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Brief abstract:

And as predicted in this November note, within a few months we'd have tail concordance play out between Treasuries (TLH) and the S&P (SPY) here going through year-end. Analysis below shows that because of tapering speculation, the 10-year Treasury yields have risen dramatically, and with high volatility, since the end of June. But once tapering uncertainties become cleared up and their actions are articulated, we should see an immediate rise in yields of nearly 0.3%, and a drop in Treasuries of more than 3%. I've also presented other complementary, prequel research showing the S&P would similarly fall over 5% over tapering bets (perhaps we are in the midst of this right now). So the stock market would drop 17 times faster than the yields would rise (5%/0.3%).

And I can prove my point that this non-linear relationship is becoming more exaggerated with tapering delay through autumn. The markets have dropped 1.5% so far in December while yields have risen 0.11%. Or the market dropping 14 times faster than yields are rising (1.5%/0.1%). And back through June, the month after the Bernanke's testimony, the markets dropped 7% while yields rose 0.6% through June. So then markets fell 12 times faster than the rate yields rose (7%/0.6%).

Notice this hidden pattern over time: 12x --> 14x --> 17x? The confluence of themes here is that the asset class relationships are getting more convex as we push through time! It would really have been great to have had a little more cash versus equity here at year-end, as we have a slightly more frequent streak of down-days for the stock market and up days in Treasury yields, in large part due to tapering bets (which again, some incorrectly have assumed was already priced-in).

Article:

In this note we look at this performance, since June, of the 10-year Treasury yield. Despite trying to sooth market participants after the May testimony, the 10-year Treasury yields have continued to rise in a very biased and fat-tailed manner. This change has been statistically relevant by a number of measures. It is anticipated therefore that some tapering is already "priced in" and a little more quick upside would result (at least 0.3%) once the speculation ends and the activities begin.

Similar to the analysis done with equities, there are numerous hypothesis that can explain the changes in the 10-year Treasuries since June, though the exceptionally large moves are most likely due to only Federal Reserve intervention that explainable by economic and risk valuations alone.

December 16, 2013 is roughly 5.5 months since June, a period we will call "Post". It represents 169 calendar days, and 118 trading days. On the flip side, the 168 calendar days through June we will call "Pre". Starting in mid-January, the Pre period this year has 116 trading days. By a range of statistical tests (both parametric such as the test for differences in means and in variance, and semi-parametric such as the Anderson-Darling or Kolmogorov-Smirnov), the Post period has seen yields rise slightly less, but not in a statistically significant way.

For example, the average daily rise in the 10-year yield was 0.5 basis points in the Pre period, while it was 0.3 basis points in the Post period. An outperformance that could have been expected about 80% of the time by random chance alone. Also the ratio of the high volatility (i.e., standard deviation) in the Pre/Post period was equal at 1.0, at medium statistical significance.

But the one thing that these above statistics leave out is that there are inherent seasonal biases in the financial markets, so what we really want to do is look at the difference in Pre versus Post performance without the seasonal bias. This way we are truly isolating just the effects of the extraordinary government intervention. Here we look at each day in the Pre and Post period, but instead just look at its performance relative to that day's typical 10-year yield change, from 1970 through 2008. Again, we have seen in the years since 2008 that government intervention (most notably TARP and ARRA) has distorted seasonal and perhaps cyclical factors, from Census hirings on employment metrics, "Cash for clunkers" on auto metrics, tax relief on retail metrics, emergency unemployment extension on jobless claims metrics, and first-time home buyer credits on housing metrics.

The various forms of quantitative easing is the latest intervention, and one with an ostensibly long tail. The daily change in yields is typically slightly positive in the Pre period and -0.2 basis point in the Post period, as investors typically have a slight shift in allocation towards less risk in the later part of the year.

As a result, the seasonally-adjusted results are only slightly more significant, with the average daily change of the 10-year Treasury yield of 0.4 basis points in this 2013 Pre period and whopping 0.7 basis points in this 2013 Post period. An outperformance that could have been expected only about 60% of the time by random chance alone. There are slight differences in this random chance portion, depending on the type of statistical test, an example of which is shown below (where the dashed and solid lines are Pre and Post, respectively). Also the ratio of the still high volatility in the Pre/Post period was is 0.8, which means there is incredibly increased volatility in the Post period, and at slightly elevated statistical significance.

(click to enlarge)The dashed and solid lines are Pre and Post, respectively, and X units are in change of bps.

We can see the results of this in the clear illustration below. The seasonally-adjusted 10-year yield changes, particularly for the Post period this year, has a slight positive skew (more exaggerated up moves in the daily change of the 10-year yield) and a wider dispersion known as fat-tails in both directions.

(click to enlarge)The seasonally-adj. daily change in the 10-year yield in the Pre period and Post periods.We see in the illustration above that the Pre period again has an average daily yield change of 0.4 basis points (with a standard deviation of 4.3, while the standard deviation through 2008 was only 0.9). And in the Post period of the illustration above we see the average daily yield change of 0.7 basis points (with an increased standard deviation of 5.4, while the standard deviation through 2008 was only 1.0).

The upward bias in the Post period, relative to the normal seasonal patterns, should not be minimized. The significant impact of these biases also shows in that the top 1% daily change in yields of 11 basis points during the Pre period. While shown in the earlier illustration that it surges to a dizzying 16 basis points in the Post period.

This upward bias in the 10-year yield since June shows the large impact of the Federal Reserve losing control of the 10-year yield, in a way that dominates any underlying seasonal patterns. Looking at these differences and error proportions, we see that well over ¾ of the variance and up-bias in the 10-year yield since then could be attributed to speculation that the Federal Reserve would eventually taper. It's the type of gains that shows it is partially "priced in", with some more additional bias once it occurs. Likely at least another 0.3% or so rise, in very short order.

Source: Federal Reserve Impact On Asset Classes