The portfolio management section contains a lot of material and much of it might never appear on the actual Level 2 test.  Consider that this is one of the most in-depth study sessions from the official curriculum, but a candidate may only see one item set (six questions).  That said much of this session’s content will resurface in Level 3.

Many of the concepts can seem abstract, so candidates are advised to review actual examples in preparation for the test.

Taking a zero on any item set is a setback, so candidates should obtain a general understanding of the material to ensure that some points will be obtained on the actual exam.

General guidance is to not get bogged down with it.  Candidates do not want to take a zero on PM, but they do not want to over-invest as it is time to start reviewing other sessions and hitting the practice exams.  Now is a good point for candidates to revisit their prep strategy and balance the amount of time left to exam day against topic strengths/weaknesses and topic weightings.

This module aligns with Study Session 18 material in the Level II CFA Program Curriculum ©.

<strong>Material:</strong>

I.          Portfolio Concepts

II.        Markowitz and Market Efficiency

III.       International Asset Pricing

IV.       Active Portfolio Management

V.        PM Process and the IPS

 

CFA Level 2: Portfolio Management – Introduction

Mean-variance analysis gives investors a framework to assess the tradeoff between risk and return as mean-variance analysis quantifies the relationship between expected return and portfolio variance (or standard deviation).

Mean-variance analysis is the theoretical foundation of Modern Portfolio Theory established by Professor Harry Markowitz and much of the material covered in this module traces its roots concept.

<strong>Mean-Variance Assumptions</strong>

The assumptions underlying the mean-variance analysis are summarized below:
<ul>
	<li>Investors are risk averse in that they prefer higher return for a given level of risk (variance, standard deviation), or they want to minimize risk for a given level of returns. The degree of risk aversion may vary from investor to investor</li>
<ul>
	<li><strong>Example:</strong> An investor is presented with two portfolios:</li>
	<li>Portfolio A offers 12% annual return with 25% standard deviation;</li>
	<li>Portfolio B offers 12% annual return with 20% standard deviation;</li>
	<li>A risk averse investor will choose portfolio B.</li>
</ul>
	<li>Expected returns, variances, and covariances for all assets are known by all investors.</li>
	<li>Investment returns are normally distributed so only returns, variances, and covariances are needed to derive the optimal portfolio.</li>
	<li>There are no transaction costs and no taxes. So, before-tax and after-tax returns are the same making all investors equal.</li>
</ul>
The mean-variance analysis is used to identify optimal/efficient portfolios.

Mean-Variance Analysis Assumptions

<h2>Expected Return for a Two Asset Portfolio</h2>
The expected return of a portfolio is equal to the weighted average of the returns on individual assets in the portfolio.
<div class="formula1">

R<sub>p</sub> = w<sub>1</sub>R<sub>1</sub> + w<sub>2</sub>R<sub>2</sub>
<ul>
	<li>R<sub>p</sub> = expected return for the portfolio</li>
	<li>w<sub>1</sub> = proportion of the portfolio invested in asset 1</li>
	<li>R<sub>1</sub> = expected return of asset 1</li>
</ul>
</div>
<h2>Expected Variance for a Two Asset Portfolio</h2>
The variance of the portfolio is calculated as follows:
<div class="formula1">

σ<sub>p</sub><sup>2</sup> = w<sub>1</sub><sup>2</sup>σ<sub>1</sub><sup>2</sup> + w<sub>2</sub><sup>2</sup>σ<sub>2</sub><sup>2</sup> + 2w<sub>1</sub>w<sub>2</sub>Cov<sub>1,2</sub>
<ul>
	<li>Cov<sub>1,2</sub> = covariance between assets 1 and 2</li>
	<li>Cov<sub>1,2 </sub>= ρ<sub>1,2</sub> * σ<sub>1</sub> * σ<sub>2</sub>; where ρ = correlation between assets 1 and 2</li>
</ul>
</div>
The above equation can be rewritten as:
<div class="formula1">σ<sub>p</sub><sup>2</sup> = w<sub>1</sub><sup>2</sup>σ<sub>1</sub><sup>2</sup> + w<sub>2</sub><sup>2</sup>σ<sub>2</sub><sup>2</sup> + 2w<sub>1</sub>w<sub>2</sub> ρ<sub>1,2</sub>σ<sub>1</sub>σ<sub>2</sub></div>
Keep in mind that this is the calculation for portfolio variance. If a test question asks for the <strong><em>standard deviation</em></strong> then you will need to take the square root of the variance calculation. Percentage values can be used in this formula for the variances, instead of decimals.

<strong>Example</strong><strong> </strong>

The following information about a two stock portfolio is available:
<table class="mytable">
<tbody>
<tr>
<th scope="colspan"><strong> </strong></th>
<th scope="colspan"><strong>Stock A</strong></th>
<th scope="colspan"><strong>Stock B</strong></th>
</tr>
<tr>
<td valign="top" width="160">Amount</td>
<td valign="top" width="160">20,000</td>
<td valign="top" width="160">30,000</td>
</tr>
<tr>
<td valign="top" width="160">Expected Returns</td>
<td valign="top" width="160">12%</td>
<td valign="top" width="160">20%</td>
</tr>
<tr>
<td valign="top" width="160">Standard Deviation</td>
<td valign="top" width="160">20%</td>
<td valign="top" width="160">30%</td>
</tr>
<tr>
<td valign="top" width="160">Correlation</td>
<td colspan="2" valign="top" width="319">
<p align="center">0.25</p>
</td>
</tr>
</tbody>
</table>
<div class="formula1">

The weights for the two assets are:

w<sub>A</sub>= 20,000/50,000 = 40%

w<sub>B</sub>= 30,000/50,000 = 60%

<strong>Expected Returns</strong> = 0.40*0.12 + 0.60*0.20 = 16.8%

<strong>Variance</strong> = (0.40)<sup>2</sup>(0.20)<sup> 2</sup> + (0.60)<sup> 2</sup> (0.30)<sup> 2</sup> + 2(0.40)(0.60)(0.25)(0.20)(0.30)

= 0.046

<strong>Standard deviation = </strong>Sqrt(0.046) = 0.2145 or 21.45%

</div>
<h2>Expected Variance for a Three Asset Portfolio</h2>
<div class="formula1">

σ<sub>p</sub><sup>2</sup> = w<sub>1</sub><sup>2</sup>σ<sub>1</sub><sup>2</sup> + w<sub>2</sub><sup>2</sup>σ<sub>2</sub><sup>2</sup> + w<sub>3</sub><sup>2</sup>σ<sub>3</sub><sup>2</sup> + 2w<sub>1</sub>w<sub>2</sub>Cov<sub>1,2</sub> + 2w<sub>1</sub>w<sub>3</sub>Cov<sub>1,3 </sub>+ 2w<sub>2</sub>w<sub>3</sub>Cov<sub>2,3</sub>

</div>
 

Expected Return and Variance for a Two Asset Portfolio

Two asset classes (stocks and bonds for example) can be combined with varying proportions to create an infinite number of portfolios.

An investor can calculate the expected returns and variances of a two asset portfolio and plotting these on the Y (returns) and X (variances) axis of a graph.

<strong>Global Minimum Variance Portfolio</strong>: The portfolio with the lowest risk/variance on the efficient frontier.

<strong>Efficient Frontier</strong>: Starting with the global minimum variance portfolio and extending to the portfolio of 100% stocks, the efficient frontier is the series of optimal portfolios that can be constructed from two assets, each offering the highest returns for a given amount of risk.

