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<!doctype html>
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<title>Study Session 17 | Reading 41 | Evaluating Portfolio Performance</title>
<meta name="description" content="Chartered Financial Analyst Level 3 Study Materials">
<meta name="author" content="MacLane Wilkison">
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<section>
<h1>Reading 41</h1>
<h3>Evaluating Portfolio Performance</h3>
<p>
<small>Created for <a href="http://alchemistsacademy.com">Alchemists Academy</a> by <a href="http://alchemistsacademy.com/about">MacLaneWilkison</a></small>
</p>
</section>
<section>
<h2>Introduction</h2>
<ul>
<li>Measurement</li>
<li>Attribution</li>
<li>Appraisal</li>
</ul>
<aside class="notes">
Measurement - What was the account's performance? Attribution - Why did the account produce the observed performance? Appraisal - Is the account's performance due to luck or skill? Evaluation encompasses the task of placing investment results in the context of the account's investment objectives.
</aside>
</section>
<section>
<h2>Performance Measurement</h2>
<p><em>Definition: Procedure of calculating an account's returns</em></p>
<ul>
<li>r<sub>t</sub>=(MV<sub>1</sub>-MV<sub>0</sub>)/MV<sub>0</sub> (assumes no external cash flows</li>
<li>Total rate of return</li>
<li>Time-weighted rate of return</li>
<ul>
<li>Chain-linking</li>
<li>Wealth relative</li>
<li>r<sub>twr</sub>=(1+r<sub>t,1</sub>)(1+r<sub>t,2</sub>)...(1+r<sub>t,n</sub>)-1</li>
</ul>
<li>Money-weighted rate of return</li>
<ul>
<li>Internal rate of return (IRR)</li>
<li>MV<sub>1</sub>=MV<sub>0</sub>(1+R)<sup>m</sup>+CF<sub>1</sub>(1+R)<sup>(m-L(1))+...+CF<sub>n</sub>(1+R)<sup>(m-L(n))</sup></li>
</ul>
<li>Linked internal rate of return (LIRR)</li>
<li>Annualized return</li>
</ul>
<aside class="notes">
The total rate of return measures the increase in wealth due to both investment income and capital gains. The time weighted return reflects compounded rate of growth over a stated evaluation period of one unit of money initially invested. Money weighted return measures compound growth rate in value of all funds invested in account over evaluation period. The linked IRR is a chain-linked money weighted return.
</aside>
</section>
<section>
<h2>Benchmarks</h2>
<ul>
<li>Portfolios have 3 components:</li>
<ul>
<li>Market, style, and active management</li>
</ul>
<li>Valid benchmarks are:</li>
<ul>
<li>Unambiguous, investable, measurable, appropriate, reflective of investment opinions, specified in advance, and owned</li>
</ul>
<li>Types of benchmarks</li>
<ul>
<li>Absolute, manager universe, broad market indices, style indices, factor-based models, returns-based models, and custom-security-based models</li>
</ul>
<li>Tests of quality</li>
<ul>
<li>Systematic biases, tracking error, risk characteristics, coverage, turnover, positive active positions</li>
</ul>
</ul>
<aside class="notes">
A benchmark is a standard or point-of-reference in measuring or judging performance.
</aside>
</section>
<section>
<h2>Performance Attribution</h2>
<ul>
<li>Identification of differential returns</li>
<li>Macro vs. micro attribution</li>
<li>Impact = weight × return</li>
</ul>
<aside class="notes">
Differential returns are returns different from those of the benchmark. Impact equals the return (selecting superior/inferior assets) multiplied by the weight of said assets in proportion to that of the benchmark.
</aside>
</section>
<section>
<h2>Macro Attribution</h2>
<p><em>Definition: Macro Attribution is the process of decomposing a fund's performance from a macro perspective</em></p>
<ul>
<li>Inputs</li>
<ul>
<li>Policy allocations</li>
<li>Benchmark portfolio returns</li>
<li>Fund returns, valuations, and external cash flows</li>
</ul>
</ul>
<aside class="notes">
Macro attribution analysis starts with a fund's beginning and ending values and decomposes the return attributable to each decision-making level. Each incremental return component is compared against a valid benchmark for performance measurement purposes.
</aside>
</section>
<section>
<h2>Illustrative Macro Attribution Analysis</h2>
<img src="images/41/macro-attribution-example.png" alt="illustrative macro attribution analysis" />
</section>
<section>
<h2>Micro Attribution</h2>
<p><em>Definition: The process analyzing investment results of individual portfolios relative to designated benchmarks</em></p>
</section>
<section>
<h2>Illustrative Micro Attribution Analysis</h2>
<img src="images/41/micro-attribution-example.png" alt="illustrative micro attribution analysis" />
<aside class="notes">
The Pure Sector Allcation return equals the difference between the allocation weight for that sector, multiplied by the difference between the sector benchmarks' return and the overall portfolio's benchmark return, summed across all sectors. The Within-Sector Selection return equals the difference between the return on the portfolio's holdings in a given secotr and the return on the corresponding sector benchmark, multiplied by the weight of the benchmark in that sector, summed across all sectors. The Allocation/Selection Interaction return equals the difference between the weight of the portfolio in a given sector and the portfolio's benchmark for that sector, multiplied by the difference between the portfolio's and the benchmark's returns in that sector, summed across all sectors.
</aside>
</section>
<section>
<h2>Performance Appraisal</h2>
<ul>
<li>Alpha: R<sub>At</sub> - r<sub>ft</sub> = α<sub>A</sub> + β<sub>A</sub>(R<sub>Mt</sub> - r<sub>ft</sub>) + ε<sub>t</sub></li>
<li>Treynor measure: T<sub>A</sub> = (R<sub>A</sub> - r<sub>f</sub>)/β<sub>A</sub></li>
<li>Sharpe ratio: S<sub>A</sub> = (R<sub>A</sub> - r<sub>f</sub>)/σ<sub>A</sub></li>
<li>M<sup>2</sup><sub>A</sub> = r<sub>f</sub> + [(R<sub>A</sub> - r<sub>f</sub>)/σ<sub>A</sub>]σ<sub>M</sub></li>
<li>Information ratio: IR<sub>A</sub> = (R<sub>A</sub> - R<sub>B</sub>)/σ<sub>A-B</sub></li>
</ul>
<aside class="notes">
Alpha is the differential return of an account compared to the return required to compensate for the systematic risk exposure. The Treynor measure relates an account's excess returns to the systematic risk assumed by the account. The Sharpe ratio compares excess returns to the total risk of the account. M<sup>2</sup> is the mean incremental return over a market index of a hypothetical portfolio formed by combining the account with borrowing or lending at the risk-free rate so as to match the standard deviation of the market index. The information ratio is the exess return of an account over its benchmark relative to the variability of its excess return.
</aside>
</section>
<section>
<h1>THE END</h1>
<h3><a href="http://alchemistsacademy.com">AlchemistsAcademy.com</a></h3>
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