Covariances? Is anyone bothering to learn this?

CFA Level III
#1

So quesiton 3 of the 3rd vignette of CFAI mock V1, has this ridiculous quesiton that requires covariances.

This seems to me like one of the “More effort than its worth” types of subjects. But just in case it’s not, has anyone been able to make sense of this answer?

Based on the correlation that Li’s team believes to exist between the CCIRP and TELIRP, the new volatility for the SCIRP is closest to:

A. 56.4%.

B. 31.8%.

C. 49.1%.

Answer = A

“Capital Market Expectations,” John P. Calverley, Alan M. Meder, Brian D. Singer, and Renato Staub Section 3.1.1.4

Begin with:

Var (M) = Var (_F_1)× (_b_1)2 + Var (_F_2) × (_b_2)2 + 2 × _b_1 × _b_2 × Cov (_F_1, _F_2) +

Var (ε).

Find the variance of the error term using values from Exhibit 2:

0.2704 = 0.0784 × (1.020)2+ 0.1024 × (1.045)2 + 2 × 1.020 × 1.045 × 0 +

Var (ε),

Var (ε) = 0.0770.

The adjustment is stated as being a correlation of 0.25.

Change the correlation into a covariance:

Cov(F1,F2) = Corr(F1,F2) × Std Dev (F1) × Std Dev (F2)

= 0.25 × (0.0784)0.5 × (0.1024)0.5 = 0.0224

The volatility of SCI after adjusting for the correlation is √0.3181 = 56.4%

#2

Practice it once or twice (or three times). Eventually, it’ll stick.

#3

Can anyone explain how they jump from Cov(F1,F2) = 0.0224 to vol = sqrt(0.3181) = 56.4%? I did this question a few weeks ago and completely blanked and haven’t looked at it since… Thanks

#4

Var (M) = Var (_F_1)× (_b_1)2 + Var (_F_2) × (_b_2)2 + 2 × _b_1 × _b_2 × Cov (_F_1, _F_2) + Var (ε).

and this with a correlation of 0 = 0.2704

with the correlation of 0.25 -> cov(F1,F2) = 0.0224

so the above become 0.2704 + 2 (1.02) * (1.045) (0.0224) = 0.3181

#5

Yea I didn’t understand that one at first either, and the explanation makes this crazy jump that it doesn’t even have to…weird. But I worked thru it and learned some of the basic covariance stuff, but there’s a lot more info about calculating it and with betas and stuff and I didn’t really go thru all that…could’ve tho, there’s enough there to eat up some precious hours. If it’s on there, those are points I’ll just be giving up. Time better spent elsewhere at this point

#6

Yeah what was the purpose of solving for e? and why do we assume the adjustment is just equal to 0.2704 + 2 (1.02) * (1.045) (0.0224) = 0.3181? I think I might have to count a loss on this if i see it…

#7

No clue. I wrote this off. If it shows up on the exam then the correct answer will hopefully be B. If it shows up on the AM session I’ll curse and try to make the points up somewhere else. Then I’ll sit in my car cursing while eating my lunch.

#8

Why always B would be right choice when someone try to guess? Urban legend. I am for A, like AAA.:slight_smile:

#9

BTW, I am able to solve for 2 factor covariance but I have totally given up from residual variance calculation.

#10

It is linear algebra, and these calculations are the way they are due to matrix multiplication properties.

For example, famous formula for the standard deviation of 2 asset portfolio is often presented as w1^2*sd1^2+w2^2+sd^2+2corr*sd1*sd2*w1*w2

If you were to do a 3 asset portfolio calculation it would get much longer. But if you know matrix multiplication and know that SD of any asset portfolio is sqrt(w’ Omega w) where w is vector of weights and omega is covariance matrix, you can calculate sd of 1000-asset portfolio.

#11

Correct if you do these steps in Excel or some other program, but working manually with limited time has probability of error in calculation of just 99% for matrix with more than 2 factors.

#12

is this required, i really wanna vomit looking at this even

#13

This shouldn’t be too difficult?

It’s just the standard formula plus an error term to remember for level 3?

#14

Which topic is this from?

#15

Capital Market Expectations. Multifactor models.