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# Refining Alphas - Scaling and Trimming Alpas - AIM 53.2

#### Hardy Noman

##### New Member
Hi David.

Could you please explain the process of Scaling and Trimming alphas
(in the Topic - Grinold & Kahn. Chapter 16 - Refining Alphas - Scaling and Trimming Alpas - AIM 53.2)

1) how do i interpret this formula for scaling :

Alpha = (Volatility) x (Information coefficient) x (Score)

Firstly, what is meant by Score, Secondly how does the formula actually work to rescale alpha?

2) how does trimming work to refine alpha

Also pls comment on the testability on this part of the curriculum.

Thank you

#### Merlinius

##### New Member
I have the same question. Also, in the study notes you mention, volatility, IC, scale and score. Then there is a table where "modified alphas" are presented:

However, there is no definition for "modified alpha". Is it the score, i.e. alpha divided by the scale?

Also, the notes suggest that this helps with constrained optimization. How? I do not see any connection.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@Nicole Seaman can we contact Lisa P @ GARP and ask "How exactly are the modified alphas calculated in the final column of Grinold's Table 14-1?" (We've asked GARP before but not Lisa ...)

@Merlinius I (we) need more help from GARP on this Chapter (feedback I've given them multiple times). I think they've assigned it without understanding much of the mechanics. As mentioned in other threads, firstly, it requires the scaffolding (prerequisite) of previous Grindold chapters.

But for this table, so far I have had to enter the modified alpha values manually because I cannot reconcile the derivation with other facts presented, here in https://www.dropbox.com/s/ffqh7qjfwfd8bg6/Grinold Table 14.1.xlsx?dl=0
... despite the text says they are based on formulas 14.1 and 14.2; so i think maybe we don't have enough information
... sorry that's the situation
... it is true that the standard deviation of the modified alphas is reduced to 0.56% from 1.95% (in my XLS) which basically matches Grinold's statements below (emphasis mine):
"[page 381]
... This constrained optimization corresponds to an unconstrained optimization using the same active risk aversion of 0.0833 and the modified alphas displayed in the last column of Table 14.1. We derive these using Eqs. (14.1) and (14.2). These modified alphas are pulled in toward zero relative to the original alphas, as we would expect, since the constraints moved the optimal portfolio closer to the benchmark. The original alphas have a standard deviation of 2.00 percent, while the modified alphas have a standard deviation of 0.57 percent....

[page 382]
Scale the Alphas:Alphas have a natural structure, as we discussed in the forecasting rule of thumb in Chap. 10: α = volatility · IC · score. This structure includes a natural scale for the alphas. We expect the information coefficient (IC) and residual risk (volatility) for a set of alphas to be approximately constant, with the score having mean 0 and standard deviation 1 across the set. Hence the alphas should have mean 0 and standard deviation, or scale, of Std{α} ~ volatility · IC. An information coefficient of 0.05 and a typical residual risk of 30 percent would lead to an alpha scale of 1.5 percent. 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 14.1, 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 that example effectively shrank the IC by 62 percent, a significant reduction. There is value in noting this explicitly, rather than hiding it under a rug of optimizer constraints. The scale of the alphas will depend on the information coefficient of the manager. If the alphas input to portfolio construction do not have the proper scale, then rescale them."

... let's see what help we can get from GARP. Thanks,

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#### Merlinius

##### New Member
Thanks for taking the time!

My subjective impression was that this problem was less prevalent in the literature for Part 1. However, in Part 2 basically every other page I come across some ambiguous wording. Then I draw my circles around the BT notes, BT forum, the original literature, Schweser and Google, which takes a huge amount of time, until I find that most of the time each source copied the same phrase and I have to decide for myself whether my own lack of understanding is at fault or if nobody understands these parts.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@Merlinius I do understand but I do think "nobody understands these parts" is not fair to us (BT) as a general statement. I hear what you are saying, but these scaled alphas are one of a few specific areas where I haven't been able to somehow compel an understanding. For a wide majority of P2 concepts (and P1), we have captured a specific understanding, and even figured out how to model them in XLS (e.g., all of Jorion's Chapters 7 and 17 where, despite GARP's lack of detailed understanding, we've been able to replicate almost all of it in XLS to the degree that we've been able to correct GARP's own mistakes on the material) . This Grinold chapter is a special problem, to be sure, and it starts with the fact that I don't think anybody at GARP understands some of what's been assigned.

