There has been discussion both recently and historically concerning the relationship of stocks and bonds. Indeed the Daily Speculations website this year started color coding the days on the calendar based on the different movements of those two basic assets.

Much of the discussion concerning this subject has been oriented around "counting". While I value that approach I must point out that the yardsticks by which stocks and bonds are measured in such analysis are of different lengths. Specifically, those markets do not open and close at identical times, which means the daily recording of their respective changes may not actually reflect their movements when they were contemporaneously open. If the daily recordings are not exactly representative, then counting those recordings in the hopes that the errors will "all come out in the wash" may not be the best approach.

Changes (as opposed to levels) are the appropriate data to study. But because of the different time periods, a period other than daily would be more representative of their respective actions.

Instead of counting the daily changes, I have been following the moving correlation of those markets. Whereas most investment professionals are of the belief that stocks and bonds are essentially opposites, we have found otherwise. For example, if you were designing a most bullish environment/setting, I believe that would be when both stocks and bonds were rising. That is, you had a positively trending stock market and declining interest rates. That can be easily modeled by a moving correlation of the two and a positive slope of their prices. Here's a chart (weekly data) of exactly that:

If it doesn't show up well, here is a link.

As you can see, periods of positive moving correlation and positive slope tend to be good times to be long equities. More importantly however is that price collapses are easily seen as periods when that best condition does not exist. The worst condition is when stocks and bonds are both declining. But the other two "not best" conditions reflect the standard (macroeconomic) business cycle and have interesting trading implications all their own. All of this can be non-subjective and can be tested. We have found it to be statistically significant. Furthermore, I show it here on a weekly chart for convenience, but the data is daily and should be watched daily.

I would posit that Daily Specs could find this an interesting area of study. For years my shop had used this as an important part of avoiding trouble, basically to tell us when to play in equities and when not. We only abandoned it when we found something better.

Some further comments/tips:

For bonds I used the DJCBTI because it is price-based and not expiring every six months. It is also third-party. I could make my own bond index, but then open myself to the charge of jury-rigging the results. N-values are hugely important. But adapt, don't optimize N-values. Also you will have to consider what level of moving correlation is significant (i.e. a positive value of .01 is somewhat of a yawner).

Bill Rafter, MathInvest

Kim Zussman writes:

Using TLT for bonds and SPY for stocks (2002-present, including divs), checked weekly return for stocks after prior weeks which were either (bonds, stocks) up up, up dn, dn up, dn dn, vs zero:

Variable    N      Mean     StDev   SE Mean      95% CI             T
BUSU      113   0.00165  0.0164  0.0015  (-0.0014, 0.0047)      1.07
BUSD      139   0.00156  0.0363  0.0030  (-0.0045, 0.0076)      0.51
BDSU      139  -0.00022  0.0213  0.0018  (-0.0038, 0.0033)   -0.13
BDSD       60    0.00519  0.0242  0.0031  (-0.0010, 0.0114)    1.66


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