.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fixed_income/bonds/plot_01_yield_to_maturity.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_bonds_plot_01_yield_to_maturity.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_bonds_plot_01_yield_to_maturity.py:


*Inside the Yield Book*: yield to maturity
==========================================

Sidney Homer and Martin Leibowitz's *Inside the Yield Book* (1972) taught
a generation of bond traders to think in yield to maturity: the single
rate that discounts a bond's cash flows to its price. The script inverts
prices for yields, shows a bond pulled to par as it ages at a constant
yield, and separates the dirty price, which drops by a coupon on each
payment date, from the quoted clean price.

.. GENERATED FROM PYTHON SOURCE LINES 14-19

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.fixed_income import bond_cash_flows, bond_price, clean_price, yield_to_maturity








.. GENERATED FROM PYTHON SOURCE LINES 20-22

Price to yield and back
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 22-28

.. code-block:: Python


    cf = bond_cash_flows(100.0, 0.06, 10.0, freq=2)
    for price in (90.0, 100.0, 110.0):
        y = yield_to_maturity(price, cf, compounding=2)
        print(f"price {price:6.2f} -> yield {100 * y:.4f}% (semiannual) -> price {bond_price(100.0, 0.06, 10.0, y, compounding=2):.6f}")





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

 .. code-block:: none

    price  90.00 -> yield 7.4351% (semiannual) -> price 90.000000
    price 100.00 -> yield 6.0000% (semiannual) -> price 100.000000
    price 110.00 -> yield 4.7332% (semiannual) -> price 110.000000




.. GENERATED FROM PYTHON SOURCE LINES 29-34

Pull to par
-----------
At an unchanged yield, a premium bond falls and a discount bond rises
toward 100 as maturity approaches. Plotting the clean price removes the
coupon sawtooth.

.. GENERATED FROM PYTHON SOURCE LINES 34-43

.. code-block:: Python


    remaining = np.linspace(10.0, 0.01, 400)
    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    for coupon, y in ((0.08, 0.05), (0.05, 0.05), (0.03, 0.05)):
        axes[0].plot(10 - remaining, [clean_price(100.0, coupon, T, y, compounding=2) for T in remaining], label=f"coupon {100 * coupon:.0f}%")
    axes[0].set_title("clean price at a 5% yield")
    axes[0].set_xlabel("years elapsed")
    axes[0].legend()




.. image-sg:: /api/gallery/fixed_income/bonds/images/sphx_glr_plot_01_yield_to_maturity_001.png
   :alt: clean price at a 5% yield
   :srcset: /api/gallery/fixed_income/bonds/images/sphx_glr_plot_01_yield_to_maturity_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x116e552b0>



.. GENERATED FROM PYTHON SOURCE LINES 44-46

Dirty versus clean
------------------

.. GENERATED FROM PYTHON SOURCE LINES 46-54

.. code-block:: Python


    remaining = np.linspace(3.0, 0.01, 600)
    axes[1].plot(3 - remaining, [bond_price(100.0, 0.08, T, 0.05, compounding=2) for T in remaining], label="dirty")
    axes[1].plot(3 - remaining, [clean_price(100.0, 0.08, T, 0.05, compounding=2) for T in remaining], label="clean")
    axes[1].set_title("8% bond, last three years")
    axes[1].set_xlabel("years elapsed")
    axes[1].legend()
    plt.show()








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

   **Total running time of the script:** (0 minutes 0.478 seconds)


.. _sphx_glr_download_api_gallery_fixed_income_bonds_plot_01_yield_to_maturity.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/bonds/plot_01_yield_to_maturity.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_yield_to_maturity.ipynb <plot_01_yield_to_maturity.ipynb>`

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

      :download:`Download Python source code: plot_01_yield_to_maturity.py <plot_01_yield_to_maturity.py>`

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

      :download:`Download zipped: plot_01_yield_to_maturity.zip <plot_01_yield_to_maturity.zip>`


.. only:: html

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

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