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Concavity

Concavity and
describe the curvature of a function. While they can easily be identified visually on a graph (concavity graphed below), they can also be determined mathematically by taking the second derivative of the curve function. A negative return indicates concavity, and a positive return indicates convexity.
For example, notice how the slope of the curve in Figure 1 decreases as it progresses down the X-axis. This represents a decelerating positive rate of change (concave up). Figure 2, on the other hand, shows a curve with a slope that becomes more negative as it progresses. This represents an accelerating negative rate of change (concave down). Both of these figures depict a concave relationship between the X and Y parameters.
Figure 1 Figure 2

How does concavity apply to investing?

An example of a concave up relationship as shown in Figure 1 is the relationship between the
of a
and a rising
price. As the underlying price increases, the put's delta will shrink until it eventually hits zero.
An example of a concave down relationship as shown in Figure 2 is the relationship between
and days till
As expiration nears, extrinsic value will decay faster and faster.

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