<img class="aligncenter" src="https://financetrain.com/wp-content/uploads/2010/06/Efficient-Frontier.gif" alt="" width="491" height="376" />

Note that in a two asset case, a portfolio of 100% bonds will fall on the minimum variance frontier, but be excluded from the efficient frontier as applying some small portion of stocks to the portfolio will offer higher returns and a lower level of risk through the benefits of diversification.
<h2>Multi Asset Portfolios (three or more asset classes)</h2>
<ul>
	<li>In a two asset class portfolio, all of the portfolio combinations will lie on the minimum variance frontier.</li>
	<li>For three or more asset classes, many portfolio combinations will be inefficient and fall inside the frontier.</li>
	<li>For a three asset class portfolio, the highest and lowest possible returning portfolios will lie on the minimum variance frontier.</li>
</ul>
No portfolios can be above the efficient frontier.

As an investment rule, only portfolios on the efficient frontier should be considered.
<h2>Instability of the Minimum Variance Frontier and Portfolio Implications</h2>
When calculating portfolios on the minimum variance frontier, it must be recognized that the output values are highly sensitive to the data input values for returns, variances, and correlations.  Small changes to these values can create large shifts in the frontier.

<strong>Data Input Challenges</strong>
<ul>
	<li>Sampling techniques to obtain return, variance, and correlation data can fall victim to sampling error.</li>
	<li>The values of these inputs change over time.</li>
</ul>
The optimal portfolio often requires taking short positions, which is not practical or not allowable for many portfolio managers.

Regularly changing estimates to inputs can indicate a need to rebalance frequently, which is expensive.

The Minimum Variance Frontier & Efficient Frontier

A diversification benefit exists when a <a title="Expected Return and Variance for a Two Asset Portfolio" href="https://financetrain.com/expected-return-and-variance-for-a-two-asset-portfolio/">portfolio’s standard deviation</a> can be reduced without reducing expected return.

The diversification benefit is possible when return correlations between portfolio assets is less than perfect positive correlation (&lt;+1.0).

If assets have less than a +1.0 correlation, then some of the random fluctuation around the expected trend rates of return will cancel each other out and lower the portfolio’s standard deviation (risk).

If assets have a perfect negative correlation (-1.0), then some combination of asset weights will eliminate all of the portfolio’s expected standard deviation (risk).

As the number of assets grows large, the variance of the portfolio will approach the average covariance of the asset pairs comprising the portfolio; this is the upper limit of portfolio diversification benefits.
<div class="formula1">Cov<sub>avg</sub> = (ρ<sub>avg</sub> * σ<sub>avg</sub><sup>2</sup>)</div>
An analyst can assess how the variance (and standard deviation) of a portfolio will decline by adding more assets with following formula:
<div class="formula1">

σ<sub>port new</sub><sup>2</sup> = σ<sub>current</sub><sup>2</sup> ((1-ρ<sub>avg</sub>)/n + ρ<sub>avg</sub>)

Where average correlation, ρ<sub>avg </sub> = Cov<sub>avg</sub> / σ<sub>current</sub><sup>2</sup>

</div>
Remember that the above formula is for variance, so if the question asks for standard deviation, the square root will need to be taken.

An exercise can be performed that shows where the initial benefits of adding assets is dramatic but the benefits increase at a decreasing rate as more and more assets are added.
<ul>
	<li>This indicates that the benefits of diversification can be realized from a small number of well-chosen assets.</li>
	<li>For example, a stock portfolio may be able to achieve strong diversification from 30 stocks; however the incremental diversification benefits from adding another 1,000 stocks may not be incredibly significant.</li>
</ul>

Diversification Benefits

The discussion of <a title="Diversification Benefits" href="https://financetrain.com/diversification-benefits/">diversification benefits</a> focused on a portfolio consisting of risky assets; when a risk-free asset is incorporated, diversification is still prevalent but a linear trade-off between risk and return is established.

The introduction of a risk-free asset does not change the construct of the <a title="The Minimum Variance Frontier &amp; Efficient Frontier" href="https://financetrain.com/the-minimum-variance-frontier-efficient-frontier/">minimum variance frontier</a> graphical structure (y-axis = expected return; x-axis = standard deviation or variance).

However, the introduction of the risk-free asset does shift the optimal risk-return trade off on the efficient frontier.

<strong>Capital Allocation Line (CAL):</strong> This line shows the highest returns for each level of risk in a portfolio containing a risky and risk-free asset.

<strong>CAL Equation</strong>
<div class="formula1">

E(R<sub>P</sub>) = R<sub>F</sub> + ((E(R<sub>T</sub>) – R<sub>F</sub>)/σ<sub>T</sub>)*σ<sub>P</sub>

E(R<sub>P</sub>) = expected return

R<sub>F</sub> = rate of return on the risk free asset

E(R<sub>T</sub>) = expected return on CAL portfolio that is tangent to the minimum variance frontier

σ<sub>T</sub> = standard deviation of the tangent portfolio

σ<sub>P </sub>= standard deviation of the portfolio analyzed

</div>
Note that when there is zero allocation to the risky asset, the portfolio’s return will equal the risk-free rate and the standard deviation will be zero; this is the y-intercept of the CAL.

<strong>CAL Slope Coefficient</strong> = <strong>Sharpe Ratio</strong>; This is the expected change in return for a given change in risk (where risk is defined as the standard deviation of returns).
<div class="formula1">Sharpe Ratio = (E(R<sub>asset</sub>) – R<sub>F</sub>)/σ<sub>asset</sub></div>
The Sharpe Ratio is a risk/return tradeoff measure; if two assets offer a similar expected return but different standard deviations, the asset with the higher Sharpe Ratio is considered superior.

<strong>Optimal Portfolio:</strong> Once the risk-free asset is introduced, the only optimal portfolio on the minimum variance frontier is the tangent portfolio.

The Capital Allocation Line – Introducing the Risk-free Asset

On a graph, the <a title="The Capital Allocation Line – Introducing the Risk-free Asset" href="https://financetrain.com/the-capital-allocation-line-introducing-the-risk-free-asset/">Capital Allocation line (CAL)</a>  starts at the risk-free return and runs tangent to the minimum variance frontier for <strong><em>any group of risk assets</em></strong>.

On a graph, the Capital Market Line (CML) starts from the risk-free return on the y-int and runs tangent to the efficient frontier <strong><em>at the market portfolio</em></strong>.

Market Portfolio is portfolio representing the weighted value of all investible assets.

The idea is that all investors all investors agree to common expectations for all assets, i.e., expected returns, standard deviations and correlations. When there is only one sent of expectations there will be only one capital allocation line, called the Capital Market Line.

Since all the investors have the same expectations, they all are agreeing on similar composition of optimal risky portfolio, which is called the market portfolio.

The line equation for the CML is the same as the CAL and the slope coefficient is the <a title="Sharpe Ratio for Measuring Return on Risk" href="https://financetrain.com/sharpe-ratio-for-measuring-return-on-risk/">Sharpe Ratio</a> formula. CML is actually a special case of CAL.

Note that there is only one CML common for all investors, while there are unlimited CALs unique for each investor.

