# blume adjustment

I was hoping someone could explain why the Blume adjustment makes sense and why it is done? Is it because in the long-term, all firms’ betas revert to 1? I don’t rally get the logic behind this. If a firm were say- a lot different than the rest of the firms in the market or industry (let’s assume the firm has a really unique product or something), wouldn’t that mean its beta is could remain very low forever?

thnx!

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!

It is to some degree but I haven’t covered quant so no need to explain further. I kind of couldn’t couldn’t wrap my head around the idea that the mean of all firms betas would be 1 but of course that is the case, so that was super helpful.

I have not covered quant yet, clearly! I’m starting on equity, fixed income, & financial reporting 1st, knocking off the heavier ones, planning to move on to the lighter ones and re-visit those 3 heavier ones before exam time…any advice on that study plan?

thnx so much