APT (Practice Question 2011)

[EIA]

Hi David,

I trust you are doing well.

Kindly shed more light on question 6 of part 1 exam 1 of the practice question 2011 and question 7 of part 1 exam 2 of the same practice question.

Thanks for your usual assistance.

BR

EMMY

 

[David Harper CFA FRM]

Hi EMMY,

Thanks, I hope your studies are going well.

I consider both of these difficult. The less difficult one is 2011.Part1.Exam2.Question 7.

This is sort of classic GARP, an basic idea is wrapped in an unfamiliar presentation and rendered more difficult.

The setup suggests that the investment return is:
return (investment) = beta/sensitivity * factor + beta/sensitivity * factor;
return (investment) = 0.75 * factor_equity + 0.20 * factor_bond
... i think it is good to hover here: this is the APT with 2 factors, it is a RETURN not a variance/volatility, and it is a linear combination and so mathematically looks very much like the classic two-asset portfolio. It is a two asset portfolio except instead of explicit weightings to positions, we are weighting factors! I think, once seen this way, the next is easy (easier)

We only need: Variance(aX + bY) = a^2*Variance(X) + b^2*Variance(Y) + 2*a*b*Covariance(X,Y)
In this case, Variance [return (investment)]
= Variance (0.75 * factor_equity + 0.20 * factor_bond) = 0.75^2*variance(factor_equity) + 0.20^2*variance(factor_bond) + 2*(0.75)(0.20)*covariance(factor_equity,factor_bond)
... so i agree with the answer
... of course you have to realize that the diagonal of the covariance matrix contains variances; e.g., covariance (factor_equity, factor_equity) = variance(factor_equity)

In regard to 2011.Part1.Exam1.Question 6, I am frankly now sure where/if the curriculum has a source here (I am not sure how you can be expected to know this). They are using a property of covariance, See sixth row under http://en.wikipedia.org/wiki/Covariance,
the solution is the Cov(aX + bY, cW + dV) ... it's not as bad as it looks, it is just all four combinations X,Y,W,V; but in this case we have:
Cov (aE + bB, cE + dB), where capital E = equity factor and capital B = bond factor, and this equals:
acCov (E,E) + adCov(E,B) + bcCov(B,E) + bdCov(B,B)
= acVariance(E) + [adCov(E,B) + bcCov(B,E)] + bdVariance(B); i.e., Cov(E,E) = Variance(E)
= acVariance(E) + (ad + bc)*Cov(E,B) + bdVariance(B); i.e., Cov(E,B) = Cov(B,E)
That is the formula used. Unfairly difficult IMO, but still instructive.

I hope that helps, David

 

[[email protected]]

Hi, David. I am wondering if there's any 2011 practice question on T1? I only found 2010's practice questions after filtering "Essential, Level 1". I also found a practice set on Grinold Chapter 7, but I dont see his name in required reading. Maybe I am missing something? Thanks.

 

[David Harper CFA FRM]

Hi sabrinaquan,

There should be 5 PDFs under T1 @ http://www.bionicturtle.com/my-account/study-planner?product=level-1
i.e., you are not missing anything if you see:

• T1.Jorion Chapter 1
• T1.Grinold Chapter 7
• T1.Stulz Chapter 3
• T1.Allen Chapter 4
• T1.Amenc Chapter 4

(The dates attached to the listings are not per se meaningful: they are used to control the SORT order in the planner)

But you are correct as I am always rotating through the AIMs, the majority of them were written in 2010.

(it shouldn't frankly matter for APT: the reading was switched from Grinold to Elton, but the exam treats APT superficially such that Grinold is applicable).

Thanks, David