The Capital Market Line

<ul>
  <li>The Capital Asset Pricing Model (CAPM) assumes only one efficient portfolio, the market portfolio.</li>
  <li>CAPM and the CML are more strict than simple Mean-Variance and the <a href="https://financetrain.com/the-capital-allocation-line-introducing-the-risk-free-asset/" title="The Capital Allocation Line – Introducing the Risk-free Asset">CAL</a>.</li>
  <li>CAPM and CAL similarities:</li>
		<ul>
			<li>Risk averse investors.</li>
			<li>Shared investor assumptions for expected returns, variances and standard deviations, and covariances of returns.</li>
			<li>The above variables are the only inputs required to calculate the efficient frontier.</li>
			<li>No taxes and no transaction costs.</li>
		
		</ul>
	<li>CAPM additional assumptions:</li>
		<ul>
			<li>All investors have the same CAL.</li>
			<li>No restrictions for borrowing and lending at the risk free rate.</li>
			<li>No restrictions on short-selling.</li>
			<li>Trading volume does not change prices.</li>
		</ul>
	<li>The CML is the efficient market portfolio, but the CAPM can describe the expected returns for all assets and portfolios.</li>
</ul>

<ul>
	<div class="formula1">
	CAPM: E(R<sub>i</sub>) = R<sub>F</sub> + &beta;<sub>i</sub>[E(R<sub>M</sub>) - R<sub>F</sub>]
	
		<ul>
			<li>E(R<sub>i</sub>) = Return for asset "i"</li>
			<li>R<sub>F</sub> = Risk-free rate of return</li>
			<li>E(R<sub>M</sub>) = Expected return of the market portfolio</li>
			<li>&beta;<sub>i</sub> = The asset's beta</li>
				<ul>
					<li>Beta is the asset's sensitivity to the return on the market portfolio</li>
					<li>Beta is a measure of an asset's risk relative to market portfolio, as asset's with a beta above 1 are considered riskier than the market and beta's below 1 are considered less risky than the market.</li>
					<li>&beta; = Cov(R<sub>i</sub>,R<sub>M</sub>)/&sigma;<sub>M</sub><sup>2</sup></li>
				</ul>
		
		</ul>
	
	</div>

	<li><b>Security Market Line (SML):</b> Line produced by the CAPM equation for asset "i"</li>
	<li><b>SMLs & Efficient Markets:</b> In an efficient market securities are correctly priced when the expected risk and expected return equal the SML price of risk.</li>
	

</ul>


CAPM & the SML

We can use the <a href="https://financetrain.com/sharpe-ratio-for-measuring-return-on-risk/" title="Sharpe Ratio for Measuring Return on Risk">Sharpe Ratio</a> to determine if adding an asset creates a better (higher) <a href="https://financetrain.com/the-minimum-variance-frontier-efficient-frontier/" title="The Minimum Variance Frontier & Efficient Frontier">minimum variance frontier</a>.

The Sharpe ratio is calculated using the following formula:

<div class="formula1">Sharpe Ratio = (E(R<sub>asset</sub>) – R<sub>F</sub>)/σ<sub>asset</sub></div>

Calculate the Sharpe ratio for the current portfolio and then calculate the Sharpe ratio after adding the new asset.

<div>If the Sharpe Ratio<sub>new port</sub> &gt; (Sharpe Ratio<sub>current port</sub> * ρ<sub>(new asset, current port)</sub>), then the new asset should be added.</div>

ρ<sub>(new asset, current port)</sub> = correlation coefficient between the current portfolio’s returns and the new asset’s returns

Adding an Asset to a Portfolio – Improving the Minimum Variance Frontier

<div>When a portfolio manager considers a security for addition to a portfolio within the construct of <a title="Mean-Variance Analysis Assumptions" href="https://financetrain.com/mean-variance-analysis-assumptions/">mean variance analysis</a>, he/she must determine what return for the x-variable represents “market portfolio”.</div>
<div></div>
<div>The Market Model assumes that some security market index, such as the S&amp;P 500, represents the market portfolio.</div>
<div></div>
<div><strong>The Market Model &amp; Quant:</strong> The Market Model is a single variable regression model, where alpha return is the constant and beta is the security’s return coefficient on the independent (x) variable of the market index’s.</div>
<div></div>
<div>The market model allows for a security’s expected return to be priced by linear regression.</div>
<div></div>
<div>Ri = αi + βi(RM) + εi</div>
<div></div>
<div>• Ri = Return of security i</div>
<div>• αi = The return from the asset that is not related to the market’s return. This is “alpha” return from the security</div>
<div>• βi = Beta or the return from the security explained by the market index’s return</div>
<div>• RM = The market index’s return</div>
<div>• εi = Error term for past returns not explained by the regression equation</div>
<div></div>
<div>There are three assumptions in the market model:</div>
<div></div>
<div>1. The expected value of the error term in zero.</div>
<div>2. The errors are not correlated with the market returns.</div>
<div>3. The firm specific evens are not correlated across the assets.</div>
<div></div>
<div>Using these assumptions, the procedure for mean-variance analysis becomes very simple.</div>
<div></div>

The Market Model for a Security’s Returns

Betas calculated purely based on historical data are unadjusted betas. However, this <a title="How to Calculate Stock Beta in Excel" href="https://financetrain.com/how-to-calculate-stock-beta-in-excel/">beta</a> estimate based on historical estimates is not a good indicator of the future. This is also called the beta instability problem.

Statistically, over time betas may exhibit mean reverting properties as extended periods significantly above 1 (one) may eventually decline and betas below one may revert toward 1.

Therefore analysts may apply models to create an adjustment calculation for the historical beta and use this adjusted beta to calculate the expected return for the security.

The generalized formula for adjusted beta can be presented as follows:

Adjusted Beta Β = α<sub>0</sub> +α<sub>1</sub>Β<sub>i,t-1</sub>

Where, α<sub>0</sub> + α<sub>1</sub> = 1

Because of the mean reverting property of beta, the adjusted beta will move closer to 1. If the historical or unadjusted beta is greater than 1, then the adjusted beta will be lesser that unadjusted beta and closer to 1, and vice versa.

Let’s take an example to understand this.

Assume that the historical beta for a company is 1.5. the adjusted beta formula for the company is 3/4 + 1/4 Β<sub>t-1</sub>

Adjusted beta = 3/4 + 1/4 * 1.5 = 1.125

The larger the value of α<sub>0</sub>, the faster the adjusted beta will move towards 1.

Adjusted and Unadjusted Beta

While the Market Model uses only a single risk factor to price a security’s return, Multifactor Models apply a set of risk factors to describe an asset’s returns.
<h2>Multifactor Model Types</h2>
<strong>Macroeconomic Factor Models </strong>

Apply economic variable as the risk factors that explain a security’s returns.
<ul>
	<li>Surprise Factor for betas of macroeconomic factor models:</li>
	<li>These models will not apply the actual value for a variable such as forecasted GDP growth rate.  Rather macroeconomic factor models apply a beta for the surprise factor of GDP growth describing the security’s expected return response when the variable “surprises” expectations.</li>
	<li><strong>Calculating portfolio returns in a two security portfolio with a macroeconomic factor model:</strong></li>
	<li>For each security, calculate the surprise return from the model; apply the security’s weighting to the surprise return; and sum the two weighted values.</li>
	<li>Surprise R <sub>security i</sub> = Expected R <sub>security i</sub> +β<sub>1</sub>(actual <sub>factor 1</sub> – expected <sub>factor 1</sub>) + … repeat for # of factors</li>
	<li>This formula shows how the surprise beta is applied to the surprise to the factor value.  When the actual values equal the expected values, then the security’s actual return will equal its expected return.</li>
	<li>The difference between the expected return and the actual return is the surprise return; this is the error term of the regression model.</li>
</ul>
<strong>Fundamental Factor Models</strong>

Apply asset-class specific variables (ex. stocks: P/E ratio, degree of financial leverage, market capitalization, etc.) to explain a security’s returns.

<strong>Statistical Factor Models</strong>

These models apply a variety of variables in a regression analysis to find the best fit of historical data in explaining a security’s returns.

