adjusted beta mean reverting level

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disptra

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Bt = a0 + a1 * Bt-1;
Schweser claims that the larger the a1, the forecast will move toward 1 more quickly. I am not able to see why it is correct.
For example, if beta = 1.04;
For a0 = 1/3, a1 = 2/3 adjusted beta = 1.02667
For a0 = 1/4, a1 = 3/4 adjusted beta = 1.03.
So the larger the a1, the slower it convergs to 1.
Another way to look at this, if a1 = 1, a0 = 0, then it will never converge to 1. what do you think?
 
pretty sure this was recently discussed but i don’t remember the outcome.
 
Yeap, I’m lost on this point too. Hope the vets can chime in on this.
The adjusted beta forecast reaches 1 much faster when a0 > a1 which contradicts Schweser’s statement.
(in the format of a0,a1,bt-1, bt)
0.67 0.33 2.00 1.33 0.33 0.67 2.00 1.67
0.67 0.33 1.33 1.11 0.33 0.67 1.67 1.44
0.67 0.33 1.11 1.04 0.33 0.67 1.44 1.30
0.67 0.33 1.04 1.01 0.33 0.67 1.30 1.20
0.67 0.33 1.01 1.00 0.33 0.67 1.20 1.13
0.67 0.33 1.00 1.00 0.33 0.67 1.13 1.09
0.67 0.33 1.00 1.00 0.33 0.67 1.09 1.06
0.67 0.33 1.00 1.00 0.33 0.67 1.06 1.04
0.67 0.33 1.00 1.00 0.33 0.67 1.04 1.03
 
The CFAI text make no such claim regarding the value of a1 and its speed to adjust beta back to 1.
I suspect whoever wrote the PM material for Schweser simply didn’t work out the example….at first glance you think their statement is correct because you’re only thinking about a1 (and thus ignoring a0). Unfortunately I would say the reality is exactly opposite to their statement.
 
I noticed in the book of slides that Schweser gives with their 3-day review course has it as the larger the a0, the forecast will move toward 1 more quickly….thus matching what we’ve all been saying.
 
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