.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fixed_income/duration/plot_03_fisher_weil_duration.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_fixed_income_duration_plot_03_fisher_weil_duration.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_fixed_income_duration_plot_03_fisher_weil_duration.py:


Fisher-Weil duration
====================

Fisher and Weil (1971) computed Macaulay's weights with each cash flow
discounted on its own zero rate instead of the bond's single yield,

.. math:: D_{FW} = \frac{1}{P}\sum_i t_i\, c_i\, e^{-r(t_i) t_i}.

It is the exact sensitivity of the price to a parallel shift of the zero
curve, which the script verifies by repricing on shifted curves.

.. GENERATED FROM PYTHON SOURCE LINES 15-29

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.fixed_income import NelsonSiegelCurve, bond_cash_flows, fisher_weil_duration, macaulay_duration, yield_to_maturity

    curve = NelsonSiegelCurve(0.05, -0.035, 0.0, 3.0)  # steeply upward sloping
    cf = bond_cash_flows(100.0, 0.06, 20.0)
    P = cf.present_value(curve)
    ytm = yield_to_maturity(P, cf)
    d_fw = fisher_weil_duration(cf, curve)
    print(f"price {P:.3f}, yield {100 * ytm:.3f}%")
    print(f"Macaulay at the yield: {macaulay_duration(cf, ytm):.4f}")
    print(f"Fisher-Weil on the curve: {d_fw:.4f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    price 122.445, yield 4.268%
    Macaulay at the yield: 12.7253
    Fisher-Weil on the curve: 12.4868




.. GENERATED FROM PYTHON SOURCE LINES 30-32

Parallel shifts of the zero curve
---------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 32-44

.. code-block:: Python


    shifts = np.linspace(-0.02, 0.02, 41)
    actual = np.array([cf.present_value(curve.shifted(s)) for s in shifts])
    fig, ax = plt.subplots()
    ax.plot(1e4 * shifts, actual, label="repriced")
    ax.plot(1e4 * shifts, P * np.exp(-d_fw * shifts), ls="--", label=r"$P e^{-D_{FW} s}$")
    ax.set_xlabel("parallel shift of zero curve (bp)")
    ax.set_ylabel("price")
    ax.legend()
    slope = (actual[21] - actual[19]) / (shifts[21] - shifts[19]) / P
    print(f"-dP/ds / P by finite difference: {-slope:.4f}")
    plt.show()



.. image-sg:: /api/gallery/fixed_income/duration/images/sphx_glr_plot_03_fisher_weil_duration_001.png
   :alt: plot 03 fisher weil duration
   :srcset: /api/gallery/fixed_income/duration/images/sphx_glr_plot_03_fisher_weil_duration_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    -dP/ds / P by finite difference: 12.4875





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.027 seconds)


.. _sphx_glr_download_api_gallery_fixed_income_duration_plot_03_fisher_weil_duration.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/fixed_income/duration/plot_03_fisher_weil_duration.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_03_fisher_weil_duration.ipynb <plot_03_fisher_weil_duration.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_03_fisher_weil_duration.py <plot_03_fisher_weil_duration.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_03_fisher_weil_duration.zip <plot_03_fisher_weil_duration.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_