There is a questionnaire on wealthfront.com that leads to a portfolio allocation across six or seven Vanguard ETFs depending on a "risk tolerance" parameter. I wondered what the returns of such a portfolio really look like. Although wealthfront's page does allow you to look at the resultant portfolio in some detail.

The ETFs that form the portfolio are: VTI, VEA, VWO, VIG, XLE, SCHP, MUB.

You can even take a look at some of the information Vanguard provides to advisors: VTI, VEA, VWO, VIG.

The other ETFs are described in more detail at: XLE, SCHP, MUB

The ETFs have low expense ratios, ranging from 0.07% to 0.25% annually.

What do the return indices of the instruments look like? Below are plotted the monthly time series for the ETFs starting from the last day of August, 2010. The data is the return index value which is a true return that the investor receives, adjusted for splits and dividends. The value can be retrieved through most common subscription based market data provider platforms such as Bloomberg or Reuters Eikon.

Summary statistics for the ETFs are shown here:

The portfolio weights to calculate the portfolio returns are shown in the following table. To calculate the "optimal" portfolio weight, I used Excel's Solver tool. I set the target cell to be the sharpe ratio of the portfolio. By changing the weights and limiting them to be bigger than zero and the sum to be equal to one, it arrived at the solution that forty percent should be allocated to VTI and sixty percent to MUB. Which is actually quite interesting, and does yield a higher sharpe ratio than the other arbitrary portfolios by wealthfront.com.

The portfolio returns can also be plotted, with the S&P 500 Total Return Index included as a comparison for the portfolio returns. The optimal portfolio benefits from having a low standard deviation and ok returns compared to the other proposed portfolio weightings. However, from the chart it is painfully obvious that it is always better to invest in the index directly.

The questionnaire mentioned above tries to come up with a risk tolerance measure. However, it is not clear how this translates into the portfolio weightings except by arbitrary rules of thumb. It would always be better for a risk averse investor to put less money into the stock market, but everything that he puts should go into the market index.

From the summary statistics for the portfolio returns below it is quite clear that you can optimally recreate similar return characteristics with just two instruments instead of seven. This is very good considering the costs of trading and other transaction costs. The other instruments do not add anything significant to the return dynamics that cannot be spanned by just VTI and MUB.