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<h1 class="header-title">Event Studies and Earnings Releases</h1>
<p class="header-date"> <a href="https://bspeice.github.io/author/bradlee-speice.html">Bradlee Speice</a>, Wed 08 June 2016, <a href="https://bspeice.github.io/category/blog.html">Blog</a></p>
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<a href="https://bspeice.github.io/tag/earnings.html">earnings</a>, <a href="https://bspeice.github.io/tag/event-study.html">event study</a> </p>
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<p>Or, being suspicious of market insiders.</p>
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<h1 id="The-Market-Just-Knew">The Market Just Knew<a class="anchor-link" href="#The-Market-Just-Knew">&#182;</a></h1><p>I recently saw two examples of stock charts that have kept me thinking for a while. And now that the semester is complete, I finally have enough time to really look at them and give them the treatment they deserve. The first is good old Apple:</p>
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<div class=" highlight hl-ipython3"><pre><span class="kn">from</span> <span class="nn">secrets</span> <span class="k">import</span> <span class="n">QUANDL_KEY</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib.dates</span> <span class="k">import</span> <span class="n">date2num</span>
<span class="kn">from</span> <span class="nn">matplotlib.finance</span> <span class="k">import</span> <span class="n">candlestick_ohlc</span>
<span class="kn">from</span> <span class="nn">matplotlib.dates</span> <span class="k">import</span> <span class="n">DateFormatter</span><span class="p">,</span> <span class="n">WeekdayLocator</span><span class="p">,</span>\
<span class="n">DayLocator</span><span class="p">,</span> <span class="n">MONDAY</span>
<span class="kn">import</span> <span class="nn">quandl</span>
<span class="kn">from</span> <span class="nn">datetime</span> <span class="k">import</span> <span class="n">datetime</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="k">def</span> <span class="nf">fetch_ticker</span><span class="p">(</span><span class="n">ticker</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">end</span><span class="p">):</span>
<span class="c1"># Quandl is currently giving me issues with returning</span>
<span class="c1"># the entire dataset and not slicing server-side.</span>
<span class="c1"># So instead, we&#39;ll do it client-side!</span>
<span class="n">q_format</span> <span class="o">=</span> <span class="s1">&#39;%Y-%m-</span><span class="si">%d</span><span class="s1">&#39;</span>
<span class="n">ticker_data</span> <span class="o">=</span> <span class="n">quandl</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;YAHOO/&#39;</span> <span class="o">+</span> <span class="n">ticker</span><span class="p">,</span>
<span class="n">start_date</span><span class="o">=</span><span class="n">start</span><span class="o">.</span><span class="n">strftime</span><span class="p">(</span><span class="n">q_format</span><span class="p">),</span>
<span class="n">end_date</span><span class="o">=</span><span class="n">end</span><span class="o">.</span><span class="n">strftime</span><span class="p">(</span><span class="n">q_format</span><span class="p">),</span>
<span class="n">authtoken</span><span class="o">=</span><span class="n">QUANDL_KEY</span><span class="p">)</span>
<span class="k">return</span> <span class="n">ticker_data</span>
<span class="k">def</span> <span class="nf">ohlc_dataframe</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="c1"># Much of this code re-used from:</span>
<span class="c1"># http://matplotlib.org/examples/pylab_examples/finance_demo.html</span>
<span class="k">if</span> <span class="n">ax</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">f</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">vals</span> <span class="o">=</span> <span class="p">[(</span><span class="n">date2num</span><span class="p">(</span><span class="n">date</span><span class="p">),</span> <span class="o">*</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">date</span><span class="p">]))</span>
<span class="k">for</span> <span class="n">date</span> <span class="ow">in</span> <span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">]</span>
<span class="n">candlestick_ohlc</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">vals</span><span class="p">)</span>
<span class="n">mondays</span> <span class="o">=</span> <span class="n">WeekdayLocator</span><span class="p">(</span><span class="n">MONDAY</span><span class="p">)</span>
<span class="n">alldays</span> <span class="o">=</span> <span class="n">DayLocator</span><span class="p">()</span>
<span class="n">weekFormatter</span> <span class="o">=</span> <span class="n">DateFormatter</span><span class="p">(</span><span class="s1">&#39;%b </span><span class="si">%d</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">xaxis</span><span class="o">.</span><span class="n">set_major_locator</span><span class="p">(</span><span class="n">mondays</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">xaxis</span><span class="o">.</span><span class="n">set_minor_locator</span><span class="p">(</span><span class="n">alldays</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">xaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><span class="n">weekFormatter</span><span class="p">)</span>
