In a previous post, I questioned how diversified a portfolio of just three assets could really be. This wasn’t really fair, since the whole point was to avoid such an analysis. To provide a fairer test, I will use 15 assets for this analysis, all of which are choices taken from an actual retirement plan. The 15 securities listed here consist of 14 mutual funds and a stock. Choices are predominately focused on US equities, though is a REIT fund (FARCX), two international funds (RERGX, VTRIX), a bond fund (PPTRX), and a money market account. Given this expanded universe of choices, what will theory tell us is best?

I used Matlab and it’s financial toolbox to retrieve four years of monthly prices for each of the funds. Since one of the funds is a target date fund, data was not available for it before then. The data was provided free of charge by Yahoo Finance. These prices where used to calculate monthly returns, which were in turn used to get means and covariance of the assets. Once this was done, Matlab’s financial toolbox was used to find the optimal weights. If you really want to get in to the details of such a calculation, this book explains it well, but be warned: linear algebra and calculus is required, so in practice, this problem is best left for software. Below is a screen capture of the results, as well as a graph of the efficient frontier.

The results of the analysis show that fewer assets are better, but raise a few questions as well. Efficient portfolios generally consist of 3 assets. This seems to support the idea that a few assets will do. Yet while these portfolios are efficient with respect the risk reward trade off, they take no account for where the return comes from. In this case, the funds are for the most part positively correlated over the time period, so funds that would provide diversification are ignored for the higher yielding choices. This points to the period being too short, or more importantly, the number of choices is too small. The needed number of assets to consider may be close to 100! This seems to indicate that for retirement planning, MPT may be a nice theory, but it’s real value is as a lesson about the value of diversification.

But what’s this say for our choices? There is no substitute for true diversification. Getting exposure to assets that are uncorrelated is key. Considering the 15-asset universe, almost every portfolio on the efficient frontier consisted of 3 assets, but a truly diversified portfolio consisting of the choices offered may be better off with a couple more funds. In this case, examining the top holdings of the funds would provide as much insight as this analysis did!