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MRMM-10-estimating-market-risk-measures.html
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<!doctype html>
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<title>Market Risk Measurement and Management | Chapter 10 | Estimating Market Risk Measures</title>
<meta name="description" content="Financial Risk Manager Part 2 Study Materials">
<meta name="author" content="MacLane Wilkison">
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<section>
<h1>Chapter 10</h1>
<h3>Estimating Market Risk Measures</h3>
<p>
<small>Created for <a href="http://alchemistsacademy.com">Alchemists Academy</a> by <a href="http://alchemistsacademy.com/about">MacLane Wilkison</a></small>
</p>
</section>
<section>
<h2>Data</h2>
<ul>
<li>Profit/loss data: P/L<sub>t</sub> = P<sub>t</sub>+D<sub>t</sub>-P<sub>t-1</sub></li>
<li>Loss/profit data: -P/L<sub>t</sub></li>
<li>Arithmetic return data: r<sub>t</sub> = (P<sub>t</sub>+D<sub>t</sub>)/P<sub>t-1</sub> - 1</li>
<li>Geometric return data: R<sub>t</sub> = ln[(P<sub>t</sub>+D<sub>t</sub>)/P<sub>t-1</sub>]</li>
</ul>
</section>
<section>
<h2>Estimating Historical Simulation VaR</h2>
<p>This approach estimates VaR by ordered loss historical observations</p>
</section>
<section>
<h2>Estimating Parametric VaR</h2>
<ul>
<li>Normally distributed profits/losses: αVaR = -μ<sub>P/L</sub>+σ<sub>P/L</sub>z<sub>α</sub></li>
<li>Normally distributed arithmetic returns: αVaR = -(μ<sub>r</sub>-σ<sub>r</sub>z<sub>α</sub>)P<sub>t-1</sub></li>
<li>Lognormal VaR: αVaR = P<sub>t-1</sub>-P<sup>*</sup> = P<sub>t-1</sub>(1-epx[μ<sub>R</sub>-σ<sub>R</sub>z<sub>α</sub>])</li>
</ul>
<aside class="notes">
'z<sub>α</sub>' = the standard normal variate corresponding to α.
</aside>
</section>
<section>
<h2>Estimating Coherent Risk Measures</h2>
<ul>
<li>Expected shortfall - the probability-weighted average of tail losses</li>
</ul>
</section>
<section>
<h2>Process Overview</h2>
<ol>
<li>Which risk measure?</li>
<ul>
<li>VaR, ES, etc.</li>
</ul>
<li>Which level?</li>
<ul>
<li>Portfolio or position level?</li>
</ul>
<li>Which method?</li>
<ul>
<li>"VaR trinity"</li>
<ul>
<li>Non-parametric methods</li>
<li>Parametric methods</li>
<li>Monte Carlo simulation methods</li>
</ul>
</ul>
</ol>
</section>
<section>
<h1>THE END</h1>
<h3><a href="http://alchemistsacademy.com">AlchemistsAcademy.com</a></h3>
</section>
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