The TAA models are good at reducing risk, but to increase return to something comparable to an equity index it seems silly to use the same amount of margin at all times. The post above gives evidence that lowering the amount of leverage in times when there is a prediction of a U.S. recession will increase the Sharpe ratio relative to a similarly levered model.
To incorporate this insight into the TAA model, as I used the same probit modeled I discussed in the first post I made regarding probit models. To use this model in an investing environment, I used a warm-up period of 200 months and then estimated the model each month to get a probability of a recession 12 months out. Since the NBER doesn't have dates for recessions in the past two years (I guestimated), I stopped the model 24 months prior to the end of February and used the coefficients as of that date with the data available to get the remaining predictions. Using this data I created two possible ways to scale in and out for leverage. I looked back four months for predictions in both cases. I did this for three reasons: the data constantly gets revised, I'm not sure always what is available on any given date and I want to be safe, and the lag time seems optimal (12 keeps you unlevered during the rebound, 1 is too sensitive, 6 works just as well, but I wanted to keep it shorter). So looking back four months, the first method will lever the portfolio when the estimated probability is greater than 50% and not lever the portfolio below that. The second method is similar except it provides three baskets levering a full amount, 50% of the full amount and none at all.
The results for the first and second method are comparable, but the second method slightly underperforms the first on a Sharpe ratio basis (the return is lower and the standard deviation is lower, but not by enough to offset the return). It's possible to fiddle with the parameters to improve the results, I'd rather just ignore it for the simplicity of the first model. The chart below gives the portfolio statistics for the first model with 0 leverage (and no probit data), 50% leverage, and 100% leverage. The first two columns are the base 0% and 50% and the probit columns represent the model with dynamic leverage ratios. Similar to before, I report the evenly weighted portfolios and the risk parity portfolios.
The results confirm my original intuition(!) and then the models even outperform what I had suspected would happen. Essentially the model reduces your leverage heading into a recession and then quickly puts it back on. Surprisingly, comparing these returns with the raw results from the last post on TAA and probits, shows an even better return for this method using the model than reducing leverage when a recession happened. I do use domestic equity volatility as a factor in the model which could help the investor get out when volatility increases (it is a small component compared to interest rates and money supply data though). Anyway, the results show an increase of the 50% leveraged portfolio's Sharpe ratio by almost .1 by reducing standard deviation substantially and keeping the returns constant. The 50% portfolio, previously with a horrible Sharpe ratio relative to the 0%, now is roughly comparable (with equal and risk parity weights). With 100% leverage, the risk parity probit model now has a Sharpe ratio equivalent to the equal weight 0% and 50% equal weight portfolios (but with more return and risk). However, the 100% leveraged probit models dramatically outperform their cousins without the probit model. Again, this is due to substantially reducing volatility by reducing leverage in periods leading up to recessions.
Given the success of the probit model in reducing volatility and keeping returns high, I now plan to investigate leverage as a function of the volatility of each asset class (individually). I'm guessing there would be similar results, but without some of the messier complications of using the probit model (not sure when data is released and it's relatively intensive computationally). Assuming I can find daily data from the site I got the monthly data, it shouldn't be that much of a problem and I can just use the percentage of large up and down days in a quarter as a proxy for volatility of each asset class.
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