FWIW, my memo last year to the GARP's Board and Trustees referenced this chapter (twice) see full memo here at https://www.bionicturtle.com/forum/...-committee-and-garps-board-of-trustees.22758/ i.e.,
"The syllabus may not be receiving enough attention
Hoping that I have earned the reader’s attention, I shift to more constructive feedback; i.e., because the following issues can be fixed with better process design. Our forum has accumulated thousands of posts that collectively constitute unstructured feedback on the details of the FRM syllabus. Some feedback is more subjective than objective.14 Further, my points below embed my own interpretations and opinions, albeit informed by customer engagements. While organizing this feedback, I decided somewhat arbitrarily to arrange the feedback into three categories: Recency, Coherence, and Relevance.
...
III. Relevance
Relevance is an umbrella that seeks to cure three defects: Discontinuous Assignments are widowed/orphaned readings that do not stand alone very well. Diligent pursuit of the LOs tends to require supplemental study. Potential Over-assignment refers to patches of the syllabus where strict adherence to the learning objectives can be extremely time-consuming, but the payoff is unclear. Frenetic Current Issues refers to implications of swapping the entire set of Topic 9 readings every year.
Discontinuous Assignments require supplemental effort. For example,
• Grinold’s Chapter 14 (Portfolio Construction, published in 2000) is almost comically absent something educators call scaffolding. If true mastery is really wanted, candidates need to backfill their knowledge with preceding chapters. One customer wrote, “Sorry for the REALLY long question. The choice of GARP to include this chapter is really bad. You need a LOT of background to even understand what is going on and to understand what the variables represent.”22 Yet we’ve observed that GARP only asks superficial questions about this material; e.g., Part 2 Question 63 is almost famous for puzzling our visitors. [footnote 23: The question applies Grinold’s σ(α) = volatility × IC. We infer a superficial application because the original question contained an error, as several customers noted. The 2018 fix has prompted a new question from Karim (one of our best customers): “why are there [now] fewer alphas than stocks?” The back-and-forth on this question, in service of correcting GARP’s error and discerning the question’s intention, in my opinion, is not very productive: there are much better questions that could be written to really test a meaningful understanding of Grinold."
• Diebold Chapter 5 (published in 2006) begins a four-chapter sequence in time series and forecasting. It’s hard to calibrate how seriously to take these learning objectives. On the one hand, to be able to truly respond to every learning objective requires diligent, time-consuming study. Diebold’s own end-of-chapter (EOC) questions are very demanding. On the other hand, the single 2018 Practice Question that refers to Diebold is a dead simple conceptual (not even quantitative) question about covariance stationary. Serious study requires EViews, the software used in the book"

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#### Detective

##### Active Member
From my 20 minutes of perusing the text, I do not think there is enough information provided in the book to numerically back out the modified alpha values in table 14.1.

Although interesting, I personally think modified alphas coming up in a capacity where you have to back into them on the exam is remote.

Notation:

alpha' = modified alpha
IR = information ratio
psi*_p = active risk
V = asset-by-asset covariance matrix
h*_PA = active portfolio holding
lambda'_A = active risk aversion

Previously in book:

#### Merlinius

##### New Member
@Merlinius I do understand but I do think "nobody understands these parts" is not fair to us (BT) as a general statement. I hear what you are saying, but these scaled alphas are one of a few specific areas where I haven't been able to somehow compel an understanding. [...]

Sorry for my poor choice of words (this is not my native language). This was in no way meant as a criticism towards you. Like in the specific example at hand what I was referring to were the - probably few in number, but very large in consuming my time - cases where there is simply not enough information in the text to make sense of what the author was trying to convey. I am very impressed by the effort you are putting into this, even addressing these issues with GARP.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Merlinius You don't need to apologize, but thank you! But I do I apologize for mis-interpreting your post. Aside from that, as you can tell (if you read the memo I sent to GARP's Board etc) I absolutely agree with the substance of your comment. Even if there are only a few cases where the assigned chapter alone is insufficient (and there are quite a few that I cited in the memo, actually), diligent candidates can experience considerable delay when confronting them. As I've told GARP many times, the irony is that the more diligent students can be effectively penalized when studying some topics because they are seeking a root understanding that may not actually be found in the text (versus a less invested student may gloss over and never grapple with undefined terms or inconsistencies). Thank you again,