Multifactor Models

<ul>
	<li>Arbitrage Portfolio Theory (APT) came along after <a title="The Capital Asset Pricing Model" href="https://financetrain.com/the-capital-asset-pricing-model/">CAPM</a> as a multifactor model to explain returns.</li>
	<li>APT explains returns under the construct where:</li>
<ul>
	<li>Multiple risks with an excess return above the risk free rate of return can be priced.</li>
	<li>Any security or portfolio has its own beta coefficient to each of the priced risk variables in the model.</li>
	<li>There is a linear relationship between the security's return and the priced risk (a basic assumption of multi-variable regression).</li>
	<li>APT calculates the alpha value, or y-intercept of the model graph.</li>
</ul>
</ul>
<h2>Comparing CAPM vs. APT</h2>
APT is less restrictive in CAPM, as:
<ul>
	<li>Asset returns can be described using a <a title="Multifactor Models" href="https://financetrain.com/multifactor-models/">multifactor model</a> (CAPM being a single factor model).</li>
	<li>Diversification eliminates the security specific risk of the individual securities in a multi-asset portfolio.</li>
	<li>Assets are priced such that arbitrage profit does not exist.</li>
<ul>
	<li>The factor sensitivities of the assets in an arbitrage portfolio equal zero and the portfolios expected return is zero.</li>
</ul>
	<li>Note: If the investor believes that the expected return on the arbitrage portfolio is not equal to zero, then a single factor or multifactor APT style model can be used to capture risk free profit.</li>
<ul>
	<li>Step 1: Identify and purchase the undervalued asset or portfolio.</li>
	<li>Step 2: Finance the long position with a short sale of overvalued assets.</li>
	<li>Step 3: Close the long and short positions once the assets return to their APT determined equilibrium model values for zero return.</li>
	<li>Whenever two portfolios have the same risk but different expected returns or the same expected return, but different risks, an arbitrage opportunity may be possible.</li>
</ul>
	<li>It is important to note a couple of key differences between CAPM and APT as these modeling techniques and their variations are extensive in financial research.</li>
	<li>CAPM assumes that investors agree on asset returns, risks, and correlations: E(R), σ, and ρ.</li>
<ul class="list2">
	<li>APT does not assume this, making the theory less restrictive than CAPM.</li>
</ul>
	<li>CAPM assumes that all investors should construct a portfolio based on the risk free asset and the market portfolio.</li>
<ul class="list2">
	<li>APT does not necessarily assume this</li>
</ul>
	<li>Other Challenges for CAPM vs. Reality:</li>
<ul class="list2">
	<li>CAPM ignores transaction costs and taxes, which is not realistic for investors.</li>
	<li>Investors rarely can borrow at the risk free rate.</li>
	<li>Not all investors can short sell.</li>
</ul>
	<li><strong>Risk Aversion as Common Ground:</strong> Both APT and CAPM assume that investors are risk averse and will take the highest return for a given amount of risk.</li>
</ul>
<h2>Pricing E(RP) with an APT Model</h2>

An APT model can be thought of an equation where alphas (the excess return of the risk factors) are applied to betas (the sensitivity of the portfolio or security to the risk factor itself).

	<div class="formula1">
	<b>	E(R<sub>P</sub>) = R<sub>F</sub> + &lambda;<sub>i</sub>&beta;<sub>P,i</sub> + &lambda;<sub>j</sub>&beta;<sub>P,j</sub>  </b>
		<ul class="list2">
		<li>&lambda;<sub>i</sub> = Factor risk premium return above the risk free rate; the compensation to the investor for accepting the risk.</li>
		<li>&beta;<sub>P,i</sub> = Coefficient representing the portfolio (or security) return's sensitivity to the risk factor</li>
		
		</ul>
	</div>


Arbitrage Portfolio Theory (APT) – A Multifactor Macroeconomic Model

<h2>Tracking portfolios</h2>


<b>Tracking Portfolio:</b> A portfolio assembled with securities that will replicate a specific risk profile.
<ul>
	<li>Tracking portfolios commonly mirror an expected benchmark index, such as an index of global large capitalization stocks.</li>
	<li>The theoretical construction of a tracking portfolio done through multifactor modeling is done by setting each factor sensitivities equal to the factor sensitivities of the benchmark.</li>
		<ul>
			<li>For example, if a mid cap stock index is made of 500 stocks, then the portfolio manager can create a tracking portfolio through a sample of the 500 stocks that has a collective risk factor sensitivity equal to that of the index.</li>
		</ul>
	<li>Tracking portfolios can be used for hedging/risk management.</li>
		<ul>
			<li>For example, a portfolio manager may want to temporarily decrease the portfolio's risk exposure to a certain asset class (stocks, bonds, commodities, etc.) or sub-asset class (small cap stocks, high yield debt, gold, etc.) sector.</li>
		</ul>


</ul>
<h2>Investor Risk Tolerance and <a href="https://financetrain.com/multifactor-models/" title="Multifactor Models">Multifactor Models</a></h2>

<ul>
<li>Different individual investors will have different individual degrees of ability to bear risk.</li>
<li>Therefore, not all investors should hold the same portfolio.</li>
<li>A multifactor model can be used to design the optimal portfolio for the individual investor by overweighting and underweighting exposure different asset classes in the portfolio.</li>
<li>Investors can increase their relative exposure to certain risk factors whenever their tolerance for the priced risk exceeds that of the average investor.</li>
</ul>
<h2>Fundamental Multifactor Models</h2>

Whereas APT is usually associated with economic risk exposures such as GDP growth, inflation, and interest rates, multifactor models can also be applied to a security's fundamental valuation traits following the multiple variable regression technique.

<div class="formula1">
	<b> Standardized Beta = (Fundamental <sub>stock i</sub> - Fundamental <sub>avg stock</sub> ) / &sigma; <sub>fund all stocks</sub> </b>
	
	<ul>
		<li>The standardized beta scales a fundamental value metric across all stocks.</li>
		<li>This formula can be applied to any stock fundamental valuation metric, such as price to earnings ratio.</li>
	</ul>
</div>
<h2>Factor Models and the Sources of Risk and Return</h2>

<ul>
			<li>Fundamental multifactor models can be used to assess the sources of return and sources of risk for a portfolio manager's performance.</li>
			<li>Portfolio managers are commonly evaluated against some benchmark.</li>
			<ul>
				<li>For example, a U.S. small cap fund manager might be evaluated against the Russell 2000 index.</li>
			</ul>
			<div class="formula1">
			<b> Active Return = Portfolio Return - Benchmark Return </b>
			<br><br>
			<b> Active Risk = Standard deviation of active returns = &sigma; <sub>active returns</sub> </b>
			
			<ul>
				<li>Active risk is also called tracking risk or tracking error.</li>
				<li>Active returns for multiple periods are required to calculate active risk.</li>
			</ul>

			</div>
			<li>Active Risk and Investment Strategy</li>
			<ul>
				<li>Indexing Strategy is a tracking error less than or equal to 1%.</li>
				<li>Enhanced Indexing is a tracking error of 2%.</li>
				<li>Moderately Active Strategy is a tracking error of 2% - 6%.</li>
				<li>Aggressive Active Strategy is a tracking error of 6% - 9%.</li>
			</ul>
		<li>The Information Ratio - Evaluating Active Risk</li>
			<ul>
				<li>Variation on the Sharpe Ratio to measure active return per unit of active risk.</li>
				<div class="formula1">
				IR = (Avg. Return <sub>Port</sub> - Avg. Return <sub>Benchmark</sub>)/ &sigma; <sub>active returns</sub>
				</div>
								
