On page 76 of Mebane T. Faber and Eric W. Richardson's book, *The Ivy Portfolio,* the authors lay out a sample portfolio made up of 20 ETFs. Five percent of the portfolio is assigned to each ETF as shown in the following analysis using Geoff Considine's Quantext Portfolio Planner (QPP).

**Ivy 20 Analysis:** In the following analysis, fifty-seven months of data is used as that is the maximum time EWX has been operational. The second critical assumption is the 7% annualized projected growth for the S&P 500.

The projected return for the Ivy 20, with the above assumptions, is 8.3% with a rather high projected standard deviation of 16.1%. The Diversification Metric (DM) at 23% is well below our goal of 40%. One would think the portfolio would be well diversified since each ETF holds a percentage (5%) of the entire portfolio.

Looking at the historical data, we see this portfolio slightly outperformed the S&P 500 over the 57-month period at slightly lower risk. What happens if we remove all percentage constraints?

**QPP Analysis With Zero Constraints:** In the following analysis, all constraints are removed. The optimizer was set to seek only maximum return. The following output is classical optimization run wild when all restraints are removed. All money is invested in one ETF, VNQ, domestic REITs. It is unlikely anyone would construct a portfolio using only VNQ.

The projected return is nearly 12%, but it comes with a high volatility of 26%. That is nearly double the goal of holding the projected standard deviation to 15% or below. DM is 0% as one might expect. This portfolio lacks diversification.

**Optimized Portfolio with Constraints:** The following analysis of the Ivy 20 portfolio involves reasonable constrants Five constraints are placed on the Ivy 20. 1) No ETF may exceed 12% of the total portfolio. 2) The sum of all allocations must equal 100%. 3) The projected standard deviation will come in at 15% or lower. 4) The projected Return/Risk ratio will reach 0.60 (60%) or higher. 5) The Diversification Metric will be 40% or higher.

Not shown in the following screen-shot are the historical performance results. The constrained Ivy 20 portfolio returned 2.4% over the 57-month period with a standard deviation of 15.3%. Over the same period the S&P 500 returned an annualized 3.5% with a standard deviation of 19.3%. The broad market had yet to hit bottom during the last severe recession and this accounts for the low return percentages.

Column B shows the percentages allocated to each ETF when the above constraints are applied. Screening again for maximum return, the projected return is 8.1% with a projected standard deviation (Risk) of 13.6%. The Return/Risk ratio is 0.60 as required and DM is 41%. Using the basic 20 ETFs advocated by Faber and Richardson, it is possible to come up with a projected return that exceeds what is projected for the S&P 500 by 100 basis points.

**Disclosure: **I am long VTI, VEU, VWO, BND, TIP, BWX, VNQ, RWX. 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.