.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/risk/drawdowns/plot_01_calmar_drawdowns.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_risk_drawdowns_plot_01_calmar_drawdowns.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_risk_drawdowns_plot_01_calmar_drawdowns.py:


Young's Calmar ratio and drawdowns
==================================

A drawdown is the fall from the highest wealth reached so far. Terry
Young (1991) proposed judging managed-futures funds by their compound
annual return divided by their maximum drawdown, the Calmar ratio,
because investors leave a fund after a deep drawdown long before its
volatility looks alarming. Two strategies with the same mean and
volatility can have very different drawdowns if their bad days cluster.

.. GENERATED FROM PYTHON SOURCE LINES 14-24

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.risk import calmar_ratio, drawdowns
    from financialkit.risk.visualizers import plot_drawdowns

    rng = np.random.default_rng(3)
    n = 3 * 252
    mu, sigma = 0.10 / 252, 0.15 / np.sqrt(252)








.. GENERATED FROM PYTHON SOURCE LINES 25-27

One path, dissected
-------------------

.. GENERATED FROM PYTHON SOURCE LINES 27-35

.. code-block:: Python


    r = mu + sigma * rng.standard_normal(n)
    res = drawdowns(r)
    axes = plot_drawdowns(res)
    axes[0].set_title(f"max drawdown {res.max_drawdown:.1%}, Calmar {calmar_ratio(r):.2f}")
    print(f"peak at day {res.peak_index}, trough at day {res.trough_index}, recovered at day {res.recovery_index}")
    print(f"longest time under water: {res.longest_duration} days")




.. image-sg:: /api/gallery/risk/drawdowns/images/sphx_glr_plot_01_calmar_drawdowns_001.png
   :alt: max drawdown 10.0%, Calmar 2.36
   :srcset: /api/gallery/risk/drawdowns/images/sphx_glr_plot_01_calmar_drawdowns_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    peak at day 705, trough at day 754, recovered at day -1
    longest time under water: 92 days




.. GENERATED FROM PYTHON SOURCE LINES 36-42

Same moments, different order
-----------------------------

Sorting the middle year of the same daily returns so the worst come
together leaves the mean and volatility unchanged but deepens the
drawdown and cuts the Calmar ratio.

.. GENERATED FROM PYTHON SOURCE LINES 42-50

.. code-block:: Python


    clustered = r.copy()
    block = slice(n // 3, 2 * n // 3)
    clustered[block] = np.sort(clustered[block])
    for name, x in [("original order", r), ("clustered losses", clustered)]:
        d = drawdowns(x)
        print(f"{name:16s} mean {x.mean() * 252:.3f}, vol {x.std() * np.sqrt(252):.3f}, MDD {d.max_drawdown:.1%}, Calmar {calmar_ratio(x):.2f}")





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

 .. code-block:: none

    original order   mean 0.223, vol 0.149, MDD 10.0%, Calmar 2.36
    clustered losses mean 0.223, vol 0.149, MDD 57.4%, Calmar 0.41




.. GENERATED FROM PYTHON SOURCE LINES 51-56

The Calmar ratio across many paths
----------------------------------

Over three years the maximum drawdown of a 15%-volatility strategy is
itself very uncertain, so a single Calmar ratio says little.

.. GENERATED FROM PYTHON SOURCE LINES 56-65

.. code-block:: Python


    calmars = np.array([calmar_ratio(mu + sigma * rng.standard_normal(n)) for _ in range(500)])
    fig, ax = plt.subplots(figsize=(7, 3.5))
    ax.hist(np.clip(calmars, -2, 6), bins=50, color="0.6")
    ax.set_xlabel("three-year Calmar ratio (same true strategy)")
    ax.set_ylabel("count")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/risk/drawdowns/images/sphx_glr_plot_01_calmar_drawdowns_002.png
   :alt: plot 01 calmar drawdowns
   :srcset: /api/gallery/risk/drawdowns/images/sphx_glr_plot_01_calmar_drawdowns_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.078 seconds)


.. _sphx_glr_download_api_gallery_risk_drawdowns_plot_01_calmar_drawdowns.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/risk/drawdowns/plot_01_calmar_drawdowns.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_calmar_drawdowns.ipynb <plot_01_calmar_drawdowns.ipynb>`

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

      :download:`Download Python source code: plot_01_calmar_drawdowns.py <plot_01_calmar_drawdowns.py>`

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

      :download:`Download zipped: plot_01_calmar_drawdowns.zip <plot_01_calmar_drawdowns.zip>`


.. only:: html

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

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