				<li>A high information ratio may indicate that increased active management is worthwhile.</li>
				<li>For two active portfolios with the same benchmark, the portfolio with the higher information ratio is considered superior.</li>
			</ul>
		</ul>
<h2>Active Risk Squared and Active Risk Factor Modeling</h2>

	<ul>
		<li>Active risk can be explained using a fundamental factor model, just the same as active return can be explained with a fundamental factor model.</li>
		<div class="formula1">
		Active Risk Squared = Variance of Active Risk = The square of the standard deviations of active return = &sigma;<sup>2</sup> <sub>active returns</sub>
		</div>
		<li><b>Active Factor Risk:</b> Comes from the portfolio manager assuming factor risk exposures that vary from the benchmark index.</li>
			<ul>
				<li>This is active risk factor mismatching by the portfolio manager.</li>
			</ul>
		<li><b>Active Specific Risk:</b> Comes from portfolio weights on the asset sub-portfolios that comprise the whole portfolio.</li>
			<ul>
				<li>This is active security selection by the portfolio manager.</li>
			</ul>
		<div class="formula1">
		Active Risk Squared translates to = Active Factor Risk + Active Specific Risk.
		</div>

	</ul>


Risk Factors and Tracking Portfolios

<ul><li><a href="https://financetrain.com/modern-portfolio-theory/" class="rank-math-link">Modern Portfolio Theory</a> (MPT) is rooted in the <a title="Mean-Variance Analysis Assumptions" href="https://financetrain.com/mean-variance-analysis-assumptions/" class="rank-math-link">mean-variance analysis</a> research performed by Harry Markowitz conducted to allocate assets through a portfolio optimization process.</li></ul>



<ul><li>The portfolio concepts presented in section I trace their roots to Markowitz groundbreaking work.</li></ul>



<ul><li>The Efficient Market Hypothesis (EMH) contents that the market correctly prices all securities.</li></ul>



<ul><li>MPT argues that all investors should hold the same portfolio of diversified securities correctly priced by the efficient market.</li></ul>



<ul><li>The conclusion of MPT would argue for passive management of investor portfolios.</li><li style="list-style-type: none;">
<ul>
<li>With this in mind, some portfolio managers have consistently out-returned a recognized market index over time.</li>
</ul>
</li><li style="list-style-type: none;">
<ul>
<li>Further, sometimes asset mispricings are correctly identified by portfolio managers and these anomalies have been exploited to generate excess returns above the market index benchmark. These issues can serve as a foundation for justifying active portfolio management over passive management.</li>
</ul>
</li><li><a href="https://financetrain.com/the-capital-asset-pricing-model/">CAPM</a> assumes that investors face no restrictions on lending and (more importantly) borrowing at the risk free rate, as well as the ability to short sell.</li></ul>



<ul><li>In reality these limitations frequently exist.&nbsp; Any investor can lend at the risk free rate buy purchasing a bond deemed as having extremely low risk.</li><li>Investors lack the ability to command the low borrowing rates of say the US, Japanese, or German sovereign governments (which would be the proxies for a risk free rate, despite a total risk free nature).</li><li>Many investors cannot short sell (even some big institutional types, such as pensions).</li><li>Those investors who can short sell could opt to borrow at their cost and sell short some of the portfolio.</li><li>Ultimately, with a spread between the lending (lower) and borrowing (higher) rates imposed on investor reality and restrictions on short selling, the market can exhibit inefficiencies.</li><li>Inefficiency causes a distortion in the linear nature of the relationship between expected returns and beta.</li></ul>

Markowitz, MPT, and Market Efficiency

An efficient market is one, which is able to absorb new information into the security prices instantly. In the context of international markets, efficiency is not just about the individual markets but also about the pricing of these individual markets relative to the world index. The issue of international market efficiency revolves around international capital market integration versus segregation.

<strong>International Capital Market Integration:</strong> Capital can flow freely across national borders where investors can respond to new global information and exploit arbitrage opportunities; the financial asset law of one price applies to assets traded in the internationally/globally integrated capital market.

<strong>International Capital Market Segregation:</strong> Barriers exist that prevent the market to be as efficient as the integrated capital market.

<strong>Capital Mobility Barriers/Impediments</strong>
<ul>
	<li><strong>Psychology:</strong> Investors fear the unknown of investing in foreign assets.</li>
	<li><strong>Legal:</strong> Governments restrict the flow of foreign capital.</li>
	<li><strong>Transaction Costs:</strong> Investment planning and maintenance for assets located abroad often incurs greater cost than similar domestic assets.</li>
	<li><strong>Taxes:</strong> Investors may be exposed to high taxation abroad and/or double taxation of an international asset’s return.</li>
	<li><strong>Exchange Rate Risk:</strong> Investors need to determine an exchange rate risk premium for the return on a foreign asset.</li>
	<li><strong>Political Risk:</strong> Governments can take any number of adverse actions against foreign investors.</li>
</ul>
<strong>Factors Favoring International Capital Market Integration</strong>
<ul>
	<li><strong>International Stock Listing:</strong> Some multinational companies have equity shares listed on multiple exchanges; this helps facilitate a law of one price environment for these securities.</li>
	<li><strong>International Banking:</strong> Corporations and governments borrow in foreign markets, facilitating the law of one price for a real/inflation adjusted rate of return</li>
	<li><strong>International Investing:</strong> Global investors hold assets in many countries; this creates pressure for transparency, liquidity and efficiency for an integrated international market.</li>
</ul>
 

International Capital Market Integration

<h2>Domestic CAPM</h2>

<ul>
<li>An efficient market allows investors to diversify away company/security specific risk and have exposure solely to the market risk.</li>
<li>The <a href="https://financetrain.com/the-capital-asset-pricing-model/" title="The Capital Asset Pricing Model">Capital Asset Pricing Model (CAPM)</a> as previously discussed was considered purely from an investor's domestic point of view.</li>
<li>Domestic CAPM: Theoretic technique for an investor that can be used to price market/systemic risk exposure of assets denominated in his/her own currency.</li>

	<ul>
		<li>Domestic CAPM: Local Currency of Asset = Domestic Currency of the Investor</li>
		<li>The domestic CAPM can only price local market risk.</li>
		<li>Internationally, the domestic CAPM fails to consider:</li>
			<ul>
				<li>Global market risks.  Ex: Only the U.S. market risk is important in pricing Wal-Mart common equity shares.</li>
				<li>Exchange rate risk.</li>
			</ul>
	</ul>
</ul>

<h2>Extending Domestic CAPM</h2>
<b>Extended CAPM:</b> Extends domestic CAPM to pricing systemic risk adjusted security returns to a world market portfolio of investible assets.