<span class="k">return</span> <span class="n">ax</span>
<span class="n">AAPL</span> <span class="o">=</span> <span class="n">fetch_ticker</span><span class="p">(</span><span class="s1">&#39;AAPL&#39;</span><span class="p">,</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">ohlc_dataframe</span><span class="p">(</span><span class="n">AAPL</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">vlines</span><span class="p">(</span><span class="n">date2num</span><span class="p">(</span><span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">26</span><span class="p">,</span> <span class="mi">12</span><span class="p">)),</span>
<span class="n">ax</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()[</span><span class="mi">1</span><span class="p">],</span>
<span class="n">color</span><span class="o">=</span><span class="s1">&#39;b&#39;</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">&#39;Earnings Release&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Apple Price 3/1/2016 - 5/1/2016&quot;</span><span class="p">);</span>
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>
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<p>The second chart is from Facebook:</p>
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<div class="prompt input_prompt">In&nbsp;[3]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span class="n">FB</span> <span class="o">=</span> <span class="n">fetch_ticker</span><span class="p">(</span><span class="s1">&#39;FB&#39;</span><span class="p">,</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">ohlc_dataframe</span><span class="p">(</span><span class="n">FB</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">vlines</span><span class="p">(</span><span class="n">date2num</span><span class="p">(</span><span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">27</span><span class="p">,</span> <span class="mi">12</span><span class="p">)),</span>
<span class="n">ax</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()[</span><span class="mi">1</span><span class="p">],</span>
<span class="n">color</span><span class="o">=</span><span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Earnings Release&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Facebook Price 3/5/2016 - 5/5/2016&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">2</span><span class="p">);</span>
</pre></div>
</div>
</div>
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<p>These two charts demonstrate two very specific phonomena: how the market prepares for earnings releases. Let's look at those charts again, but with some extra information. As we're about the see, the market "knew" in advance that Apple was going to perform poorly. The market expected that Facebook was going to perform poorly, and instead shot the lights out. Let's see that trend in action:</p>
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<div class=" highlight hl-ipython3"><pre><span class="k">def</span> <span class="nf">plot_hilo</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">end</span><span class="p">,</span> <span class="n">data</span><span class="p">):</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">date2num</span><span class="p">(</span><span class="n">start</span><span class="p">),</span> <span class="n">date2num</span><span class="p">(</span><span class="n">end</span><span class="p">)],</span>
<span class="p">[</span><span class="n">data</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">start</span><span class="p">][</span><span class="s1">&#39;High&#39;</span><span class="p">],</span> <span class="n">data</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">end</span><span class="p">][</span><span class="s1">&#39;High&#39;</span><span class="p">]],</span>
<span class="n">color</span><span class="o">=</span><span class="s1">&#39;b&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">date2num</span><span class="p">(</span><span class="n">start</span><span class="p">),</span> <span class="n">date2num</span><span class="p">(</span><span class="n">end</span><span class="p">)],</span>
<span class="p">[</span><span class="n">data</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">start</span><span class="p">][</span><span class="s1">&#39;Low&#39;</span><span class="p">],</span> <span class="n">data</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">end</span><span class="p">][</span><span class="s1">&#39;Low&#39;</span><span class="p">]],</span>
<span class="n">color</span><span class="o">=</span><span class="s1">&#39;b&#39;</span><span class="p">)</span>
<span class="n">f</span><span class="p">,</span> <span class="n">axarr</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">ax_aapl</span> <span class="o">=</span> <span class="n">axarr</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">ax_fb</span> <span class="o">=</span> <span class="n">axarr</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="c1"># Plot the AAPL trend up and down</span>
<span class="n">ohlc_dataframe</span><span class="p">(</span><span class="n">AAPL</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax_aapl</span><span class="p">)</span>
<span class="n">plot_hilo</span><span class="p">(</span><span class="n">ax_aapl</span><span class="p">,</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">15</span><span class="p">),</span> <span class="n">AAPL</span><span class="p">)</span>
