I began by collecting total return series for 1, 2, 3, 5, 10, and 30 year government bonds along with interest data that's available for bills, bonds, and corporate debt. Some of the series are active in some time periods and not in others, so I just stuck with 3 month t-bill and 1, 3, 5, and 10 year bonds, along with BAA corporate interest rates.
I first looked at the returns for the different bonds. In general, I am interested in holding for several months, so I took the geometric average three month returns and created holding 10 year (5 years back, five years forward) windows to evaluate each time period. The evaluation was simply which (not decile or quartile, but) quintile or 20% range the return would fall into. So if a time period is ranked a five, it would perform in the top 80% relative to the performance five years prior or forward. This way the select periods of time where bonds dominate don't outweigh the whole dataset and there are still runs where it makes sense to be in bonds. The only reason I don't do the whole series is that I believe doing so would result in too much trading.
The chart above is the average monthly (not 3 month) return for each of the bonds I looked at and each decile. Below that is the same chart except if given a 4 or a 5 above, the left-most column is a 1 and 0 otherwise. Since we expect that bonds with longer maturities should have longer durations it makes sense that the 30 year has the largest spread and the greatest opportunity to profit or lose. I also looked into the correlation of the returns to the 6 bonds. For the most part correlations like 3 year vs. 5 year are very high, but as you get larger differences, there are larger differences. However, what is striking is that the correlation between many bonds, even like the 10 year vs. 2 year, are higher than 80%. That suggests that for the most part if you can build a good model for one of them, the idea should work for all (with the 10 and 30 relative to the 1 year having lowest correlations).
I think it is interesting to look at conditional means (or categories) for different statistics. For example, what are the returns like on average over the next three months when the yield curve inverts (or steepens). The only problem with that is that I have so much data and so many different yield curves to compare. I didn't want to specify one way that would work best (ie. do I only look at when the 10 year inverts relative to the 1 year, or do I look at 2 and 5, do some outperform in different central bank regimes?). To give myself as much flexibility without doing something crazy like a neural network, I decided that it would be best (at least in a preliminary sense) to look into using a probit model to categorize the returns.
I described what probit models are and how to use them to look into the probability of a crisis or recession previously. Essentially, I have the series of 0s and 1s and the goal is to use the independent variables to estimate the probability that an event will occur (in this case, the event is that it is worthwhile to invest in bonds for at least three months). I estimated the model for each bond series using two methods, in the first I focused on the interest rates mentioned above without reference to their past values, in the second I used the interest rates and each of the past 12 lags. The first method is less successful than the second, but it also avoids a lot more curve-fitting problems than the first method. The first method classifies 63% to 72% (from 30 year to 1 year) correctly whereas the second method is up to 73% to 80% (from 30 year to 1 year). For comparison, using the binary decision of greater than the 10 month MA or less, classifies at about 60% for each bond (and including it in the decision-making doesn't help). Note that I consider classifying correctly to mean a probability greater than 50%.
What will be interesting is to look at the false positive rate and the returns in situations when there is a false positive. In other words, I think the value of the probit model is identifying risk/return better than other models. If I can identify situations with good average wins relative to average losses, then I can control my risk better. Using the model incorporating 12 lags (which I am worried about), I calculated the times where there are false positives for the 10 year bond and found a 2% annual return with 3% volatility compared to a 18% return with 9% volatility for the normal (note that this is just what the returns are and ignores the fact that it will be in cash for significant periods of time, just want to get an idea of the conditional means). As expected, the periods when the model says to get out of the market, there are negative annualized returns(-10% with 7% volatility). However, I am a little worried about false negatives, but after looking at how often the model invests (since it invests for three months), it appears that the problem goes away. Obviously the problem with this is that I use the whole series to develop the probit model rather than going with information available to develop the coefficients. I would suspect that these good returns would get slightly reduced by using the actual trading model (which is what I intend to test when I am back from DC). In comparison, the 10 month MA rule, returns 8.5% with 8.5% standard deviation (ignoring interest) though it is invested more often. Incorporating commercial paper yield into the second model would reduce its return (though risk/reward stays high) though also reduce volatility by more in this model than in the 10 month MA rule.
Nevertheless, it appears to be an interesting development, I am worried that the coefficients are a bit difficult to interpret (too black boxy) and that they won't be stable enough to generate significant returns. I also don't doubt there are problems with autocorrelation, but fixing that in probit models can be a pain.
