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Choosing Bond Returns for an Unanticipated Risk Premium Factor

Article Quant Q&A · Author: Mayou
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Summary

The document concerns construction of the unanticipated risk premium factor used in a stock-return study. It describes URP as the return difference between a low-grade bond index and a portfolio of long-term government bonds, then asks which return measure should be used to calculate that spread. Possibilities raised include a month-to-date total return and yield to maturity.

This is a measurement question rather than a resolved methodology: the document supplies no answer, formula details, data source, or empirical comparison of candidate measures. It nonetheless highlights a practical issue in factor replication. Bond returns and yields are distinct quantities, and the chosen return horizon and treatment of income and price changes can affect the resulting factor series. The source provides no basis for deciding among these conventions, so replication would require consulting the original study’s data definitions or independently documenting a consistent choice.

Key ideas

  • URP is described as a spread between low-grade corporate bonds and long-term government bonds.
  • The document leaves unclear which bond return convention defines the factor.
  • A yield to maturity is conceptually distinct from a realized holding-period total return.
  • Replicating a factor requires documenting the return measure, horizon, and data construction.

Tags

Factor investingFixed incomeEquities
Full text
# Input for unanticipated risk premium estimation


# Input for unanticipated risk premium estimation












In the paper "Economic Forces and the Stock Market" by Chen, Roll and Ross, unanticipated risk premium (URP) is tested as a potential risk factor for stock returns. This factor is commonly calculated as the difference between the return on a low-grade bond index and the return on a portfolio of long-term government bonds.

However, in this paper, there is no mention as to what type of return is used to compute URP. Any guess as to whether it would be Month-to-date total return, Yield to maturity, ...?

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.