Grinold, Chapter 14: Portfolio Construction

[kik92]

Hi David,

Page 5 of Chapter 14: Portfolio Construction (Grinold) states the following

Consider for instance, an Information Coefficient (IC) of 0.05 and a typical residual risk (volatility) of 30 percent would lead to an alpha scale of 1.5 percent (0.05 x 0.3 = 1.5%).
In this case, the mean alpha would be 0, with roughly two-thirds of the stocks having alphas between -1.5 percent and +1.5 percent and roughly 5 percent of the stocks having alphas larger than +3.0 percent or less than -3.0 percent. In Table 1 below, the original alphas have a standard deviation of 2.00 percent and the modified alphas have a standard deviation of 0.57 percent. This implies that the constraints in this example effectively shrank the IC by 62 percent, a significant reduction.

Could you kindly explain how you arrived to the statement highlighted in bold, namely the 2/3 and 5%?

Thanks,

Karine

 

[David Harper CFA FRM]

Hi @kik92 Once this example (it's Grinod's statement not really mine, btw) scales the raw alpha into a refined alpha scale such that that alpha has a standard deviation of 1.5%, it is just applying the rule-of-thumb concerning the normal distribution:

• In a normal distribution, approximately two-thirds of the distribution is within one standard deviation' in this case where mean, µ = 0 and σ = 1.5%, because ~ 2/3rds is within µ +/- 1.0*σ, ~2/3 is within 0 +/- 1.0*1.5%. Note the rule is supported by: NORM.S.DIST(1,true) - NORM.S.DIST(-1, true) = 68.27%
• and approximately 95% (or 95.5%) is within two standard deviations, such that ~95% is within 0 +/- 2.0*σ = 0 +/- 2.0*1.5% = 0 +/- 3.0%. Note the rule is supported by: NORM.S.DIST(2,true) - NORM.S.DIST(-2, true) = 95.45%

For previous discussion on the section, see https://forum.bionicturtle.com/thre...n-ratio-formula-garp16-p2-72.1933/#post-50848 ... The 2017 GARP P2 Practice Exam has a question on this (Question 63) which is almost a literal duplicate, although as I've been asked to review the practice paper, my feedback on this alpha scaling is that the syllabus lacks sufficient context (scaffolding) to be asking this question. It presupposes unassigned Grinold chapters. I don't know what GARP will do (of course) but I consider this question type to be borderline inappropriate because aside from this perfunctory normal distribution dynamic, the entire Grinold has not been assigned and there is a lot of preamble actually. Thanks!

 

[sajedian]

his implies that the constraints in this example effectively shrank the IC by 62 percent, a significant reduction.

Hi @David, can you please explain how we are getting the 62% shrank in IC?

 

[David Harper CFA FRM]

Hi @sajedian I frankly cannot recall where Grindold infers that "in the example effectively shrank the IC by 62%", sorry. Per the related discussion (and GARP's practice question) at https://forum.bionicturtle.com/thre...n-ratio-formula-garp16-p2-72.1933/#post-50848

We know the key relationship, although it clearly lacks sufficient scaffolding (i.e., insufficient build-up and context) is: standard deviation (std) of the alphas = Residual Risk (volatility) x Information Coefficient (IC). His example (Table 14.1) contains alphas and modified alphas. He says the original alphas have sigma = 2.0% and the modified alphas have sigma = 0.57%, which itself (to me) implies a reduction of, I guess, 1 - 0.57/2.0 = 71.5 rather than 62%. So I think maybe we're missing a variable, I'm just not sure ...

 

[sajedian]

Hi @sajedian I frankly cannot recall where Grindold infers that "in the example effectively shrank the IC by 62%", sorry. Per the related discussion (and GARP's practice question) at https://forum.bionicturtle.com/thre...n-ratio-formula-garp16-p2-72.1933/#post-50848

We know the key relationship, although it clearly lacks sufficient scaffolding (i.e., insufficient build-up and context) is: standard deviation (std) of the alphas = Residual Risk (volatility) x Information Coefficient (IC). His example (Table 14.1) contains alphas and modified alphas. He says the original alphas have sigma = 2.0% and the modified alphas have sigma = 0.57%, which itself (to me) implies a reduction of, I guess, 1 - 0.57/2.0 = 71.5 rather than 62%. So I think maybe we're missing a variable, I'm just not sure ...

Thanks David for quick reply, I was thinking the same. Glad that I am on the right path

 

[enjofaes]

Was also confused by this 62%, It's actually not mentioned anymore in the books (if it was in the past) so would suggest to remove it in next revisions