<span class="n">plot_hilo</span><span class="p">(</span><span class="n">ax_aapl</span><span class="p">,</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">18</span><span class="p">),</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">26</span><span class="p">),</span> <span class="n">AAPL</span><span class="p">)</span>
<span class="n">ax_aapl</span><span class="o">.</span><span class="n">vlines</span><span class="p">(</span><span class="n">date2num</span><span class="p">(</span><span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">26</span><span class="p">,</span> <span class="mi">12</span><span class="p">)),</span>
<span class="n">ax_aapl</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ax_aapl</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()[</span><span class="mi">1</span><span class="p">],</span>
<span class="n">color</span><span class="o">=</span><span class="s1">&#39;g&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Earnings Release&#39;</span><span class="p">)</span>
<span class="n">ax_aapl</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">ax_aapl</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;AAPL Price History&#39;</span><span class="p">)</span>
<span class="c1"># Plot the FB trend down and up</span>
<span class="n">ohlc_dataframe</span><span class="p">(</span><span class="n">FB</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax_fb</span><span class="p">)</span>
<span class="n">plot_hilo</span><span class="p">(</span><span class="n">ax_fb</span><span class="p">,</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">30</span><span class="p">),</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">27</span><span class="p">),</span> <span class="n">FB</span><span class="p">)</span>
<span class="n">plot_hilo</span><span class="p">(</span><span class="n">ax_fb</span><span class="p">,</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">28</span><span class="p">),</span> <span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="n">FB</span><span class="p">)</span>
<span class="n">ax_fb</span><span class="o">.</span><span class="n">vlines</span><span class="p">(</span><span class="n">date2num</span><span class="p">(</span><span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">27</span><span class="p">,</span> <span class="mi">12</span><span class="p">)),</span>
<span class="n">ax_fb</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ax_fb</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()[</span><span class="mi">1</span><span class="p">],</span>
<span class="n">color</span><span class="o">=</span><span class="s1">&#39;g&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Earnings Release&#39;</span><span class="p">)</span>
<span class="n">ax_fb</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">ax_fb</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;FB Price History&#39;</span><span class="p">)</span>
<span class="n">f</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">18</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
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<p>As we can see above, the market broke a prevailing trend on Apple in order to go down, and ultimately predict the earnings release. For Facebook, the opposite happened. While the trend was down, the earnings were fantastic and the market corrected itself much higher.</p>
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<h1 id="Formulating-the-Question">Formulating the Question<a class="anchor-link" href="#Formulating-the-Question">&#182;</a></h1><p>While these are two specific examples, there are plenty of other examples you could cite one way or another. Even if the preponderance of evidence shows that the market correctly predicts earnings releases, we need not accuse people of collusion; for a company like Apple with many suppliers we can generally forecast how Apple has done based on those same suppliers.</p>
<p>The question then, is this: <strong>how well does the market predict the earnings releases?</strong> It's an incredibly broad question that I want to disect in a couple of different ways:</p>
<ol>
<li>Given a stock that has been trending down over the past N days before an earnings release, how likely does it continue downward after the release?</li>
<li>Given a stock trending up, how likely does it continue up?</li>
<li>Is there a difference in accuracy between large- and small-cap stocks?</li>
<li>How often, and for how long, do markets trend before an earnings release?</li>
</ol>
<p><strong>I want to especially thank Alejandro Saltiel for helping me retrieve the data.</strong> He's great. And now for all of the interesting bits.</p>
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<h1 id="Event-Studies">Event Studies<a class="anchor-link" href="#Event-Studies">&#182;</a></h1><p>Before we go too much further, I want to introduce the actual event study. Each chart intends to capture a lot of information and present an easy-to-understand pattern:</p>
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<div class=" highlight hl-ipython3"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">from</span> <span class="nn">pandas.tseries.holiday</span> <span class="k">import</span> <span class="n">USFederalHolidayCalendar</span>
