Gauss Portfolio: Reducing Risk Using Modified 'Ivy Portfolio' Model

by: Lowell Herr

Motivated by the writing of Faber and Richardson in their book, The Ivy Portfolio, I launched the Gauss Portfolio on 12/27/2011 as a test portfolio to see if the Ivy risk reduction model would work. Below is the asset allocation plan, a Quantext Portfolio Planning (QPP) analysis of this portfolio, a correlation matrix, and future projections ("Delta Factor") as to which investments have a high probability of doing well over the next six to twelve months. First, the Dashboard or Strategic Asset Allocation plan is displayed in the first slide.

Fourteen asset classes, including cash, are used to populate the Gauss Portfolio. The assets are skewed toward value and it has a strong international flavor with 40% of the assets targeted abroad. Currently, small-cap value is above target (red background) and this is due to holding two "Piotroski" stocks, CRA International (NASDAQ:CRAI) and P&F Industries (NASDAQ:PFIN). More on this later.

The portfolio is aggressive as only 9% is allocated to bond and treasury holdings. BND, TLT, TIP, and JNK are the ETFs used to fill the Bond and Income asset class. The target percentages have the white background and the light green indicates the actual percentages currently held in the Gauss.

The following Quantext Portfolio Planning analysis lays out future projections for this array of assets. While this portfolio currently does not hold any growth ETFs, open positions for VUG, VOT, and VBK are included should growth eventually be added to the current 12 asset classes.

The following analysis assumes the S&P 500 will grow at 7.0% annually. Due to the aggressive allocation plan, the Gauss is projected to grow at 9.5% or 2.5% above the S&P 500. We pay for that growth rate as the projected standard deviation is 17.5%. This is higher than one might prefer, but the volatility can be tamed by using the ITA Risk Reduction model, a slight variation from the timing model suggested by Faber and Richardson.

The Diversification Metric (DM) exceeds our basic goal of 40%. One of the reasons for holding individual stocks is to beef up DM and one way to do that is to include Piotroski style stocks.

When the Gauss comes up for review, and I do this every 32 days, I screen for Piotroski stocks. If any stock meets all nine criteria, it is carefully analyzed to see if it is a good fit for the portfolio. So long as the stock maintains a Piotroski High F-score of seven or higher, it stays in the portfolio. For example, CRAI currently has a score of nine while PFIN is below seven. Therefore, PFIN will be sold.

Correlation Matrix: The following matrix is a guide to finding investments that have low to moderate correlations with each other. A quick glance shows that most of the equity ETFs are highly correlated. Even the international ETFs are highly correlated with VTI, the U.S. Equity holding. Piotroski High F-score stocks tend to be lower in correlation and that is one reason for including them in this portfolio.

Delta Factor: The "Delta Factor" is a modeling system that shows the probability of an investment doing well or poorly over the next six to twelve months. In the following table, CRAI, one of the Piotroski stocks has the highest probability of doing well.

Due to the decline in Europe, it comes as no surprise that international ETFs such as VWO, VEA, VEU, and RWX are projected to do well, as this model relies on investments returning to the mean. The Delta Factor is built around this principle.

How has the Gauss performed with respect to a benchmark over the past eleven months? Since employing the ITA Risk Reduction model, the Gauss improved by 48.1% annually. I consider this an outlier, since the starting point Internal Rate of Return value was exaggerated due to the very short time frame. Over the past six months the Gauss improved on the benchmark by a more modest 3.6%.

The Gauss is not the only portfolio I am using as a test of the modified Faber - Richardson risk reduction model. I selected four more portfolios to see if the model would bring about gains when compared to one of the benchmarks, Vanguard's Total Stock Market Index fund, the VTSMX. Of the five portfolios (including Gauss) in this test experiment, four have shown improvement when measured against the VTSMX. While the testing period is short, and there are other factors to consider, it appears as if the modified Faber-Richardson risk reduction model is adding value.

Disclosure: I am long VTI, TLT, TIP, VNQ, VO, VB, VOE, VTV, RWX, DBC, PFIN, CRAI, PCY, VEA. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: This is a real operating portfolio tracked using the TLH Spreadsheet.