What Yield Curve PCA Factors Say About Variance, Not Event Frequency

Summary

The document explains how principal component analysis (PCA) is used to summarize yield curve movements. In the example, the first three components account for 58%, 85%, and 93% of cumulative variance, and their coefficient patterns are commonly interpreted as level shifts, twists, and curvature changes. The question is whether the ordering implies that curvature movements occur more often or that shifts are more frequent.

The answer is that PCA ranks components by the amount of variance they explain, not by how often the underlying type of movement occurs. A component can rank highly because its associated changes contribute more to total variation; frequency cannot be inferred from that ranking alone. The response also observes that movements may combine several types of change, including curvature. The figures are an illustration from one data set, and the document does not describe the sample construction or offer a method for estimating event frequencies. Frequency would require a separate definition and analysis of curve movements.

Key ideas

• PCA orders yield curve components by the variance they explain.
• The example interprets the leading three components as level, twist, and curvature movements.
• A component's explained variance does not reveal how often that type of movement occurs.
• Yield curve changes can combine multiple movement types, including curvature changes.
• Estimating movement frequency requires analysis beyond PCA variance rankings.

Tags

# Yield curve PCA vs real life frequency


# Yield curve PCA vs real life frequency












The yield curve can be explained using principal component analysis (PCA), where the cumulative proportion explained for many practical purposes is high enough with three factors.

For one set of data, used here, they explained 58% with factor1 and 85% by adding factor2 and 93% by adding factor3. This is inline with other data sets I have seen, e.g., Tsay's Analysis of Financial Time Series. The three factors are interpreted from the signs and sizes of the coefficients as "shift, twist and curvature". Since curvature explains the least amount of variability, does that imply shifts happen more seldom in the real world than a shift does? I.e., does the ordering tell us something about the frequency with which they occur? Or is it just that when shifts do happen the change the look so much that it is the first principal component?

## Answer by Will Gu (score 2, accepted)

https://quant.stackexchange.com/a/31344

Re: does the ordering tell us something about the frequency with which they occur?

No it doesn't. It's more about how much this component contributes to the final variance. Probably every bit of move of the yield curve contains some extent of curvature change. It's just a matter of how much of it can be explained by the variables.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.