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Over the long run, the correlation between Treasury bonds and the stock market has averaged about zero. This point has been repeated many times on this forum. However, the relationship has been variable, changing over time.

The latter point is maybe less well established, so I wanted to do a quick check to make sure it seemed as right and as obvious as I thought it was.

I used the following data:

1) Stock market excess returns (Fama-French daily Mkt-RF series) above cash

2) 10-year Treasury bond yield constant maturity series, accessed via FRED

Then I computed the change in 10-year Treasury bond yield and used that rather than the actual level itself. The change in yield corresponds very closely to the inverse of (excess) bond returns over short periods of time. That's good enough for these purposes. I decided to resample to weekly data, as daily may be a bit noisy especially with bond yields.

Finally I computed rolling 52-week correlations between the excess stock market returns and the change in Treasury yields. For good measure I also looked at linear regressions between the two as well, also on 52-week windows.

As a point of reference, I took the same weekly data and generated four different random permutations of the same, breaking the pairs of data apart for the two series. These permutations have the same means and variances as the original, actual data, but the relationship between the two series has been scrambled. The resulting correlations should be zero.

Here are the resulting plots of the actual data and the random permutations. Click the images to see larger versions:

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edit: using a different model, described in a below post:

viewtopic.php?f=10&t=246444&p=3882010#p3882010

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*Remember, positive correlation between yield changes and stock returns means negative correlation between stock and bond returns.*Notice how the computed correlation coefficients for the randomly permuted data are bouncing around, mostly in the [0.2, 0.2] range but sometimes outside. That's what to expect when the true relationship is 0. Similar things can be said for the beta plots.

Any thoughts? I don't think there's too much to say here, and that's about it for me.

Actually, I'm thinking I probably should have used some longer-running bond yield series than DGS10. Is there anything with granularity on this scale that goes back further than 1962 or so?

For some reading on the relationship and how it might have been influenced, one relatively recent paper to check is "Stock-Bond Correlations, Macroeconomic Regimes and Monetary Policy" by Lieven Baele and Frederiek Van Holle (2017).