### GCRTX ETF Portfolio Optimization with Omega Hedge Fund Optimization Techniques

Today we are going to cover one of my favorite new forays into ETF investments, the Hedge Fund ETF. First, a brief refresher: Hedge Funds are investment companies that are unregulated, and that traditionally attempt to maximize geometric (or total) returns as opposed to arithmetic relative mean returns. For example, a Mutual Fund will have a return mandate that requires them to attempt to beat an investment index, such as the S&P 500, by some number of basis points. A Hedge Fund on the other hand will mandate a yearly positive return of some basis points regardless of what the market is doing. In a perfect world this creates a situation where Hedge Funds can effectively ‘hedge’ your exposure to the overall market by offering a positive return in bad times or good. Hedge Funds gain these uncorrelated returns using a variety of different strategies that are complex, and require equally complex and exotic financial instruments.

The problem however, is that the law says you must be an ‘accredited investor’ in order to invest in Hedge Funds. This requires a yearly income of $200,000.00+ (joint $300,000.00+) and a net worth upwards of $1,000,000.00. Hedge Funds therefore are not accessible to all investors, and remain an underutilized and misunderstood asset class.

In recent years, Mutual Funds have attempted to synthetically recreate absolute returns that are akin to those of Hedge Funds. Their level of success, however, has been varied and inconsistent. In addition, their expense ratios are extremely high.

The best example so far of a Hedge Fund Mutual Funds is the GCRTX, or Goldman Sachs Absolute Return Tracker C. It has an extraordinary expense ratio of 2.35%, and has total five-year growth of about 11.28%.

To synthetically create a hopefully superior instrument, we will be using a variety of ETFs with cheaper expense ratios and similar mandates. They are as follows:

· ** (QEH) **: QAM Equity Hedge Fund ETF, 1.64%

· ** (ALFA) **: AlphaClone Alternative Alpha ETF, .95%

· **($HDG)**: Hedge Replication ETF, .95%

· **($WDTI)**: Managed Futures Strategy Fund, .95%

· **($MCRO)**: IQ Hedge Macro Tracker ETF, .75%

· **($MNA)**: IQ Merger Arbitrage ETF, .75%

· **($QAI)**: IQ Hedge Multi-Strategy Tracker ETF, .75%

· ** (RLY) **: SPDR Multi-Asset Real Return ETF, .70%

· **($RRF)**: Global Real Return Fund, .60%

· ** (CSMA) **: Merger Arbitrage Liquid Index, .55%

· ** (CSMB) **: 2x Monthly Leveraged Credit Suisse Merger Arbitrage Liquid Index ETN, .55%

· **($CPI)**: IQ Real Return ETF, .48%

· ** (CSLS) **: Long/Short Liquid Index (Net) ETN, .45%

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**Optimization Process:**

Since we are attempting to optimize a Hedge Fund based Mutual Fund, we are going to attack it from a Hedge Fund methodology.

Previously the concept of non-normal returns and asymmetrical payoffs has been discussed, for a more detailed description see our article on Conditional Value at Risk (link here). Hedge Funds engage in complex financial practices, and so as a result cannot always rely on the normal distribution of returns that we use for Mean-Variance Optimization.

The Omega Ratio is something that has almost become synonymous with Hedge Fund quantitative techniques, and understanding it is actually quite simple.

Above is a picture of the standard normal distribution we use so often in quantitative equity portfolio management (QEPM). It is at its core a probability distribution, with the points with a higher portion of the curve having a larger probability of occurring, and vice versa for the opposite. On the bottom is a cumulative probability scale, making it easy to see that the total area underneath the standardized curve is 100%. What the Omega Ratio does is take the ratio of returns that are above a threshold, and divide it by the returns below the threshold.

The image above should provide an easy visual representation of this. The threshold in this case is 7%, or .07, and the Omega Ratio is going to be below 1 because the area of the curve beyond the threshold is smaller than the area of the curve less than the threshold.

Since we have this handy ratio that is immune to non normal and asymmetrical distributions, we can now use computer models to find the correct combination of assets that maximizes this metric.

We begin by setting the threshold of returns that we deem acceptable. This number is important because the optimization program will then look for the optimal portfolio that exceeds this level most often.

Since the Portfolio of securities we are working with are based on absolute returns, we will set the threshold level at 0. So now effectively we are looking for the mixture of security allocations that will yield a portfolio with a maximum density of returns on the absolute positive side. Running the process gives us the results below.

The output above is a little different than what we are used to with the efficient frontiers, but since our Omega ratio defines a risk parameter differently, this is more appropriate. Above is the kernel smoothed distribution of returns of both GCRTX (Red) and the Omega optimized portfolio (Green). The x axis is a measure of the daily returns in percentage form, while the y axis is how many times that return occurred, or the density of the distribution at that point. The results here are not as intuitive as the efficient frontier output, but zooming in on the graph gives us a better idea of the benefits.

The two images above are the zoomed in portions of the graph at the peak and towards the right tale. The first picture shows the main results we are looking for, which is the slight shift in the peak of the distribution towards positive returns as opposed to the Mutual Fund. The advantage here being that more of our distributions are going to lie in the absolute return area. The second image shows more of the same. The green line protrudes further out than the red line, showing that again our density of positive returns is greater for the Omega portfolio.

The results for this procedure were actually quite good. Comparability of Omega portfolios with Mean-Variance portfolios is difficult to quantify, so we are not going to attempt it. Sometimes an efficient frontier with an inverse Omega Ratio as the proxy for risk can be created, but it does not always paint a complete picture.

The Omega ratio can be a powerful tool for dealing with non normal assets and returns. Simpler than many quantitative metrics, it eliminate some of the more unrealistic normality assumptions we have to make, and provides a good estimation of optimization processes. There is a reason it is so popular amongst many Hedge Funds. For interested investors, the output of the Omega Optimization is listed below.

· ** (QEH) **: QAM Equity Hedge Fund ETF, 1.64% (10% Allocation)

· ** (ALFA) **: AlphaClone Alternative Alpha ETF, .95% (13% Allocation)

· **($HDG)**: Hedge Replication ETF, .95% (8% Allocation)

· **($WDTI)**: Managed Futures Strategy Fund, .95% (6% Allocation)

· **($MCRO)**: IQ Hedge Macro Tracker ETF, .75% (5% Allocation

· **($MNA)**: IQ Merger Arbitrage ETF, .75% (8% Allocation)

· **($QAI)**: IQ Hedge Multi-Strategy Tracker ETF, .75% (8% Allocation)

· ** (RLY) **: SPDR Multi-Asset Real Return ETF, .70% (5% Allocation)

· **($RRF)**: Global Real Return Fund, .60% (4% Allocation)

· ** (CSMA) **: Merger Arbitrage Liquid Index, .55% (10% Allocation)

· ** (CSMB) **: 2x Monthly Leveraged Credit Suisse Merger Arbitrage Liquid Index ETN, .55% (11% Allocation

· **($CPI)**: IQ Real Return ETF, .48% (6% Allocation)

· ** (CSLS) **: Long/Short Liquid Index (Net) ETN, .45% (7% Allocation)

For the more commission conscious investor, a simple elimination of the asset allocations under 10% will solve your problem, but if you are working with a large portfolio and want to get as much of the Omega advantage as possible, a full allocation is recommended. Once again we have significant cost savings in the form of lower expense ratios. Our Mutual Fund has an expense ratio of 2.35%, while the weighted expense ratio of the ETF portfolio is .805%, a huge yearly savings.

**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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