooth/gum diseases, of course. The cost of two minutes + dental floss every day is ultimately very cheap compared to the much more expensive cost of filling cavities, not to mention much less physically painful.

If there were to be a pithy slogan for flossing that also demonstrates the power of convexity, it would be something along the lines of, 2 minutes a day keeps the drilling at bay! If that sounds familiar, it’s because it is closely related to everyone’s favorite adage, “An apple a day keeps the doctor away!” Notice the convexity lurking behind the words here as well – the small cost of an apple to avoid the much larger cost of ill health.

The point here isn’t about flossing or one’s health, although both are important, but that a small payment is regularly made in order to avoid a much more expensive one later. Again, small changes that contribute to future asymmetric outcomes.

How are you positioned against convexity?