[paper_website]: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr340.pdf
[inference_atribute]: https://github.com/gusamarante/pyacm/blob/ba641c14e450fc83d22db4ef5e60eadbd489b351/pyacm/acm.py#L203
# pyacm
Implementation of ["Pricing the Term Structure with Linear Regressions" from
Adrian, Crump and Moench (2013)][paper_website].
The `NominalACM` class prices the time series and cross-section of the term
structure of interest rates using a three-step linear regression approach.
Computations are fast, even with a large number of pricing factors. The object
carries all the relevant variables as atributes:
- The yield curve itself
- The excess returns from the synthetic zero coupon bonds
- The principal components of the curve used as princing factors
- Risk premium parameter estimates
- Yields fitted by the model
- Risk-neutral yields
- Term premium
- Historical in-sample expected returns
- Expected return loadings
- Hypothesis testing (Not sure if correct, more info observations below)
# Instalation
```bash
pip install pyacm
```
# Usage
```python
from pyacm import NominalACM
acm = NominalACM(
curve=yield_curve,
n_factors=5,
)
```
The tricky part of using this model is getting the correct data format. The
`yield_curve` dataframe in the expression above requires:
- Annualized log-yields for zero-coupon bonds
- Observations (index) must be in either monthly or daily frequency
- Maturities (columns) must be equally spaced in **monthly** frequency and start
at month 1. This means that you need to construct a bootstraped curve for every
date and interpolate it at fixed monthly maturities
- Whichever maturity you want to be the longest, your input data should have one
column more. For example, if you want term premium estimate up to the 10-year
yield (120 months), your input data should include maturities up to 121 months.
This is needed to properly compute the returns.
# Examples
The estimates for the US are available on the [NY FED website](https://www.newyorkfed.org/research/data_indicators/term-premia-tabs#/overview).
The jupyter notebook [`example_br`](https://github.com/gusamarante/pyacm/blob/main/example_br.ipynb)
contains an example application to the Brazilian DI futures curve that showcases all the available methods.
<p align="center">
<img src="https://raw.githubusercontent.com/gusamarante/pyacm/refs/heads/main/images/DI%20term%20premium.png" alt="DI Term Premium"/>
<img src="https://raw.githubusercontent.com/gusamarante/pyacm/refs/heads/main/images/DI%20observed%20vs%20risk%20neutral.png" alt="Observed VS Risk Neutral"/>
</p>
# Original Article
> Adrian, Tobias and Crump, Richard K. and Moench, Emanuel,
> Pricing the Term Structure with Linear Regressions (April 11, 2013).
> FRB of New York Staff Report No. 340,
> Available at SSRN: https://ssrn.com/abstract=1362586 or http://dx.doi.org/10.2139/ssrn.1362586
The version of the article that was published by the NY FED is not 100% explicit on how the data is being manipulated,
but I found an earlier version of the paper on SSRN where the authors go deeper into the details on how everything is being estimated:
- Data for zero yields uses monthly maturities starting from month 1
- All principal components and model parameters are estiamted with data resampled to a monthly frequency, averaging observations in each month
- To get daily / real-time estimates, the factor loadings estimated from the monthly frquency are used to transform the daily data
# Observations
I am not completely sure that computations in the [inferences attributes][inference_atribute]
are correct. If you find any mistakes, please open a pull request following the contributing
guidelines.
Raw data
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