10 year US Treasury bond returns for different return horizons

The returns of 10 year US Treasury bond are shown for various return horizons.

The first figure shows the gross returns with horizons from 1 month to 5 years; it shows the s-month returns for s=1,...,60. In the left panel the y-axis is different for each return horizon but in the right panel the y-axis is same for each return horizon.

The second figure is otherwise similar to the first figure but now the gross returns are talen to the power 1/s, where s is the return horizon. This means that we show the geometric means of the monthly returns. The geometric means make a time series with an autocorrelation larger when the return horizon is larger.