www.diversifyportfolio.com - Entries for the tag EfficientFrontierhttp://www.diversifyportfolio.com/blog/tags/EfficientFrontier/The last entries tagged with EfficientFrontieren-usZinniaThu, 16 Nov 2017 07:57:09 +0000Efficient Frontier
http://www.diversifyportfolio.com/blog/2017/10/03/efficient-frontier/<p>The concept of an efficient frontier is a cornerstone of modern portfolio theory. It provides an excellent way to not only understand the relationship between the risk, return and correlation within a portfolio but also to visualize this data in an effort to optimize your portfolios performance.</p>
<h3>Portfolio Construction</h3>
<p>
To illustrate how an efficient frontier is created and then used to assist with investment decisions, we will
start with a simple 3 position portfolio. The portfolio consists of the following stocks:
</p>
<table class="table table-condensed table-bordered">
<tbody>
<tr class="info">
<th>Stock</th>
<th>Position Weighting</th>
<th>Expected Return</th>
<th>Risk / Volatility</th>
</tr>
<tr>
<td>$TSLA</td>
<td>34%</td>
<td>54%</td>
<td>34%</td>
</tr>
<tr>
<td>$WDC</td>
<td>45%</td>
<td>40%</td>
<td>31%</td>
</tr>
<tr>
<td>$JPM</td>
<td>21%</td>
<td>39%</td>
<td>17%</td>
</tr>
</tbody>
</table>
<p>
If we create a chart of these 3 stocks with their percentage returns on the y-axis and their volatilities
(ie: standard deviation) on the x-axis, we get the following:
</p>
<img src="/media/uploads/zinnia/2017/10/03/01.png" class="" />
<p>
Next, if we combine these 3 positions into a portfolio and plot the resulting risk and return we get the following:
</p>
<img src="/media/uploads/zinnia/2017/10/03/02.png" class="" />
<p>
The resulting portfolio has an expected return of <b>44%</b>. What is important to understand is that the expected return
is the cumulative total of the weighted returns from each individual position. In other words the weight of each position is
multiplied by the expected return and then summed to get the expected return of the portfolio.
</p>
<p>
Now if we move our focus to the volatility of the portfolio, we see that it is <b>21%</b>. However, if we were to perform the same
calculation that was used to get the expected return of the portfolio, the resulting portfolio volatility would be higher than <b>21%</b>.
The reason for this is that the stocks in this portfolio are not perfectly correlated. The correlations of the stocks are as follows:
</p>
<img src="/media/uploads/zinnia/2017/10/03/03.png" class="" />
<p>
This is the key to creating a diversified portfolio. We are trying to maximize our expected return while minimizing the
volatility for that level of return. To do this we should be looking for stocks that have a low correlation to the rest
of our portfolio. For more information on this concept, please refer to this article:
<a href="/blog/2017/03/23/why-diversify-your-stock-portfolio/" target="_blank">Why diversify your stock portfolio</a>.
</p>
<h3>Portfolio Variations</h3>
<p>
We can see from the above example that both the correlation and position weights played a role in the portfolios risk and
expected return. In the example the position weights used were 34%, 45% and 21%. But what if we used different weights? What if
we created thousands of different portfolios consisting of the same positions but with different weights in an effort to find the
optimal position sizes for the portfolio. This is exactly what the <a href="https://www.portfoliovisualizer.com/efficient-frontier" class="dphiddenlink" target="_blank">efficient frontier</a> does for us.
</p>
<p>
In the below chart, thousands of different portfolios have been created comprising the same 3 positions from above, each with
different position size variations.
</p>
<img src="/media/uploads/zinnia/2017/10/03/04.png" class="" />
<p>
As you can see, a distinct structure has been created in the form of an envelope or parabola around all the possible portfolios.
This means there is a limit to the return that can be achieved for a certain level of risk, and vice-versa.
</p>
<p>
Depending on your portfolio construction you can increase your expected return while maintaining the same risk up to a limit as defined
by the parabola (see green line below). You are also able to decrease your risk while maintaining the same level of expected return,
once again up to a limit as defined by the parabola (see red line below).
</p>
<img src="/media/uploads/zinnia/2017/10/03/05.png" class="" />
<h3>Optimal Portfolio</h3>
<p>
Now that we have defined all the possible portfolios that can be constructed from the above 3 positions, the goal is to select
a portfolio that has the highest possible return for the lowest possible risk for that level of return. The portfolios that
satisfy this constraint are a part of the <a href="http://www.investopedia.com/terms/e/efficientfrontier.asp" class="dphiddenlink" target="_blank">efficient frontier</a>. These are the portfolios that fall along the upper limit of the parabola.
</p>
<p>
In the below chart we have removed all the portfolios that are below the efficient frontier. The result is a chart of our original
3 positions along with the portfolio of those positions and an efficient frontier depicting the universe of optimal portfolios.