	
	<div class="formula1">
		<b>	Domestic CAPM formula:<br><br> E(R<sub>iLC</sub>) = R<sub>FLC</sub> + &beta;<sub>iLC</sub>[E(R<sub>MLC</sub>) - R<sub>FLC</sub>] </b>
		
		<ul>
			<li>E(R<sub>iLC</sub>) = Domestic return for global asset "i", as measured in the asset's local currency</li>
			<li>R<sub>FLC</sub> = Risk-free rate of return in the investor's domestic currency</li>
			<li>E(R<sub>MLC</sub> = Expected return of the domestic market portfolio, used in calculating the domestic market risk premium, where the domestic currency is the local currency for the market.</li>
			<li>&beta;<sub>iLC</sub> = The asset's beta, its sensitivity to domestic market returns, where the investor's domestic currency is the local currency</li>
			
		</ul>
	</div>
	
	<div class="formula1">
		<b> Extended CAPM formula: <br><br>
		
		R<sub>iDC</sub> = R<sub>FDC</sub> + &beta;<sub>iDC</sub>[E(R<sub>WDC</sub>) - R<sub>FDC</sub>] </b>
		
		<ul>
			<li>R<sub>iDC</sub> = Return for risky global asset "i" measured in investor's domestic currency</li>
			<li>R<sub>FDC</sub> = Global risk-free asset's rate of return in the investor's domestic currency.</li>
			<li>R<sub>WDC</sub> = Return on world market of investible assets in the investor's domestic currency; used in calculating the world market risk premium in the investor's domestic currency.</li>
			<li>&beta;<sub>iDC</sub> = The global asset's beta, its sensitivity to world market returns, in the investor's domestic currency</li>
		</ul>
	</div>
<h3>Assumptions Needed to Justify an Extended CAPM</h3>
<ul>
	<li>Consumer price index for all nations is composed of a like basket of goods and services.</li>
	<li>Capital markets across all nations are integrated, so the model's real risk free rate is the same for all global investors.</li>
	<li>Asset returns have systemic risk exposure to the world market portfolio, a cap weighted portfolio of all risky assets on planet earth.</li>
	<li>Purchasing Power Parity (PPP) is persistent.</li>
		<ul>
			<li>PPP implies that when an investor observes a change in his/her global asset's price in terms of domestic currency, the only difference in price change for an investor in the same asset residing in another country relates to the difference in expected inflation rates of the two countries where the investors reside.</li>
			<li>PPP thus implies no real exchange rate risk</li>
		</ul>
	<li>Modeling under the assumptions of the Extended CAPM still fails to compensate investors for <i><b>exchange rate risk</b></i>.</li>
		<ul>
			<li>PPP may rarely hold under empirical analysis.</li>
			<li>The next section explores changes to the real exchange rate.</li>
		</ul>		
</ul>



Domestic CAPM and Extended CAPM

<ul>
<li>Nominal Exchange Rates represent how many units of one currency can be exchanged for one unit of another currency.</li>
	<ul>
		<li>Nominal exchange rates are the rates quoted in the global markets for foreign currency exchange.</li>
	</ul>
<li>Real Exchange Rates represent the amount of purchasing power in one currency can be exchanged for one unit of another currency.</li>
	<ul>
		<li>Example: 10 Euros buys one "global burger joint chain meal deal" in Paris; converting 10 Euros to US dollars and going into the same chain in downtown Cincinnati buys 1.5 of the same meal deals.</li>
	</ul>
<li>Determining Change to Real Exchange Rate</li>
	<ul>
		<li>Real and Nominal Exchange Rates under PPP</li>
		
		<div class="formula1">
		<b> S<sub>R X/Y</sub> = S<sub>N X/Y</sub> / (P<sub>X</sub> / P<sub>Y</sub>) </b>
		
			<ul>
				<li>S<sub>R X/Y</sub> = Real X/Y exchange rate measuring purchasing power</li>
				<li>S<sub>N X/Y</sub> = The nominal X /Y exchange rate; i.e. the forex market quote</li>
				<li>P<sub>X</sub> = Price of a standard basked of goods in country X</li>
				<li>P<sub>Y</sub> = Price of the same basket of goods in country Y</li>
			</ul>
		</div>
		<li>Percent Change of the Nominal Exchange Rate under PPP</li>
		<div class="formula1">
		<b> % S<sub>N PPP X/Y</sub> = ((1 + I <sub>X</sub> )/ (1 + I <sub>Y</sub> )) - 1 </b>
		
			<ul>
				<li>I = Inflation rate over measurement period</li>

			</ul>
		</div>
		<li><i>The amount of change in the real exchange rate between the currencies of two countries can be calculated by comparing an observed change in nominal exchange rates of the two currencies with the currency change predicted by Purchasing Power Parity.</i></li>
		<div class="formula1">
		<b> % S<sub>R X/Y</sub> = ((1 + %&Delta;S <sub>N X/Y</sub> ) / (1 + % S<sub>N PPP X/Y</sub> )) - 1 </b>
		
			<ul>
				<li>The real exchange rate between two currencies will change whenever the nominal exchange rate changes by an amount that is not explained by inflation.</li>

			</ul>
		</div>
	</ul>

</ul>


Changes in Real Exchange Rates

<ul>
	<li>The ICAPM attempts to explain the required return on a risky asset, measured in its own local currency.</li>
	<li>ICAPM assumption divergences from <a href="https://financetrain.com/domestic-capm-and-extended-capm/" title="Domestic CAPM and Extended CAPM">Extended CAPM</a></li>
		<ul>
			<li>The market basket for goods used in calculating CPI does not need to be the same goods, in the same percentages.</li>
			<li>Purchasing Power Parity does not always prevail.</li>
		</ul>
	<li>Theoretically, the ICAPM should offer investors sufficient returns for taking on systemic/market risk of returns on the world market of investible securities, measured in the same currency as the one in which the asset's return is attempted to be measured.</li>
	
	<div class="formula1">
	<b>	R <sub>ADC</sub> = r<sub>DC</sub> + (&beta;<sub>AWM</sub> * (R <sub>WMDC</sub> - r<sub>DC</sub>)) + (<span style="font-family:times new roman; font-size:20px;">&gamma;</span> <sub>ADC,1/LC</sub> &times; SRP <sub>1/LC</sub>) + … + (<span style="font-family:times new roman; font-size:20px;">&gamma;</span> <sub>ADC,i/LC</sub> &times; SRP <sub>i/LC</sub>) </b>
	
		<ul>
			<li>R <sub>ADC</sub> = Expected/required return measured in an investor's domestic currency for a foreign risky asset denominated in its own local currency</li>
			<li>r<sub>DC</sub> = Risk free rate in the investor's country</li>
			<li>&beta;<sub>AWM</sub> = Sensitivity of the risky asset's returns to changes in world market portfolio returns, when both are measured in the investor's domestic currency</li>
			<li>(R <sub>WMDC</sub> - r<sub>DC</sub>) = World market risk premium measured in the investor's domestic currency</li>
			<li><span style="font-family:times new roman; font-size:20px;">&gamma;</span> <sub>ADC,i/LC</sub> = Currency exposure of the risky asset, measuring the sensitivity of the risky asset's returns, measured in the investor's domestic currency, to changes in the value of the asset's local currency against the kth currency represented in the world market portfolio</li>
			<li>SRP <sub>i/LC</sub> = Foreign currency risk premium; risk compensation to the investor for the risk that the value of the asset's local currency against the ith currency in the world market portfolio might be different from its expected value.</li>
				<ul>
					<li>The foreign currency risk premium is the difference between the expected future spot exchange rate and the current forward exchange rate, divided by the current spot rate.</li>
				</ul>
		</ul>
		
	</div>
</ul>


International CAPM (ICAPM) - Beyond Extended CAPM

<ul>
	<li>Currency exposures measure, in the investor's domestic currency, an asset return's sensitivity to returns on the ith/LC exchange rates.</li>
	<li>Currency exposure risk must be captured this way when the <a href="https://financetrain.com/international-capm-icapm-beyond-extended-capm/" title="International CAPM (ICAPM) – Beyond Extended CAPM">ICAPM</a> is used to determine the domestic currency returns for a domestic investor purchasing a foreign asset.</li>
	<li>For example, if a Canadian investor wants to determine the required Canadian dollar (CAD) return for the common stock shares of U.S. auto maker Ford (NYSE: F) using ICAPM, then he/she needs to know how sensitive the Canadian dollar returns on the Ford shares might be to changes against the value of the US dollar (USD) against all world currencies, including the CAD.</li>
	<li>Currency exposures are calculated by regressing the foreign risky asset's return as measured in the investor's domestic currency against the percentage change in the value of the foreign asset's local currency against currencies 1 through k, for the ith currency.</li>