<span class="kn">from</span> <span class="nn">pandas.tseries.offsets</span> <span class="k">import</span> <span class="n">CustomBusinessDay</span>
<span class="kn">from</span> <span class="nn">datetime</span> <span class="k">import</span> <span class="n">datetime</span><span class="p">,</span> <span class="n">timedelta</span>
<span class="c1"># If you remove rules, it removes them from *all* calendars</span>
<span class="c1"># To ensure we don&#39;t pop rules we don&#39;t want to, first make</span>
<span class="c1"># sure to fully copy the object</span>
<span class="n">trade_calendar</span> <span class="o">=</span> <span class="n">USFederalHolidayCalendar</span><span class="p">()</span>
<span class="n">trade_calendar</span><span class="o">.</span><span class="n">rules</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span> <span class="c1"># Remove Columbus day</span>
<span class="n">trade_calendar</span><span class="o">.</span><span class="n">rules</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span> <span class="c1"># Remove Veteran&#39;s day</span>
<span class="n">TradeDay</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">days</span><span class="p">:</span> <span class="n">CustomBusinessDay</span><span class="p">(</span><span class="n">days</span><span class="p">,</span> <span class="n">calendar</span><span class="o">=</span><span class="n">trade_calendar</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">plot_study</span><span class="p">(</span><span class="n">array</span><span class="p">):</span>
<span class="c1"># Given a 2-d array, we assume the event happens at index `lookback`,</span>
<span class="c1"># and create all of our summary statistics from there.</span>
<span class="n">lookback</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="n">array</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">norm_factor</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">array</span><span class="p">[:,</span><span class="n">lookback</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">array</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">centered_data</span> <span class="o">=</span> <span class="n">array</span> <span class="o">/</span> <span class="n">norm_factor</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">lookforward</span> <span class="o">=</span> <span class="n">centered_data</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">lookback</span>
<span class="n">means</span> <span class="o">=</span> <span class="n">centered_data</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">lookforward_data</span> <span class="o">=</span> <span class="n">centered_data</span><span class="p">[:,</span><span class="n">lookforward</span><span class="p">:]</span>
<span class="n">std_dev</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="n">lookforward_data</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)])</span>
<span class="n">maxes</span> <span class="o">=</span> <span class="n">lookforward_data</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">mins</span> <span class="o">=</span> <span class="n">lookforward_data</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">f</span><span class="p">,</span> <span class="n">axarr</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">range_begin</span> <span class="o">=</span> <span class="o">-</span><span class="n">lookback</span>
<span class="n">range_end</span> <span class="o">=</span> <span class="n">lookforward</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">range_begin</span><span class="p">,</span> <span class="n">range_end</span><span class="p">),</span> <span class="n">means</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">range_begin</span><span class="p">,</span> <span class="n">range_end</span><span class="p">),</span> <span class="n">means</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">range_end</span><span class="p">),</span>
<span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="p">:]</span> <span class="o">+</span> <span class="n">std_dev</span><span class="p">,</span>
<span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="p">:]</span> <span class="o">-</span> <span class="n">std_dev</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;$\pm$ 1 s.d.&quot;</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">range_end</span><span class="p">),</span>
<span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="p">:]</span> <span class="o">+</span> <span class="n">std_dev</span><span class="p">,</span>
<span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="p">:]</span> <span class="o">-</span> <span class="n">std_dev</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;$\pm$ 1 s.d.&quot;</span><span class="p">)</span>
<span class="n">max_err</span> <span class="o">=</span> <span class="n">maxes</span> <span class="o">-</span> <span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span>
<span class="n">min_err</span> <span class="o">=</span> <span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span> <span class="o">-</span> <span class="n">mins</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">range_end</span><span class="p">),</span>
<span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="o">+</span><span class="mi">1</span><span class="p">:],</span>
