How can we describe cross-correlation differences between the U.S. long-term bond market and the U.S. equity market? Let's look at the daily returns, on both the 10-year U.S. Treasury yield and the S&P 500. Both going back to the early 1960s.
In the illustration below, we show the middle performance in each quartile for both asset classes. The bubble size and label corresponds to the historical portion of the next day's returns, which are in the same direction as the historical contemporary daily return (e.g, 56% of the serial returns associated with the 4th quartile of contemporary S&P 500 daily returns).
We see that in each of the four quartiles, the portion of directional consistency is lower for long-term government bonds as it is for the S&P 500. Yet for larger performance, auto-correlation corresponds more along the U.S. Treasury bond yields versus the S&P 500. We can see this in the more vertical slope of the former asset class versus the latter asset class. To interpret the vertical data mapped in this chart, we go through an example. The typical 1st quartile S&P 500 daily performance is -0.9% (along x-axis). Of the quarter of the serial performance data associated with this quartile, we show the typical 1st quartile of this marginal serial performance as -1.2% (along y-axis).
In the illustration below, we show the middle performance in each quartile for both asset classes. The bubble size and label corresponds to the historical portion of the next day's returns, which are in the same direction as the historical contemporary daily return (e.g, 56% of the serial returns associated with the 4th quartile of contemporary S&P 500 daily returns).
We see that in each of the four quartiles, the portion of directional consistency is lower for long-term government bonds as it is for the S&P 500. Yet for larger performance, auto-correlation corresponds more along the U.S. Treasury bond yields versus the S&P 500. We can see this in the more vertical slope of the former asset class versus the latter asset class. To interpret the vertical data mapped in this chart, we go through an example. The typical 1st quartile S&P 500 daily performance is -0.9% (along x-axis). Of the quarter of the serial performance data associated with this quartile, we show the typical 1st quartile of this marginal serial performance as -1.2% (along y-axis).
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