Convergent and divergent risk taking

Trading strategies can be divided into two categories based on their return streams: convergent and divergent. These two different mindsets affect our risk-taking behaviour differently.

Risk takers who think that the world is static and can be modeled and predicted over a reasonable time period tend to be convergent. Conversely, divergent risk takers are rather skeptical of their knowledge of the world. They believe that since the world is unpredictable and dynamic, we have structural ignorance.

Convergent trading strategies assume that fundamental factors will not change dramatically in the short run. An investor executing convergent strategies calculates the fair value of an asset. If the market price is above that intrinsic value, they will short that asset; otherwise, they will go long. One of the most popular convergent strategies is value investing which means buying an underpriced asset and selling an overpriced one.

Since most of the time things happen as predicted, convergent risk takers tend to have frequent small gains. If a trader has done his/her homework properly in finding out the fair value of the asset, he is likely to be proven to be true — fundamentals and structural knowledge do matter most of the time.

However, occasionally something unpredictable and unknowable happens. In these cases, losses of convergent risk takers are large. So gains of convergent investors are small and frequent, but their losses are big and rare. In statistics we call this kind of things a return distribution with negative skew.

Divergent risk taking tends to have frequent small losses with rare big gains. These strategies exhibit positive skew and positive convexity. In finance, when we say that something is convex we mean that thing is non-linear, i.e, its output doesn’ change linearly with the change in input. To put it simply, positive convexity is a good thing. It implies that a small change in input can result in bigger gains than predicted by a mathematical model. Positive convexity is when you risk a small amount but can win a much larger amount of money. Think of a lottery; your gain from winning the lottery can outweigh significantly what you paid for a lottery ticket.

In contrast to convergent trading strategies, divergent strategies don’t involve mean reversion; instead they take advantage of directional market moves. They take positions in the direction in which the market is moving. These strategies tend to perform well when volatility in financial markets increase, e.g. during crises.

Under normal market circumstances, convergent and divergent strategies are not correlated. However, as the volatility increases, the two types of strategies start to exhibit negative correlation. As markets experience exceptional directional moves, assets diverge from their values more and more; as a result, convergent trading strategies experience those occasional big losses. However, divergent strategies due to their positive convexity benefit from increase in volatility. They experience right-tail events which just means they will have big gains much larger than the initial risk amount.