Adjusted Beta

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ptan54

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Can someone please explain why for larger value of alpha-1, the mean reverting process will get back to 1 more quickly?
Adjusted Beta = alpha0 + alpha1*(previous Beta)
Does it not follow that Adjusted Beta will tend to 1 when alpha0 tends to 1 and alpha1 tends to 0?
If you look at Schweser book 3, page 224 it says “adjusted beta forecast will move towards 1 more quickly for larger values of alpha1”
Also in Schweser Practice Exams Vol 1, Exam 2, Question 18 - the answer explanation contends that De Jong is correct for asserting that larger alpha1 means that the beta estimate will move more quickly back to mean reverting level.
Very confused here, thanks.
 
Take a look at question 18 in Schweser Exam 2, vol 1 practice exams.
Typically the company uses alpha0 = 1/3, alpha1 = 2/3
In this case, they want to use alpha0 = 1/4, alpha1 = 3/4
Will the adjusted beta now be closer to the mean reverting level using the new alpha values?
2(1.04)/3 + 1/3 = 1.0266666666666666666666
3(1.04)/4 + 1/4 = 1.03
Surely this means that the 1/3, 2/3 scenario results in the adjusted beta forecast reverting to 1 more quickly? But their answer explanation says the opposite.
 
ok heres how….
1) if they use the earlier adjusted beta factor of 1/3 : 1/3 + 2/3(1.04) = 0.33+0.67(1.04) = adjusted beta 1.023 .
but De Jong used 1/4 so:
1/4 + 3/4(1.04) = 0.25 + 0.75(1.04) = adjusted beta 1.03
remeber mean reverting level of beta is always 1: WHY? because 1/3 + 2/3 =1 or even 1/4 + 3/4=1
so De Jong’s adjusted Beta is bigger than 1.023 used by the 1/3 beta adjustment.. so its more further away from the mean reverting level.
Why is deJong’s adjusted beta further away? because its 2nd term (3/4) is bigger than (2/3) so its further away from the mean reverting beta.. :)
 
ur calculation is wrong Ptan… its not 2(1.04)/3 + 1/3 = 1.0266666666666666666666 but instead its 1/3 + 2/3(1.04) = 0.33+0.67(1.04) = adjusted beta 1.023 .
 
ERRATA
The adjusted beta forecast will move toward 1 more quickly for larger values of á0 ( Posted: 2008-05-19)
You can check it also from Schweser website.
 
yes that makes sense if aO is bigger because aO is always constant..and unchanged.. the one most sensitive to change is the 2nd term… which has the tendency to move further (either above or below) the mean reverting level.
 
That’s what I have been saying all along.
So the correct answer to Q18 should be D?
BTW - 0.67 is an approximation of 2/3.
0.6666666666666666666666666666666(1.04) + 0.33333333333333333333333333333
= 1.02666666666666
De Jong’s beta IS further away - but their initial answer explanation said De Jong’s adjusted beta is closer to 1.
 
yeah.. i guess they made a mistake on this one… F*cking schweser… can someone please explain whether the answer should be D!! it should be D instead of C
 
The solution is just spend the extra 30 seconds and calculate two values to compare them if the question comes up on the actual exam. Case settled.
 
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