Component Tactical Asset Allocation: Part 1

Mebane Faber published an article in the Journal of Wealth Management in the Spring of 2007 called a Quantitative Approach to Tactical Asset Allocation. The thrust of the paper is that if you invest in U.S. stocks, foreign stocks, bonds, commodities, and REITs when they are above their respective 200 day moving averages and invest in commercial paper otherwise, you can achieve returns similar to equity investments with significantly lower volatility. Mr. Faber has graciously provided the monthly returns from the strategy as well as much more information on his website, World Beta. Based on the data on the website (more up to date than the original paper), the timing model returned 12% since 1972 with a standard deviation of 6.43% (.93 Sharpe) compared to an 11.5% return on the buy and hold asset allocation strategy (20% in each asset mentioned above) with a 9.78% standard deviation (.56 Sharpe). I programmed his strategy into Matlab using the same data and found similar results (slightly different due to the vagaries of Matlab rounding and computing returns statistics based on monthly data instead of yearly data).

Lately I have been interested in how to improve on this concept. First, I would like to discuss two additions I made and I will make an additional post to discuss the results of what I tested.

On his blog, Mr. Faber compares different methods that readers have requested to improve the returns (that he doesn't use). The first is to enter long positions above the 200 day MA and short positions below while the second is to enter each position "all in," equally weighted for each buy signal, no positions in cash . Each of these methods fails to improve the Sharpe ratio. I expect the L/S portfolio fails due to the fact on that most of the top 50 best and worst days are when the market is below the 200 day moving average. It is possible to profit by shorting the worst, but you can get burned on the best.

I believe the "all in" portfolio fails by ignoring the correlations between the assets (and would require more re-balancing costs than the traditional TAA). In order to test this, I followed a white paper by Panagora Research which describes the Risk Parity Portfolio. Their concept is to adjust the weights of a portfolio so that the amount you can risk on each position is equal. The traditional method to do this is to estimate the Value at Risk for a portfolio and break it into the component parts for each security. This method takes into account the correlations among each asset and the Beta. As a technical concern, I waited a year to create the Risk Parity weights (but used the initial 20% allocation during that period to make comparisons to Faber's paper) and brute forced the first weights using the covariance matrix and existed at the time of investment decisions and only changed the weights if the Component Value at Risk of an individual asset went outside predefined bounds. The weights stay relatively constant over time, but I could have created tighter bounds where they would change more often. As of the time of writing, bonds would have 34.8% weight, REITs 15.9%, Commodities 19.3%, Domestic Stocks 15.1%, Foreign Stocks 14.9%. In other words, REITs and Stocks would have their shares reduced and bonds would increase their weights in order to take into account the fact that they are more strongly correlated with each other than Commodities and Bonds and have higher variances. Based on the research provided by Panagora, I expected a slightly lower return, but a substantially reduced standard deviation.

The other method I used was investigating the j-k Momentum strategy proposed by Jegadeesh and Titman. In this paper, J and T investigate ranking stocks based on their returns from j periods ago and holding them for k periods forward. They used this model to show that stocks have a momentum factor like a size or value factor that helps determine their future returns. Within the context of the TAA model, I chose to test this strategy by choosing a proportion of the ETFs for an asset class and then applying the j, k methodology to a proportion of the ETFs with returns. I waited until a certain proportion of the total ETFs (in each classand that I considered representative of the asset class) began to trade to start the momentum strategy for that asset class. I will only report (and compare) the returns since the earliest strategy began to take effect (Select Spiders began trading in December of 1998, but it requires j months before the strategy can work). Since they have uneven start times, I used the returns from the normal TAA strategy when the Momentum strategy cannot work. I should emphasize that I am not using only a Momentum strategy on ETFs, but investing in a j-k Momentum strategy based on a TAA model. Within each Momentum category, the ETFs are equally weighted and I don't think it makes sense to use Risk Parity Portfolios in this context.

Furthermore, if I am not mistaken, Mr. Faber uses a method similar to this in actual practice, however, he does not report his results using this method. The most obvious reason is that he created his model in Excel which is substantially more cumbersome the model gets more complex. Also, ETFs have a short history that may not be indicative of the 35 years of returns where the TAA model has shown considerable strength. There's also no doubt that using ETFs in this strategy would require more trading costs and more taxes (unless in a tax-free account). Even if this strategy is not successful (it is), it is at least interesting to investigate and note the return characteristics for different levels of j and k.

The next post will compare the Equal Allocation (no TAA) model to the TAA and their Risk Parity equivalent portfolios, it will compare the TAA models with the Momentum TAA models (equal allocation and risk weighted), and some discussion about future additions I plan on testing.

On to Part 2.