Convexity

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a “convex” risk is one where the the relationship between changes in the risk and potential gains or losses is non-linear. If plotted on a graph the relationship is curved — the payoff becomes more extreme for each incremental change in the price of the asset.

There is no such thing, by the way, as a “concave” risk. That is, rather, a risk that is negatively convex.

Convex risks may also be asymmetric. If you buy a put or call option for example, your downside is limited to the option premium.

Important to know, therefore, whether you are long or short convex risk, and whether it is positive or negative.

Convex risks tend to be more sensitive to volatility. As market volatility increases, the value of convex positions tends to increase as well.

See also

• Agency problem
• The Black Swan: The Impact of the Highly Improbable
• Non-linear interaction and complexity