## Efficient Frontier

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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.

### Portfolio Construction

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:

Stock Position Weighting Expected Return Risk / Volatility
\$TSLA 34% 54% 34%
\$WDC 45% 40% 31%
\$JPM 21% 39% 17%

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: Next, if we combine these 3 positions into a portfolio and plot the resulting risk and return we get the following: The resulting portfolio has an expected return of 44%. 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.

Now if we move our focus to the volatility of the portfolio, we see that it is 21%. 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 21%. The reason for this is that the stocks in this portfolio are not perfectly correlated. The correlations of the stocks are as follows: 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: Why diversify your stock portfolio.

### Portfolio Variations

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 efficient frontier does for us.

In the below chart, thousands of different portfolios have been created comprising the same 3 positions from above, each with different position size variations. 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.

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). ### Optimal Portfolio

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 efficient frontier. These are the portfolios that fall along the upper limit of the parabola.

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. 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.

The goal is to have the portfolio sitting on the efficient frontier.

### Global Minimum Variance Portfolio

One last concept to be aware of is what is known as the global minimum variance portfolio. 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. ### Summary

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.

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.

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.

To determine where your portfolio sits relative to the efficient frontier you can use the Stock Portfolio Analyzer 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.

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