<span class="n">yerr</span><span class="o">=</span><span class="p">[</span><span class="n">min_err</span><span class="p">,</span> <span class="n">max_err</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Max &amp; Min&#39;</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">((</span><span class="o">-</span><span class="n">lookback</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">lookback</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">((</span><span class="o">-</span><span class="n">lookback</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">lookback</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">plot_study_small</span><span class="p">(</span><span class="n">array</span><span class="p">):</span>
<span class="c1"># Given a 2-d array, we assume the event happens at index `lookback`,</span>
<span class="c1"># and create all of our summary statistics from there.</span>
<span class="n">lookback</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="n">array</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">norm_factor</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">array</span><span class="p">[:,</span><span class="n">lookback</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">array</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">centered_data</span> <span class="o">=</span> <span class="n">array</span> <span class="o">/</span> <span class="n">norm_factor</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">lookforward</span> <span class="o">=</span> <span class="n">centered_data</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">lookback</span>
<span class="n">means</span> <span class="o">=</span> <span class="n">centered_data</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">lookforward_data</span> <span class="o">=</span> <span class="n">centered_data</span><span class="p">[:,</span><span class="n">lookforward</span><span class="p">:]</span>
<span class="n">std_dev</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="n">lookforward_data</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)])</span>
<span class="n">maxes</span> <span class="o">=</span> <span class="n">lookforward_data</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">mins</span> <span class="o">=</span> <span class="n">lookforward_data</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">range_begin</span> <span class="o">=</span> <span class="o">-</span><span class="n">lookback</span>
<span class="n">range_end</span> <span class="o">=</span> <span class="n">lookforward</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">range_begin</span><span class="p">,</span> <span class="n">range_end</span><span class="p">),</span> <span class="n">means</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">range_end</span><span class="p">),</span>
<span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="p">:]</span> <span class="o">+</span> <span class="n">std_dev</span><span class="p">,</span>
<span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="p">:]</span> <span class="o">-</span> <span class="n">std_dev</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;$\pm$ 1 s.d.&quot;</span><span class="p">)</span>
<span class="n">max_err</span> <span class="o">=</span> <span class="n">maxes</span> <span class="o">-</span> <span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span>
<span class="n">min_err</span> <span class="o">=</span> <span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span> <span class="o">-</span> <span class="n">mins</span>
<span class="n">plt</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">range_end</span><span class="p">),</span>
<span class="n">means</span><span class="p">[</span><span class="o">-</span><span class="n">lookforward</span><span class="o">+</span><span class="mi">1</span><span class="p">:],</span>
<span class="n">yerr</span><span class="o">=</span><span class="p">[</span><span class="n">min_err</span><span class="p">,</span> <span class="n">max_err</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Max &amp; Min&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">((</span><span class="o">-</span><span class="n">lookback</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">lookback</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">fetch_event_data</span><span class="p">(</span><span class="n">ticker</span><span class="p">,</span> <span class="n">events</span><span class="p">,</span> <span class="n">horizon</span><span class="o">=</span><span class="mi">5</span><span class="p">):</span>
<span class="c1"># Use horizon+1 to account for including the day of the event,</span>
<span class="c1"># and half-open interval - that is, for a horizon of 5,</span>
<span class="c1"># we should be including 11 events. Additionally, using the</span>
<span class="c1"># CustomBusinessDay means we automatically handle issues if</span>
<span class="c1"># for example a company reports Friday afternoon - the date</span>
<span class="c1"># calculator will turn this into a &quot;Saturday&quot; release, but</span>
<span class="c1"># we effectively shift that to Monday with the logic below.</span>
