 # Schweser - Book1 2AM - Mean reverting beta

Q18 part II, Is De Jong correct with respect to her estimate of a0 with regards to mean reverting level of beta? "De Jong considers using adjusted beta in her analysis. Typically her company uses 1/3 for the value of a0. However, in this case, she is considering using a0 = 1/4. She determines that her adjusted beta forecast will be closer to the mean reverting level using this value. My response: De Jong is NOT correct with regard to her estimate of a0. Schweser response: De Jong is correct. My rationale: try historical beta 1.8 and check impact of a0 =1/3 vs a0 = 1/4 a0 = 1/3 ; adjusted beta = 1/3 + ((2/3)*1.8) = 1.5333 a0 = 1/4 ; adjusted beta = 1/4 + ((3/4)*1.8) = 1.6000 since 1.53 is closer to the mean reverting level than 1.60; De Jong’s assumption that the a0 =1/4 will provided adjusted values closer to the mean reverting level is incorrect. What am i missing? Thanks for your help.

my rationale: mean revert = b0/(1-b1) : b0 -> infinite, then no revert, therefore if b0 larger, no revert… b0=.333 vs b0=.25

a0 = 1/3 a0+ a1 SHOULD be 1 therefore, a1 = 2/3 which gives adjusted beta of 1.5333 For her presumption a0 = 1/4 a0+ a1 SHOULD be 1 therefore, a1 = 3/4 which gives adjusted beta of 1.6 (AWAY from the Mean Reverting Level of 1 for BETA’s) so the statement is not correct…

So is this one of the rare occasions that schweser makes a mistake? They have categorically stated “The adjusted beta forecast will move toward 1 more quickly for larger values of a1 (e.g., as a1 approaches value of 1).” in the notes. los. 68.h.? This seems like a fundamental error on schweser’s behalf or a major disconnect in our interpretation of the same?

Anyone know what the deal is?

bump^

Beta adj = a0 + a1 Beta from regression = 0.25 + 0.75* 1.04 = 1.03 vs = 1/3 + 2/3 * 1.04 = 1.0267 Mean reverting level for a0=0.25 = 0.25/(1-0.75) = 1 Mean Reverting level for a0 = 1/3 = (1/3)/( 1-2/3) = 1 So, if you think the comparison is between using a0 as 1/4 or 1/3, then ofcourse, the answer is closer to mean reverting level in case of a0 = 1/3 However. the language is… " De jong consider using adjusting beta in her analysis… she determines that her adjsuted beta forecast will be closer to the mean reverting level using this level…". that is, she is comparing the “closeness” of adjusted beta to “mean reverting level”, vis-a-vis closeness of “raw” beta from regression. Hence, she is correct 1.03 - 1 = 0.03 ( adjusted beta) 1.04 - 1 = 0.04 (raw beta)

agreed…I got this one wrong too… but its not in the errata…however i’m sure my answer (as yours sarthak) is correct

I believe there is an errata for that one. Check the Schweser website and no I won’t post the link.

apologies…i’m going blind there is errata Page: 213, Q18 - Correction The correct answer to question 18 is D. The last part of the online explanation has been changed to: Since á0 = 1 – á1, then De Jong’s smaller value of á0 will result in her adjusted beta forecast being further from 1 than if she used the firm’s á0. Please note that there is also an update for the notes, Book 2, page 224.

From the errata: Page: 213, Q18 - Correction The correct answer to question 18 is D. The last part of the online explanation has been changed to: Since á0 = 1 – á1, then De Jong’s smaller value of á0 will result in her adjusted beta forecast being further from 1 than if she used the firm’s á0. Please note that there is also an update for the notes, Book 2, page 224. Posted: 2008-05-20

Thata girl!

^^ beat ya hahah! i knew that was coming!

thanks so much folks!