.. _sphx_glr_api_gallery_portfolio_performance:

Performance measurement
-----------------------

Return per unit of risk, its sampling error, and where skill comes from.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="William Sharpe (1966) ranked 34 mutual funds by their reward-to-variability ratio, the mean excess return divided by its standard deviation. By Tobin&#x27;s separation it is the right yardstick for an investor&#x27;s whole portfolio: leverage changes the return but not the ratio. It is also an estimate, and Andrew Lo (2002) showed how noisy: with independent returns its standard error is \sqrt{(1 + SR^2/2)/n} per period, so years of data separate good managers from lucky ones only slowly.">

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  .. image:: /api/gallery/portfolio/performance/images/thumb/sphx_glr_plot_01_sharpe_ratio_thumb.png
    :alt:

  :doc:`/api/gallery/portfolio/performance/plot_01_sharpe_ratio`

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      <div class="sphx-glr-thumbnail-title">The Sharpe ratio</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Richard Grinold (1989) decomposed an active manager&#x27;s information ratio into skill and breadth:">

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  .. image:: /api/gallery/portfolio/performance/images/thumb/sphx_glr_plot_02_fundamental_law_thumb.png
    :alt:

  :doc:`/api/gallery/portfolio/performance/plot_02_fundamental_law`

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      <div class="sphx-glr-thumbnail-title">Grinold's fundamental law of active management</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Volatility penalizes a fund for its best months as much as for its worst. Frank Sortino and Lee Price (1994) measured risk instead by the downside deviation, the root mean square shortfall below a minimum acceptable return \tau,">

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  .. image:: /api/gallery/portfolio/performance/images/thumb/sphx_glr_plot_03_sortino_ratio_thumb.png
    :alt:

  :doc:`/api/gallery/portfolio/performance/plot_03_sortino_ratio`

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      <div class="sphx-glr-thumbnail-title">The Sortino ratio</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/portfolio/performance/plot_01_sharpe_ratio
   /api/gallery/portfolio/performance/plot_02_fundamental_law
   /api/gallery/portfolio/performance/plot_03_sortino_ratio