Choosing Par or Zero Rates for Yield Curve Principal Components

Summary

The document poses a methodological question about applying principal component analysis to daily yield curve changes. It compares using observable par rates, as in influential work on common factors in bond returns, with first bootstrapping a curve and analyzing zero or spot rates. It asks what advantages and disadvantages each representation has and what other choices matter.

The choice affects what the resulting components describe. Par rates are directly observed market quotes, while zero rates are derived from instruments through a curve construction procedure. Bootstrapping can make zero-rate movements sensitive to instrument selection, interpolation, and fitting conventions; par-rate PCA avoids that conversion but analyzes coupon-yield quotes rather than discount rates at individual maturities. The document itself provides no answers, empirical comparison, or dataset, so it does not establish which representation is preferable. A practical study would need to specify the market, instruments, curve methodology, sampling, and intended interpretation of the factors.

Key ideas

• Yield curve PCA can be performed on changes in observed par rates or bootstrapped zero rates.
• Par rates are quoted directly, whereas zero rates depend on a curve construction method.
• Instrument choices and interpolation conventions can affect zero-rate histories and resulting components.
• The appropriate representation depends on the analysis objective and the interpretation desired.
• The document raises the comparison but supplies no empirical evidence favoring either approach.

Tags

# 85655


# What are pros and cons of using par rates v. zero rates for principal component analysis of daily history of a yield curve?












The seminal paper Robert Litterman, José Scheinkman (1991) Common Factors Affecting Bond Returns. Journal of Fixed Income, 1, 54-61. https://doi.org/10.3905/jfi.1991.692347 used the history of daily changes in observable par rates. Some people prefer to bootstrap & convert to zero/spot rates. What are the advantages/disadvantages of each approach, abd are there are any choices that one should consider?

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