</ul>
<h2>Correlations Between Asset Returns and Exchange Rate Movements</h2>

<ul>
	<li><b>Zero Correlation:</b> A foreign risky asset's price will have no systemic reaction to a change in the Investor Domestic Currency/Asset's Local Currency exchange rate.</li>

	<li><b>Positive Correlation:</b> A foreign risky asset's local currency price will change in the same direction as any change in the DC/LC exchange rate.</li>
	<li><b>Negative Correlation:</b> A foreign risky asset's local currency price will change in the opposite direction as any change in the DC/LC exchange rate.</li>
	<li>Importance of Real Exchange Rates:</li>
		<ul>
			<li>Only changes in the real exchange rates will produce real changes in asset returns.</li>
			<li>When changes in nominal exchange rates only reflect inflation rate differences between countries, reported nominal asset returns will only reflect inflation rate difference between the local country of the foreign asset and the investor's domestic country.</li>
		</ul>
		
	
</ul>


Measuring Currency Exposure

The stock value of a company will be affected by the changes in the real value of its local currency based on how much exchange rate exposure it has. The response of a company’s stock value in different scenarios is discussed below:


<ul>
	<li>Company earns material revenues in foreign countries or faces international competition domestically and has primarily domestic costs.</li>
		<ul>
			<li>Negative correlation with movements in the real values of local currencies in the international currency markets.</li>
			<li>Local currency exposure value is negative.</li>
		</ul>
	<li>Company earns material revenues domestically, but costs are mostly incurred in foreign currencies.</li>
		<ul>
			<li>Positive correlation with movements in the real value of local currencies in the international currency markets.</li>
			<li>Local currency exposure value is positive.</li>
		</ul>
	<li>Company earns revenues domestically and incurs costs domestically with no international firms.</li>
		<ul>
			<li>Zero correlation with movements in the real value of their local currencies in international currency markets.</li>
			<li>Local currency exposure value is zero.</li>
		</ul>


</ul>


Company Stock Value Responses to Changes in Real Exchange Rates

<ul>
	<li>Both assume unlimited borrowing and lending at the risk free rate.</li>
	<li><a href="https://financetrain.com/international-capm-icapm-beyond-extended-capm/" title="International CAPM (ICAPM) – Beyond Extended CAPM">ICAPM</a> becomes <a href="https://financetrain.com/domestic-capm-and-extended-capm/" title="Domestic CAPM and Extended CAPM">Extended CAPM</a> when international capital markets are integrated and Purchasing Power Parity holds.</li>
	<li>ICAPM can be used to value any security in the world if all national markets are integrated.</li>
	<li>ICAPM indicates that if global markets are integrated and efficient, then the optimal portfolio is global market index hedged based on the investor's currency exposures to the foreign assets in the index.</li>
	<li>Investor time horizon influences application of ICAPM.</li>
</ul>


ICAPM vs. Domestic CAPM

The domestic activity in an economy is related to its exchange rate movements. In the traditional theory to explain this, there are two components: long-run and short-run.

In the long-run an economy's competitiveness increases with a decline in the country's currency value.

In the short-run, the country's trade balance widens, and inflation increases if the country's currency depreciates. This happens because the cost of imports increases. 

This combination of short-term decline, and long-term increase is called the J-curve.

<ul>
	<li><b>Nominal Exchange Rate Movements:</b> Reflect only inflation differences and do not have a macroeconomic affect.</li>
	<li><b>Real Exchange Rate Movements:</b> Shift the terms of trade between countries, altering macroeconomic behavior.</li>
	<li>J-Curve Plot:</li>
		<ul>
			<li>Y-axis = Balance of Trade</li>
			<li>X-axis = Years since currency devaluation</li>
			<img src="/wp-content/uploads/j-curve.gif" />
		</ul>
</ul>

<h2>Traditional J-Curve Sequence</h2>

<ul>
<li>Real currency depreciation produces to opposite effects.</li>
	<ol>
		<li><b>Price Effect</b>: Domestic prices rise, reducing consumer demand for domestic produced goods, increases the trade deficit and causes the domestic economy to contract.</li>
		<li><b>Income Effect</b>: Depreciating currency makes export goods cheaper in foreign markets; the economy becomes more globally competitive and real GDP improves.</li>
	</ol>
<li>The price effect takes place first and the balance of trade dips initially, but then the income effect kicks in and balance of trade improves.</li>
	<ul>
		<li>This produces the J shaped curve on the plot described above.</li>
		<li>The implication of the J-curve theory is bad short term impacts followed by a positive long term trend.</li>
	</ul>

</ul>
<h2>J-Curve as Downward Spiral - Counter Traditional</h2>

The traditional view of the J-Curve may not hold as:
<ul>
	<li>Depreciating currency produces domestic inflation.</li>
	<li>Inflation reduces demand and GDP contracts.</li>
	<li>Inelastic demand for foreign products cuts the percent of consumption by less than the percent of the price increase.</li>
	<li>The trade balance continues to worsen (income effect does not kick in).</li>
	<li>The domestic currency weakens even more.</li>
	<li>More inflation kicks in and the situation facilitates itself.</li>

</ul>


The J-Curve – Impact of Exchange Rate Changes on National Economies

Two theories attempt to explain the relationship between exchange rates, real economic activity, and equity markets.
<ol>
	<li>Traditional Trade Theory</li>
		<ul>
			<li>This is the traditional view of the J-Curve effect.</li>
			<li>The value of the domestic currency and the performance of the domestic stock market are positively correlated in the short run but negatively correlated over the long term.</li>
		</ul>
	<li>Model Demand Model</li>
		<ul>
			<li>Theorizes the following sequence:</li>
				<ul>
					<li>Real economic growth spurs domestic currency demand.</li>
					<li>More demand translates to appreciation in the international currency markets.</li>
					<li>The stock market responds positively to real economic growth.</li>
				</ul>
			<li>The money demand model indicates that domestic currency values and domestic stock markets are positively correlated.</li>

		</ul>	

</ol>

<h2>Reality and Exchange Rate Movements</h2>


<h3>Developed Markets:</h3>
<ul>
	<li>Correlations between domestic exchange rates and domestic stock markets can be positively, negatively or zero correlated.</li>
	<li>Reasons:</li>
		<ul>
			<li>Only changes to real exchange rates impact trade terms.</li>
			<li>Different countries will have a different mix of exporters and importers in their stock markets, causing different responses to exchange rate movements.</li>
			<li>Real exchange rate movements have opposite short term and long term impacts, so the equity market response depends on the view taken by market participants.</li>
			<li>Real exchange rate movements have opposite short term and long term impacts, so the equity market response depends on the view taken by market participants.</li>
		</ul>
</ul>
<h3>Emerging Markets:</h3>

<ul>
	<li>Emerging equity market returns tend to correlate positively with domestic currency exchange rate movements against developed market currencies.</li>
	<li>Reasons:</li>
		<ul>
			<li>Emerging economies are heavily reliant on foreign capital for financing.</li>
			<li>Real currency appreciation signals economic strength.</li>
			<li>Emerging market stocks and currencies are positively correlated with domestic economic and political outlooks.</li>
		</ul>
	<li>Foreign investor face high risk in the positive correlation environment of emerging markets, because they will suffer losses on both the declining equity prices and depreciating local currencies of the equities.</li>
</ul>

 

