**Description of the Mutual Fund:** FFNOX, or the Fidelity Four in One Fund is a mid-risk mutual fund of funds that makes use of both equities and fixed income for its instruments. Since it’s defined as an aggressive allocation fund, it traditionally invests in an adjusting 80, 20 split between equity and fixed income respectively. It has initial investment requirements of $2,500.00 and a minimum investment balance of $2,000.00. This means that if the investment loses more than $500.00, assuming you put in the minimum, you would need to begin adding more money to the account. The fund has an expense ratio of .24% and no back end or front loaded fees. As a fund of funds, it invests in four other Fidelity mutual funds.

ETF Selection Process: The process for selecting ETF’s that would mirror the Fidelity Four in One Fund was relatively simple. Since the fund primarily invests in Large Cap Developed Market Equities, the initial inputs for the equity section were with their expense ratios were;

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

· ** IWB:** iShares Russell 1000 ETF, .15%

· ** IWL: ** iShares Russell Top 200 ETF, .15%

· **VEA: ** Europe Pacific, .12%

· **MGC: ** Mega Cap 300 ETF, .12%

· **SCHF: ** International Equity ETF, .09%

· **SPY:** SPDR S&P 500, .09%

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

· ** IVV:** Core S&P 500 ETF, .07%

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

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

· **SCHX:** U.S. Large-Cap ETF, .04%

The other part of the mutual fund is made up from fixed income, so the fixed income ETF inputs and their expense ratios were:

· **LAG:** SPDR Barclays Aggregate Bond ETF, .17%

· **BIV:** Intermediate-Term Bond ETF, .11%

· **BLV:** Long-Term Bond ETF, .11%

· **BND:** Total Bond Market ETF, .10%

· **AGG:** Core Total U.S. Bond Market ETF, .08%

The most important parameter for ETF selection was the expense ratio and composition of the ETF. While the overarching categories were always correct, some ETF’s were eliminated immediately due to their fundamental make up (i.e. an ETF that shorts the market or takes advantage of a specific sector). Moreover, if the ETF had an expense ratio that was above the mutual fund, it was eliminated.

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 an 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. Equities are limited to 80% of the portfolio, the total amount of the portfolio must equal 100% of available assets, and all asset weights must be positive. This creates a portfolio with no cash holdings, a hard line at an 80-20 equity fixed income split and no short positions.

Final Results: Depending on the preferences of the investor, three portfolios are given as output here. The first is effectively a mirrored return portfolio of the mutual fund.

Portfolio with Replicated FFNOX Performance Weight

IWL 57.39%

BLV 42.61%

The graph given above is referred to as an efficient frontier. In the y axis is the annualized return of the portfolio while the x axis is the annualized standard deviation (risk). The blue line is the selection of portfolios that maximize return for each given risk level. Think of the blue line as a wall, no portfolio without leverage can be better than the blue line given the restrictions. In the top right corner we have the mutual fund, FFNOX. Its return is excellent, but you can see that the risk level is unacceptably high. Moving to the left we have a portfolio that is made up from equally weighting all the ETF’s. While this is an improvement over the mutual fund, it is overly complicated (buying and watching 19 ETF’s is certainly not simple), and can be improved significantly. Lastly, the green dot on the blue line is the portfolio with mirrored performance to the mutual fund that has less than half the risk. This comes from the diversification element gained from increased assets and the benefits of quantitative equity portfolio management (QEPM). Lastly, and perhaps most significant, is a massive decrease in expenses. The mutual fund (a cheap one relative to the industry), will cost roughly .24% of your assets each year. Assuming a $100,000.00 portfolio that grows at an annual rate of 5%, this comes out to a total expense of $3018.70. With the ETF Portfolio we have a weighted annual expense of .133%, roughly half the expense ratio of the mutual fund. Assuming the same $100,000.00 portfolio growing at 5%, your total expense is now $1672.31.

The second portfolio given is the maximum Sharpe ratio allocation. The Sharpe ratio is the return above the risk free rate divided by the risk. What it effectively shows is the portfolio that maximizes the units of return given for each unit of risk taken.

Portfolio with Maximum Sharpe Ratio Weight

LAG 41%

IWL 39.10%

BLV 19.90%

It is immediately evident that the portfolio has a lower expected return, but significantly reduced risk as well. This portfolio is for more risk adverse investors, its benefit is in the increase diversification, and overall protection against market downturn. The weighted expense is .15%, and the ten year total expense assuming the same $100,000.00 portfolio growing at 5% is $1,889.70, $1128.99 better than the mutual fund.

The third portfolio has a targeted return above that of the mutual fund, namely performance of 12% annualized.

Portfolio with 12% Target Return Weight

EUSA 25.86%

IWL 54.14%

BLV 20%

The advantages of a portfolio like this are extremely visible. The risk, return and risk/return tradeoff are all significantly better than the mutual fund. The weighted annual expense for this portfolio is .142%, and the total expense for a $100,000.00 portfolio growing at a 5% annual rate is $1,786.06, $1232.63 better than the mutual fund. This portfolio will offer increased diversification and less risk over the mutual fund, while performing better in strong market times simultaneously.

Conclusion: Through optimization processes and disciplined ETF selection we have two portfolios with significantly less expenses, better diversification, and a range of returns that can be customized. Each of these portfolios only need to be readjusted when the equity portion breaks the 80% mark, an unlikely scenario for at least a year or two. So we have increase simplicity, decreased risk, a better tradeoff between risk and return, and decreased expenses.

**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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