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Fixed-Income Attribution: Expected and Unexpected Return

Article Quant Q&A · Author: user506602
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Summary

The document clarifies terminology in fixed-income return attribution. It considers whether implied forward rates and the market-implied return from forward rates refer to the same expected-return benchmark, and whether realized return can be split into expected and unexpected components.

The answer treats the two descriptions of the forward-rate benchmark as equivalent in the cited passage. It distinguishes that benchmark, called expected return, from unexpected return, defined as the difference between actual realized return and the benchmark. Thus realized return equals expected return plus unexpected return. The explanation is a brief interpretation of a textbook passage; it does not develop a method for estimating forward rates or address how the attribution behaves across portfolios or changing market conditions.

Key ideas

  • The passage uses implied forward rates as the expected-return benchmark.
  • The market-implied return from forward rates is described as the same benchmark.
  • Unexpected return is the difference between realized return and that benchmark.
  • Realized return is expressed as expected return plus unexpected return.

Tags

Fixed incomeStatistics
Full text
# Fixed Income Attribution


# Fixed Income Attribution












Q: In the passage below, is the implied forward rates (expect return) considered the same as the market implied return from forward rates (unexpected return)?

For instance,

- Expected return = Implied forward rate

- Unexpected return = The actual realized return minus the market implied return from forward rates

Therefore, actual realized return = expected return + unexpected return.

Here is a section from Managing Investment Portfolios: A Dynamic Process edited by John L. Maginn, part of the CFA Curricuum (page 764)

Am I correct to consider these two bold words to be the same?

## Answer by Alex C (score 2, accepted)

https://quant.stackexchange.com/a/45212

Yes, I believe the same thing is being referred with different words. First the author uses "the implied forward rates", later he uses "the market implied return from the forward rates", but he is describing the same thing. It is described briefly the first time and with more detail the second time (which is unusual, people most often do the reverse).

However the words "(the expected return)" and "(the unexpected return") are not referring to the same thing and should not be in yellow. "(the expected return)" refers to the thing mentioned while "(the unexpected return") refers to the difference betwen the actual realized return and the thing mentioned.

Therefore, the equation you wrote is correct:

actual realized return = expected return + unexpected return

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