Minimum Variance Portfolios

I am interested in the cross-section of stock returns, why some companies with particular characteristics outperform others. According to the conventional Capital Asset Pricing Model, stock returns have a linear relationship with market risk. The model predicts that companies with high sensitivities (Beta) to the market will tend to outperform the market in the future. In practice, many of the greatest long-term investors choose stocks (whether they know it or not) that fluctuate less than the average stock (and have a lower Beta).

Falkenstein Financial Data’s blog, Falkenblog, describes a possible arbitrage of going long stocks with small Betas and shorting stocks with big Betas. The aim is to profit if CAPM is wrong. Since many of the stocks in their universe are small that would be difficult to short, they came up with an alternative on their website. It is called a Minimum Variance Portfolio. In simplest terms, I would say that it is just the portfolio of the stocks with the smallest Betas, but the actual algorithm is a little more complicated. The algorithm chooses the weights of the stocks in order to minimize the variance after taking into account the correlations of each stock (so you can’t take all low Beta stocks that are highly correlated). The minimum variance portfolios have greater returns with lower volatility (though they may under-perform the market during boom times as conservative investors tend to do) than their base indices.

Looking on their website, I noticed that several of the top 50 holdings of the S&P500 minimum variance portfolio contain holdings of Warren Buffett and Berkshire Hathaway. Anheuser-Busch, Coca Cola, Johnson and Johnson, Proctor and Gamble, United Parcel Service, and United Health Group are the overlapping holdings. Almost all of the companies on the list are well-established, well-run companies.

I was curious if the reason for the out-performance of this group was due to any remaining factors that may not have been presented on their website. I performed a multiple regression analysis of the returns of the S&P500 and its accompanying minimum variance portfolio against six technical and fundamental factors available on Kenneth French’s website. The six are the equity risk, size, value, momentum, short-term reversal, and long-term reversal premiums. The equity risk premium is similar to Beta from above, but it is relative to the entire market and not just the S&P500 (so we can assume it won’t equal 1). Size (SMB) and value (HML) premiums are from the Fama-French literature and reflect the risk of small companies and companies with low Price/Book ratios. Momentum is based on the relative performance of portfolios formed based on 2-12 month returns. Short and long term reversal portfolios are similar to momentum except instead of assuming higher momentum leads to higher returns, they assume mean-reversion. All things considered, I wanted to throw as many factors as I had data on out there to see if anything stuck.

The regressions are both highly significant in their F tests. The coefficients and intercepts are all significant at the 1% level except the coefficient on long-term reversal for the S&P500. What I found most interesting is that this model almost perfectly explains the S&P500 with an adjusted R squared of 98.8%, but the adjusted R squared for the minimum variance portfolio is only 60%. In other words, this model does not describe minimum variance portfolios and there could be some other factor out there that might help explain the returns. All things considered, the reversal factors add very little to the analysis. While the S&P500 returns are mostly determined by the market risk premium, less than 50% of the variance of the returns of the minimum variance portfolio is described by the market risk premium alone while the remaining factors add about 15%.

Comparing the coefficients of the full model, I noticed that the minimum variance portfolio has a lower coefficient on the size factor indicating that it holds larger companies. However, these companies are more exposed to growth than value. The momentum effect is virtually identical, but there is a strong long-term reversal tendency of the minimum variance portfolio, but smaller (and negative) short-term reversal relative to the S&P500.

If I have free time, I might create price to cash flow and dividend yield factors from Professor French’s data and combine it with some of the other portfolios on the Falkenstein website. It is likely that the minimum variance portfolios really do have some quality (such as idiosyncratic volatility) that is difficult to model. Nevertheless, I am quite convinced that MV Portfolios will have more promise than building portfolios with CAPM (just buy the market) or Fama-French (buy small-cap value, hold 20-50 years). CAPM is too lazy for the entrepreneur in me and it is hard to buy small-caps as an institutional investor without moving the markets. Building a MVP could be the first step in a screen and then one could shorten that list to 15-25 names based on fundamental information and industry trends. However, it seems like there could be something else that is explaining their returns that is worth investigating.