Moving Exchange Rates and Equity Markets

<ul>
	<li>The ICAPM is used by some investors to value any and all risky assets on a global basis.</li>
	<li>The ICAPM is only valid if international capital markets are integrated.</li>
	<li>If international capital markets are segmented, then assets with the same risk characteristics will be priced differently in different national markets.</li>
	<li>When barriers to capital market integration cause investors to avoid the balanced world market portfolio, higher allocations will be made to specific countries and specific securities, causing inefficient asset pricing.</li>
	<li>This inefficiency makes an argument for active portfolio management.</li>
</ul>


Impacts of Market Segmentation on ICAPM

<ul>
	<li>Two arguments can be used to justify active portfolio management for investors:</li>
		<ol>
			<li>Given that the mispricing of securities takes place from time to time (2007 would have been a great time to short U.S. mortgage backed securities), highly skilled active managers can exploit mispricings to generate excess returns.</li>
			<li>Even with a passive strategy, an allocation decision must be made between the risk free asset (such as government debt) and a portfolio comprised of risky assets.</li>
				<ul>
					<li>Forecasts for risks and returns must be made in order to design the individual investor's optimal portfolio.</li>
				</ul>
		</ol>
	<li>Successful limited active management can be highly beneficial for investors as periodic allocation weighting adjustments can facilitate higher returns during economic expansion and mitigate losses during economic contraction.</li>

</ul>

 

Justifying Active Portfolio Management

<ul>
	<li>Treynor and Black developed a portfolio optimization model that seeks to maximize a portfolio's Sharpe Ratio through a combination of an actively managed portfolio component built with a few select mispriced securities and a passively managed market index portfolio component.</li>
	<li>Treynor-Black assumes that markets are highly, but no perfectly efficient.</li>
	<li>Macroeconomic forecasting can be applied to calculate the expected return and standard deviation of the portfolio.</li>
	<li>Securities can be assessed for mispricing by comparing the forecasted return with the required return based on the Security Market Line.</li>
	<li>Mispricing presents the opportunity for abnormal return, where abnormal return is the analyst's expected return minus the required return dictated by the Security Market Line.</li>
	<li>The cost of less than full market diversification is reflected by the variance of the residual error of the active securities.</li>

</ul>

<h2>Treynor-Black Process</h2>


<ul>
	<li>Economists create forecasts to derive inputs for the security representing the market portfolio.</li>
	<li>Security analysts isolate the few securities mispriced by the market.</li>
	<li>The portfolio manager constructs the optimal portfolio.</li>
	<li>Post investment period quality analysis can be done by:</li>
		<ul>
			<li>Measuring the correlation squared of the security analyst's forecasted alphas to actual alphas realized.</li>
			<li>A high correlation will give the portfolio manager confidence in the analysts' abilities to correctly identify mispriced securities in the future.</li>
		</ul>
</ul>

<h2>Limitations of Treynor-Black for Investors</h2>


<ul>
	<li>Some investors may prohibit their portfolio managers from short selling, which limits the ability to exploit overpriced assets.</li>
	<li>Treynor-Black relies on successfully forecasting alpha, which is incredibly difficult for even well trained analysts.</li>


</ul>

 

The Treynor-Black Model

<h2>The Portfolio Perspective</h2>

In studying the <a href="https://financetrain.com/mean-variance-analysis-assumptions/" title="Mean-Variance Analysis Assumptions">mean-variance analytical</a> foundation created by Harry Markowitz, candidates have come to see how Modern Portfolio Theory emphasizes whole portfolio over its individual pieces.

The goal of portfolio management is to build a portfolio of assets with an appropriate risk/return profile for the individual investor (who could be a person or an entity, such as a foundation).

<h2>Steps in the Portfolio Management Process</h2>

The following list represents the steps in the portfolio management process.
<ol>
	<li>Planning</li>
		<ul>
			<li>Identify investor Objectives and Constraints.</li>
			<li>Formulate the Investor Policy Statement (IPS).</li>
			<li>Forecast risk and returns for asset classes to derive capital market expectations.</li>
			<li>Use IPS and capital market expectations to create the investor's strategic asset allocation (SAA).</li>
		</ul>
	<li>Execution</li>
		<ul>
			<li>Select securities for portfolio inclusion based on the Planning step.</li>
			<li>Purchase the selected securities.</li>
			<li>Sometimes portfolio managers are temporarily allowed to deviate from the strategic asset allocation based insights related to perceived asset mispricings. These temporary deviations are called Tactical Asset Allocations (TAA).</li>
		</ul>
	<li>Feedback</li>
		<ul>
			<li>Analyze returns through performance measurement.</li>
			<li>Determine the sources of returns through performance attribution.</li>
			<li>Use the results of the portfolio measurement and performance attribution to make a performance appraisal of the portfolio manager. This appraisal determines if the portfolio manager should be retained or fired.</li>
			<li>Over time the portfolio needs to monitor the investor's changes and the capital market expectation changes to rebalance the portfolio as appropriate.</li>
		</ul>


</ol>



Portfolio Management Process

The IPS is the document that governs how an investor’s portfolio is managed.
<ul>
	<li>Designing an IPS is a critical part of the Planning phase of the portfolio management process.</li>
	<li>The IPS will bring together an investor’s objectives and constraints (see below) to create a logical investment strategy.</li>
</ul>

<h2>Investment Objectives</h2>


<ul>
	<li>The investment objectives of an IPS are specific and quantified statements regarding risk and return for the portfolio's investment time horizon.</li>
	<li>Risk Objective</li>
		<ul>
			<li>The Risk Objective is commonly quantified by standard deviation of returns and this value is based on both the investor's willingness and ability to bear risk.</li>
			<li>Even though a client may be very willing to assume risk, he/she may be unable to bear risk.</li>
			<li>Risk factors include: spending needs to be funded by the portfolio, the client's level of wealth, and the client's overall financial situation.</li>
		</ul>
	<li>Return Objective</li>
		<ul>
			<li>A relationship exists between risk and return, so the Return Objective is a realistic goal for returns based on the degree of risk that a client is willing and able to absorb.</li>
			<li>It will be important for a portfolio manager to consider: current spending in relation to long term wealth accumulation needs; the inflation impacts on spending needs; and whether or not the expected return is sufficient based on the client's needs.</li>

		</ul>		
</ul>

<h2>Investment Constraints</h2>


<ul>
	<li>The Investment Constraints of an IPS outline any client specified (internal) or external constraints or considerations for the portfolio.</li>
	<li>The 5 Types of Investment Constraints</li>
		<ol>
			<li>Investment Time Horizon</li>
			<li>Taxes</li>
			<li>Liquidity Needs</li>
			<li>Legal and Regulatory Constraints</li>
			<li>Investor Unique Circumstances</li>
		</ol>


</ul>

<h2>Importance of Capital Market Expectations</h2>

<ul>
	<li>Formulating capital market expectations is a critical component of the Planning Phase.</li>
	<li>The portfolio manager will forecast expected returns and standard deviations for the asset classes and the correlations between asset classes.</li>
	<li>Capital markets expectation data will help inform the strategic asset allocation and will be considered within the context of the objectives and constraints of the portfolio.</li>


</ul>

<h2>Investment Time Horizon</h2>

<ul>
	<li>The time horizon is the period over which the portfolio objectives are to be achieved.</li>
	<li>An investor's time horizon can consist of multiple periods.</li>
	<li>While there are exceptions, a longer time period typically increases the investor's ability to absorb risk.</li>
	<li>Directionally, less than three years could be considered a short time horizon and greater than ten years could be considered a long-term time horizon.</li>


</ul>


The Investor Policy Statement

Portfolio Management

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Portfolio Management

Lessons

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