Anyone has data on that? If there is a chart somewhere of how that relatioship has changed I would appreciate it
you can approximate in excel if rough calcs are fine for you with =DURATION(C7, C7+365*30, D7, D7, 2) where c7 = observation date, d7 = 30y yield on the observation date. The ratio will asymptotically decrease as yields go higher. In the below red assumes that 30y yield = 10y yield and blue that 30y = 10y yield + 1.5%
Have you plugged historical data in to see how that evolved? I found some data here https://www.portfoliovisualizer.com/backtest-asset-class-allocation#analysisResults It didn't had yields but annual returns. Looking at the ratio between long-term treasury % changes and 10y treasury % changes (and removing the negative ratios), I'm getting a 1.75 ratio of long-term treasury to 10y treasury
@Daal attached pic with fred2 data. @pyradius yields as decimals. also you haven't changed 30 to 10 for calculation of 10y duration.