<span class="n">td_back</span> <span class="o">=</span> <span class="n">TradeDay</span><span class="p">(</span><span class="n">horizon</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="n">td_forward</span> <span class="o">=</span> <span class="n">TradeDay</span><span class="p">(</span><span class="n">horizon</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="n">start_date</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">events</span><span class="p">)</span> <span class="o">-</span> <span class="n">td_back</span>
<span class="n">end_date</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">events</span><span class="p">)</span> <span class="o">+</span> <span class="n">td_forward</span>
<span class="n">total_data</span> <span class="o">=</span> <span class="n">fetch_ticker</span><span class="p">(</span><span class="n">ticker</span><span class="p">,</span> <span class="n">start_date</span><span class="p">,</span> <span class="n">end_date</span><span class="p">)</span>
<span class="n">event_data</span> <span class="o">=</span> <span class="p">[</span><span class="n">total_data</span><span class="o">.</span><span class="n">ix</span><span class="p">[</span><span class="n">event</span><span class="o">-</span><span class="n">td_back</span><span class="p">:</span><span class="n">event</span><span class="o">+</span><span class="n">td_forward</span><span class="p">]</span>\
<span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">horizon</span><span class="o">*</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>\
<span class="p">[</span><span class="s1">&#39;Adjusted Close&#39;</span><span class="p">]</span>
<span class="k">for</span> <span class="n">event</span> <span class="ow">in</span> <span class="n">events</span><span class="p">]</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">event_data</span><span class="p">)</span>
<span class="c1"># Generate a couple of random events</span>
<span class="n">event_dates</span> <span class="o">=</span> <span class="p">[</span><span class="n">datetime</span><span class="p">(</span><span class="mi">2016</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">27</span><span class="p">)</span> <span class="o">-</span> <span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">TradeDay</span><span class="p">(</span><span class="n">x</span><span class="o">*</span><span class="mi">20</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">40</span><span class="p">)]</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">fetch_event_data</span><span class="p">(</span><span class="s1">&#39;CELG&#39;</span><span class="p">,</span> <span class="n">event_dates</span><span class="p">)</span>
<span class="n">plot_study_small</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">gcf</span><span class="p">()</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">6</span><span class="p">);</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s1">&#39;Mean price for days leading up to each event&#39;</span><span class="p">,</span>
<span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="o">-.</span><span class="mi">01</span><span class="p">),</span> <span class="p">(</span><span class="o">-</span><span class="mf">4.5</span><span class="p">,</span> <span class="o">.</span><span class="mi">025</span><span class="p">),</span>
<span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="p">(</span><span class="o">-.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">005</span><span class="p">),</span> <span class="p">(</span><span class="o">-.</span><span class="mi">5</span><span class="p">,</span> <span class="o">.</span><span class="mi">02</span><span class="p">),</span>
<span class="n">arrowprops</span><span class="o">=</span><span class="p">{</span><span class="s1">&#39;facecolor&#39;</span><span class="p">:</span> <span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="s1">&#39;shrink&#39;</span><span class="p">:</span> <span class="o">.</span><span class="mi">05</span><span class="p">})</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s1">&#39;$\pm$ 1 std. dev. each day&#39;</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="o">.</span><span class="mi">055</span><span class="p">),</span> <span class="p">(</span><span class="mf">2.5</span><span class="p">,</span> <span class="o">.</span><span class="mi">085</span><span class="p">),</span>
<span class="n">arrowprops</span><span class="o">=</span><span class="p">{</span><span class="s1">&#39;facecolor&#39;</span><span class="p">:</span> <span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="s1">&#39;shrink&#39;</span><span class="p">:</span> <span class="o">.</span><span class="mi">05</span><span class="p">})</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s1">&#39;Min/Max each day&#39;</span><span class="p">,</span> <span class="p">(</span><span class="o">.</span><span class="mi">9</span><span class="p">,</span> <span class="o">-.</span><span class="mi">07</span><span class="p">),</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-.</span><span class="mi">1</span><span class="p">),</span>
<span class="n">arrowprops</span><span class="o">=</span><span class="p">{</span><span class="s1">&#39;facecolor&#39;</span><span class="p">:</span> <span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="s1">&#39;shrink&#39;</span><span class="p">:</span> <span class="o">.</span><span class="mi">05</span><span class="p">});</span>
</pre></div>
</div>
</div>
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