The** ($FGCKX)** is a subset of the Fidelity Growth Company Fund. The funds invest in larger cap growth stocks, or companies they believe to have superior growth potential to the overall market. It holds virtually no fixed income or cash, and tends to stay away from equities in emerging markets. The fund has achieved relative success, growing at an annual rate of more than 10% for the last 10 years, and achieving roughly 24.33% growth this year. It has a net expense ratio of .77%, average for a fund with such active management, and no minimum investment.

ETF Selection Process: Since the FGCKX invests predominantly in large cap growth companies, long growth ETF’s or ETF’s that tracked growth indices were included in the selection process. ETF’s that varied significantly in their strategy from the stated goal of the Mutual Fund were eliminated. In order for our ETF Portfolio to be more efficient than the Mutual Fund, we need lower expenses, so only ETF’s with an expense ratio lower than .77% were included. They are as follows:

· **($FAD)**: Multi Cap Growth AlphaDEX Fund, .7%

· ** ($FVI)**: Value Line Equity Allocation Index Fund, .7%

· ** ($FVL)**: Value Line 100 ETF, .7%

· ** ($CSD)**: Guggenheim Spin-Off ETF, .6%

· **($NFO)**: Insider Sentiment ETF, .6%

· **($PDP)**: DWA Technical Leaders Portfolio, .6%

· ** ($PIQ)**: Dynamic Magniquant, .6%

· **($PKW)**: Buyback Achievers, .6%

· ** ($PWO)**: Dynamic OTC Portfolio, .6%

· **($PWC)**: Dynamic Market Portfolio, .59%

· ** (ONEQ) **: Nasdaq Composite Index Tracking Stock, .3%

· ** ($IWW)**: iShares Russell 3000 Value ETF, .25%

· ** ($IWZ)**: iShares Russell 3000 Growth ETF, .25%

· ** (NYC) **: iShares NYSE Composite ETF, .25%

· **($IWV)**: iShares Russell 3000 ETF, .21%

· **($IYY)**: iShares Dow Jones U.S. ETF, .20%

· ** (EUSA) **: iShares MSCI United Kingdom ETF, .15%

· ** (VTHR) **: Russell 3000 ETF, .15%

· **($ITOT)**: Core S&P Total U.S. Stock Market ETF, .07%

· ** (VTI) **: Total Stock Market ETF, .05%

· ** (SCHB) **: U.S. Broad Market ETF, .04%

Optimization Process: Markowitz seminal work in the 1950’s changed portfolio selection forever. Pioneering the concept of a risk return relationship, he used mathematics to find to optimal portfolio under a certain set of parameters and restrictions. This portfolio was designed so the fundamental structure was within the mutual funds set of restrictions. The restrictions of the Mutual Fund were only that large cap growth stocks exist in the universe, no asset allocation limitations were present. No short positions were allowed, and the portfolio had to make use of all its cash reserves.

Final Results: The results for this optimization were exceptional. A portfolio with significantly increased return did not always result in significantly more risk.

Graphical Description: The y axis on the graphs represent the return of the portfolio in decimal points(i.e. .21 is 21%, .02 is 2%). Higher is clearly better. The x axis represents the risk of the portfolio in terms of standard deviation. The exact definition of standard deviation is beyond the scope of this article, but what is important to recognize is that higher risk is undesirable. The blue line represents the best possible portfolios. Think of the blue line as a wall, no portfolio without leverage can achieve lower risk or higher returns than the portfolios along the blue line.

Usually the first portfolio demonstrated is one that replicates the performance of the Mutual Fund, however; this is not possible with the output, some closer inspection reveals why. Since the blue line represents the best possible set of feasible portfolios with the selection of ETF’s, and the y axis is the return, the upper right end of the line and the lower left end of the line represent the highest and lowest possible returns one can attain with optimization methods. The lower left corner of the line is still above the return of the Mutual Fund, which you can see in the far right corner (FGCKX). This means that even when creating a portfolio out of the available ETF’s with the absolute minimum amount of risk, you are still achieving a higher return than the Mutual Fund. In addition, if you look at the point towards the bottom, labeled ‘Equally Weighted Portfolio’, you can see the benefits of optimization. The equally weighted portfolio shows the results of investing an equal amount of your assets in each ETF, it has higher risk and significantly lower returns than any of the optimized portfolios on the blue line. By using optimization methods we can reduce risk by roughly 16%, and increase return by more than 45%.

Next we will look at the Portfolio with the maximum Sharpe ratio. The Sharpe Ratio is the amount of return above the risk free rate that an investor receives for taking an additional unit of risk. If you think about it from a visual perspective, if the blue line on the graph is very steep, you are gaining units on the y axis faster than you are gaining units on the x axis. Since the y axis is desirable (return), and the x axis is undesirable (risk), a steeper blue line is desirable. The steepness of the blue line is the Sharpe Ratio.

FGCKX ETF Portfolio with Maximum Sharpe Ratio

Ticker Symbol Weight

**($CSD)** 46.82%

**($PKW)** 53.18%

An initial advantage of this portfolio is its simplicity. With only two assets, you don’t need to worry about transaction costs eating into your profits, and it is easy to follow. The costs of this portfolio are also lower than the Mutual Fund. With expense ratios of .60% for both CSD and PKW, you are saving .12% each year in costs. To put this into prospective, assume you have a portfolio of $100,000.00 that grows at an annual rate of 15% over 10 years. You would save more than $2,500.00 with the ETF portfolio over the Mutual Fund. This is also assuming that the Mutual Fund and the ETF grow at the same pace, which is shown to be untrue according to the optimization process. Expected growth of $100,000.00 over 10 years for the ETF portfolio is $619,822.70 while that same number is only $455,181.00 for the Mutual Fund.

**DISCLOSURE**:
*The views and opinions expressed in this article are those of the authors, and do not represent the views of equities.com. Readers should not consider statements made by the author as formal recommendations and should consult their financial advisor before making any investment decisions. To read our full disclosure, please go to: http://www.equities.com/disclaimer*

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