Have you already seen the chapter of “Time-Series Analysis” from Quantitative methods?
In this chapter we analyze regressions of time series. One of the main requirements for a correct regression is that the series used in the model were stationary, if not, then at least to be co-integrated. Stationary means the time-serie has a single mean and a constant variance over time. When a time-serie is stationary, any deviation from its mean is reverted in the next or future periods back to the mean.
An autoregressive (AR) model helps to see this:
X(t) = a + b*X(t-1) + e
If a time-serie is stationary, we can say with reasonable experience that Xt would be very similar to Xt-1 and so on. Then we can replace values above and get the following:
X(t) = a + b*X(t)
X(t) - b*X(t) = a
X(t) = a / (1-b)
In order to X(t) have a known value, then b must be below 1 in absolute terms (i.e 0.75, 0.65, 0.12, etc)
Knowing this, do you think that systematic risk is stationary over time? If so, then the market betas would also be stationary over time because betas measure systematic risk. The mean of all betas in a entire market or group of markets is 1, a known value. So yeah betas and systematic risk are stationary time series.
Blume made an empirically driven study of betas and found that all betas reverted to its mean (because betas are stationary over time), in this case to 1.
So in order to predict the next future value of a beta we just need to know the value of “a” and “b” from the regression set at the beginning. Blume found them to be a=1/3 and b=2/3.
Any question please ask.
Hope this is clear now!