weighing scheme to estimate volatility and correlation

[ajsa]

Hi David,

I read we must use the same weighing scheme for estimating both volatility and correlation.. But the question below does not. could you clarify?

thanks.

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Company B makes a bid for Company A at € 15 per share. Although the bid may or may
not ultimately be successful, the price of Company A jumps because of the bid. A merger
arbitrage manager acquires a long position in Company A and a short position in
Company B. When constructing the variance-covariance matrix used for the VaR
calculation, which of the following is the best choice among the following alternatives
when computing the volatility of the companies and their correlations?
a. EWMA volatility, EWMA correlation
b. EWMA volatility, Equal weight correlation
c. Equal weight volatility, EWMA correlation
d. Equal weight volatility, Equal weight correlation
CORRECT: B
EWMA volatility estimate captures the higher volatility of Company A’s price following the
price jump. Since equal weight correlation would provide a longer view of the correlation,
this estimate would be preferred to the higher correlation provided by EWMA, particularly
in the event that the deal falls through.

 

[David Harper CFA FRM]

Hi ajsa,

You are on your game (you are in great shape for the exam, IMO. My only concern for you is that you are starting to "know too much" if you know what i mean) ... it's a sophisticated observation few would notice... i don't know the question source, but it's a bad question. The first problem with the question is that an FRM candidate, given the cirriculum, probably should answer (a), right? Aside from the consistency, (a) reflects the conservative VaR (i..e., higher volatility, higher correlation)...seeing (a) as conservative, the consistency is a bow on top that gives comfort...i think the answer screams (a)

Re: "Since equal weight correlation would provide a longer view of the correlation, this estimate would be preferred to the higher correlation provided by EWMA"
I don't know where the cirriculum supports this assertion?? The fact that correlation time-varies overrides

the consisteny criteria is esoteric (certainly "above" the exam): consistency ensures we can do the Cholesky decomposition on the covariance matrix
(e.g., which i did in the structured Monte Carlo http://www.bionicturtle.com/premium/spreadsheet/4.a.5_structured_monte_carlo/)

so in summary:
* consistency is technically desirable but not necessarily needed depending on the use of covariance matrix
* I would frankly ignore this question (my opinion, right?) .... in doubt, i would select here (a) to reflect the conservatism (higher VaR) sort of the same camp as "correlations spike during stress"

David

 

[ajsa]

Hi David,

Thank you! I personally feel FRM is more difficult than CFA since there are many "uncertainties" (if you know what i mean too). The question is 2007 practice exam q85

“Since equal weight correlation would provide a longer view of the correlation, this estimate would be preferred to the higher correlation provided by EWMA”
I think it means that equal weight put less weight on recent correlation, so it provides longer view.. Do i miss anything?

Frankly, I think consistency is part of an AIM:
"Discuss how correlations and covariances are calculated, and explain the consistency condition for covariances."

Thanks.

 

[David Harper CFA FRM]

Hi asja,

Yes, i know exactly what you mean (and some of it is not good difficulty)

Re: "I think it means that equal weight put less weight on recent correlation, so it provides longer view"
Yes, that is what it means ... but we are supposed to consider the trade-off between a longer view (more data) and relevance/recency (the use of VaR is going forward; longer is only better if its more representative going forward)

Thanks for the AIM reference, I see that now. The problem with including "explain the consistency condition for covariances" is they are referencing a deeper level without the associated depth; e.g., is this condition required or not? it depends on whether we require a "positive-semidefinite" covariance matrix...sometimes the answer isn't glib...

David

 

[rahul.goyl]

Hi David,

As far as I understand, lets take an example of 2 IT stocks A & B. The volatility of A & B are moderately different & have same (+ or -) correlation to market.
Suppose that firm A is Acquirer & B is Target, what we would probablt see in merger arbitrage is the stock prices of Acquirer (A) will decrease & target (B) will increase.
This will definately produce negative correlation between two IT firm in short-run (which is flawed), and that will be corrected itself after the merging of two firm. So I understand since we know the correlation is negative only for short period & wudn't stay long, we shouldn't use EWMA correlation but instead will use Equal weights.

I hope this make some sense for the answer B being correct. Plz correct if i am wrong..

Regards,
Rahul

 

[David Harper CFA FRM]

Hi Rahul,

I like your reasoning very much ... I think it's logical and consistent with what the questions expects for the correct answer.

Yet i still feel the question is unfair:
1. Can't you apply your reasoning to the volatility, also? i.e., volatility is artificially high due to merger announcement, so better to take a longer (equally weighted)
2. (the more technical point) an advanced candidate might recall Hull's consistency criteria and throw out (b) and (d), which I think would be valid if you remembered Hull's consistency criteria (to asja's point)

...so i see nothing wrong with your reasoning, I just see 2 other arguments that (IMO) make the question very debatable.

David

 

[rahul.goyl]

Hi david,
Thanks for you feedback, to take your first point.

I would like to put it in VaR termenology, the purpose here is VaR calculation, and you might need to take accurate volatility estimation to abide by strict Risk Controlling.
So taking EWMA is the only option from which you will be able to measure VaR with high precision. Recent Volatility may be high but not due to one factor (Merger) but there could be several other factors.
I am not so sure about Hull Consistency.
So as you pointed this is very debatable question.

Thanks
Rahul