Using the Efficient Frontier Tool

InvestorCraft's Efficient Frontier tool is a powerful portfolio optimizer that is based on key concepts of modern portfolio theory.  Professor Harry Markowitz, a nobel-prize winning economist, introduced the concept of the Efficient Frontier.  This tool analyzes trade-offs between risk and expected return of various portfolios composed of various asset weightings.   Changing asset weightings will change both the expected return and expected risk (measured by standard deviation) of the portfolio.  The Efficient Frontier tool analyzes all possible portfolio combinations (by varying asset weights) and finds the ones that offer the best expected return for a given level of risk. It plots these portfolios on a curve called the Efficient Frontier.  The Efficient Frontier curve corresponds to the most efficient investment strategies.  Any given portfolio on the Efficient Frontier is said to dominate all other possible portfolios that have either the same level of expected return or standard deviation.  All results are based on analysis of historical prices of each security in the portfolio. 

After plotting the Efficient Frontier curve, the tool then determines an optimal portfolio.  It does this by selecting the portfolio that falls at the point of tangency with the straight line starting at the risk-free rate of return on the y-axis.  This line, sometimes called the capital market line, assumes that the investor will either invest in cash (at the risk-free interest rate) or a portfolio on the efficient curve.  The point of tangency maximizes the slope of the capital market line, which is given by the equation:

                    Slope = (Return – RiskFreeRate)/ (StandardDeviation)

This slope is also known as the Sharpe Ratio, which is a ratio of reward to risk.  The higher the Sharpe Ratio, the better.  The Efficient Frontier tool finds the point on the efficient frontier that maximizes the Sharpe Ratio. 

To use the Efficient Frontier Tool to analyze your portfolio, perform the following steps:

• Select the Efficient Frontier tool.
• Add your securities to the list of portfolios, either by selecting the security in the asset selection tree, or by using the search feature.  Select the “Add” button or “Remove” button to add or remove each security from the list.
• Once you have added the securities, select the “Next” button.  
• Select the time range to analyze historical data for the analysis.  It is important to select a time range long enough to provide a good representation of stock price movements under different market conditions (up and down).  All results provided the tool are based on price behaviors of this time period.
• Enter the risk-free interest rate.  This is the rate it which you could invest your cash with no risk.  The 10-year treasure rate is often used here.
• If you want to specify an allowed weight for any single security in the portfolio, you can enter a minimum and maximum.  These are optional, but if you specify them, the tool will adjust its calculated theoretical optimal portfolio (which may have asset weights outside your desired range) to fit within your specified limits.  The resulting portfolio will be reported as the Adjusted Portfolio.
• Select the “Calculate” button.
• At this point, the tool will calculate the efficient frontier curve and the Optimal Portfolio and Adjusted Portfolio (if you specified minimum/maximum weights).  The results are reported in several tables and graphs as follows: 

The Portfolio Details table shows each asset in the portfolio and its characteristics, including:

·       Expected return – the expected annual return based on the asset’s mean return over the time period analyzed.

·       Standard deviation – the standard deviation of the asset over the time period.

·       Optimal Weight – the calculated weight of the security to achieve the optimal point of tangency on the efficient frontier.  Optimal weights can be negative, indicating short selling.

·       Adjusted Weight – the calculated weight of the security that adjusts the optimal weight to fit within the allowable range specified by you.

·       Minimum Variance Weight – the calculated weight of the security that results in the minimal standard deviation for the overall portfolio.

The composition of three different portfolios is shown: Optimal, Adjusted and Minimum Variance.  The overall characteristics of each portfolio are shown in the next table:

Metrics for Above Portfolio Mixes

Name	Annual Return (Er)	Annual Standard Deviation (StDev)	Sharpe Ratio	Er/StDev Ratio
Optimal Portfolio	22.4 %	10.6 %	1.716	2.101
Adjusted Portfolio	20.4 %	9.8 %	1.668	2.087
Minimum Variance Portfolio	17.2 %	9.1 %	1.439	1.889

Time period:	3 years	Single asset Maximum weight:	60.0 %
Risk free rate:	4.10 %	Single asset Minimum weight:	1.0 %

This table shows the expected overall annual return and standard deviation for each of the three portfolios.  Note that the optimal portfolio will always have the maximum Sharpe Ratio.  Also, note that the minimal variance portfolio is expected to have the minimum standard deviation, but without regard to return.  The ratio of expected return (Er) to standard deviation (StDev) is shown as a reference point. It is similar to the Sharpe Ratio, but does not take into account the offset of the return exceeding the risk-free rate.    

The graph shows the efficient frontier curve (in blue), which is all portfolios that dominate others at any given level of return or standard deviation.  It shows the location of the optimal portfolio at the point of tangency on the efficient frontier with the line that intersects the y-axis at the risk-free rate (in green).  It also shows the point for the adjusted portfolio, which is always somewhat less "efficient" (since it is constrained by your allowed minimum and maximum weights). The minimum variance portfolio is located at the apex of the curve (left-most point).

 

For your reference, the tables of correlation factors for all assets is also shown.  This is useful reference information as you study the data. 

It is important to study and understand the tables and graph.  Some key points to look for:

• Study the optimal portfolio numbers in the first two tables.  It will show you the recommended weighting of each asset in your portfolio to achieve a theoretical optimum ratio of reward-to-risk.  It is theoretical since it is based on past history, which is unlikely to exactly repeat itself.   But it is a good starting point.  Often, the optimal portfolio will have extreme weights that involve short selling.
• Study the adjusted portfolio numbers if you specified minimum/maximum allowed weights.  It will usually be much more practical, since confines the asset weightings to your specified range for each asset.  However, realize it is not as efficient (in theory) as the optimal portfolio.    The overall return will be less than the optimal portfolio, and the Sharpe ratio will not be quite as good.
• Study the minimum variance portfolio also.  It is the portfolio that provides the absolute minimum variance, without regard to return.  So you can look at it as the lowest risk portfolio.  Note how it has the lowest standard deviation, which is a measure of volatility. 

At this point, you may want to make adjustments to the portfolio by going back to the first page of the Efficient Frontier and removing or adding assets to see how they contribute to better diversifying the portfolio.  You can experiment with a virtually unlimited variety of portfolios.

Finally, be aware that all results of the Efficient Frontier tool are based on past price history behavior of each security, and that past history is often not an indicator of future behavior.  Market conditions can change, as can managers of mutual funds and companies.  This is why it is important to select a time period for analysis that you feel will be a good representation or model for the future.  It is also why it is essential that you carefully research each individual security on its own merits to understand its prospects for the future. 

Once you are done building and analyzing the portfolio, you can choose to save it if you wish.  To do this, select the “Save portfolio” button.  If you are not already logged-in, you will be prompted to log-in so that the portfolio can be associated with your user-name.  You can later reference this portfolio in My Portfoliois, and track its performance and perform further analysis on it in the future.