</p>
<img src="/media/uploads/zinnia/2017/10/03/06.png" class="" />
<p>
As we can see, our current portfolio is below the efficient frontier which means it is not the optimal portfolio available to us
for that level of risk. Depending on how we adjust our position sizes within the portfolio, it will be possible to increase the
expected return of the portfolio while maintaining the same level of risk.
</p>
<p>
The goal is to have the portfolio sitting on the efficient frontier.
</p>
<h3>Global Minimum Variance Portfolio</h3>
<p>
One last concept to be aware of is what is known as the <b>global minimum variance portfolio</b>. This is the portfolio with the
minimum possible risk / volatility out of all the possible portfolio combinations. This portfolio is always found at the
left most point of the efficient frontier.
</p>
<img src="/media/uploads/zinnia/2017/10/03/07.png" class="" />
<h3>Summary</h3>
<p>
The efficient frontier is a concept from modern portfolio theory which allows us to determine all the possible portfolio variations
from a group of stocks. From that universe of possible portfolios we can extract the optimal portfolios based on achieving the
highest levels of expected return for each level of risk.
</p>
<p>
The above example was kept simple to illustrate the concept with a small portfolio of 3 positions. As you increase the number of
positions in your portfolio, the number of portfolio variations increases dramatically which makes efficient frontier analysis
exceptionally powerful.
</p>
<p>
By inserting your portfolio into an efficient frontier chart, you are able to see where your portfolio sits relative to the universe
of optimal portfolios. You are then able to adjust your portfolio and positions in an effort to get as close to the efficient frontier
as possible.
</p>
<p>
To determine where your portfolio sits relative to the efficient frontier you can use the
<a href="/stock-portfolio-analyzer/" target="_blank">Stock Portfolio Analyzer</a> tool. As you adjust the positions in your portfolio as
well as their relative weightings, you will see how the correlation, diversification and risk vs return of your positions impacts your
portfolios performance.
</p>
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brendon@diversifyportfolio.com (DiversifyPortfolio)Tue, 03 Oct 2017 07:32:36 +0000http://www.diversifyportfolio.com/blog/2017/10/03/efficient-frontier/Analysis ToolsEducationEfficient Frontier Announcement
http://www.diversifyportfolio.com/blog/2017/05/11/efficient-frontier-announcement/<p>Diversify Portfolio is pleased to announce the release of a new addition to our analysis platform - the Efficient Frontier. The Efficient Frontier is a concept from modern portfolio theory which can aid traders and investors optimize their portfolio.</p>
<p>
Our Efficient Frontier tool generates a chart of the portfolios that fall on the efficient frontier in terms of risk and expected return data. Your portfolio along with all of your individual positions is then inserted into the chart to illustrate where your portfolio performs in terms of the efficient frontier.
</p>
<p>
The portfolios and resulting Efficient Frontier chart which is generated tends to exhibit specific patterns and is impacted highly by the correlation of the constituent stocks. As a result, incorporating Efficient Frontier analysis is an excellent addition to the existing tools offered by Diversify Portfolio which focus on correlation, asset allocation and efficient portfolio construction.
</p>
<p>
Whether you're a short term trader or long term investor, knowing how the positions in your portfolio relate to each other is critical in determining optimal asset allocations. The following article discusses a few principles around correlation, allocation and portfolio diversification:
</p>
<ul>
<li>
<a href="/blog/2017/03/23/why-diversify-your-stock-portfolio/" title="Diversify your stock
portfolio">Why Diversify your Stock Portfolio</a>
</li>
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<p>
The Efficient Frontier provides a way to put the principles discussed in the above article into practice by analyzing the effect of differing correlations on stock portfolio performance. When the insight gained from the Efficient Frontier is combined with the existing <a href="/asset-allocation/" title="Asset Allocation">Allocation Tool</a>, you gain an incredible level of insight into optimal allocation for your stock portfolio.
</p>
<p>
We have several strategy and educational articles planned for the coming weeks which will show how Efficient Frontier, Modern Portfolio Theory and Correlation analysis can be tied together to create better performing, lower risk portfolios. These articles will be published on our blog and free mailing list which you can <a href="#" data-toggle="modal" data-target="#newsletterModal">subscribe to here</a>.
</p>
<p>
In addition to articles specific to the new Efficient Frontier tool, the mailing list gives you access to general strategy, education and stock market analysis articles which will benefit you even if you do not use any of our tools.
</p>
<p>
The get access to the Efficient Frontier and all our other tools focused on correlation, diversification and efficient portfolio construction - <a href="/member/register/" title="Free Trial">Sign up for a Free Trial</a>
</p>
<p>If you're new to the concept of an Efficient Frontier, <a href="http://www.investinganswers.com/financial-dictionary/investing/efficient-frontier-1010" target="_blank">this article</a> provides a good overview</p>
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brendon@diversifyportfolio.com (DiversifyPortfolio)Thu, 11 May 2017 15:31:05 +0000http://www.diversifyportfolio.com/blog/2017/05/11/efficient-frontier-announcement/Analysis ToolsAnnouncements