Calculating Covariance - Required

CFA Level III
#1

I saw this on 2011 Mock PM #29, having to calculate covariance of 2 markets based on market factor sensitivities and residual risk. I don’t remember seeing this in the 2013 curricculum - does anyone else?

Thanks!

#2

under cap mkt epecataions. it’s there

annoying but there. See 2013 mock #27

#3

That’s a sneaky formula. You never know but I’d guess that it’s just there to make the mocks more challenging.

#4

The LOS it’s under, 18C, is one of the most ambiguous descriptions of all time. “Demonstrate the application of formal tools for setting CME…etc…”

Anyone have a good way to remember that formula? It’s a fucking bear…

#5

isn’t it just the formula to calculate the standard deviations of 2 correlated assets, just saying Var instead of sd^2?

#6

Right. Use variance times beta coefficient for each.

#7

you’re mixing up covariance and variance / std dev.

#8

you also need to use beta instead of weight. just calculate the error term first from the given numbers then calculate it with the new correlation

#9

Portfolio Variance formula. Check. Beta instead of weights. Check. Where does the error term fit in?

#10

you will be given the varriance (A) of the index and 2 variances (B & C) and their betas that are correlated to the index the question will ask you to calculate a new variance given a new correlation.

Step 1) find the error term ( just a plug in)

Variance A = Variance B x Beta B squared + variance C x beta C squared +2 x SD B x SD c X beta b x beta c x corelation + ERROR TERM ( this is the plug in that you will have to find first)

step 2) calculate the ne variance given the new estimates.

Variance A = Variance B x Beta B squared + variance C x beta C squared +2 x SD B x SD c X beta b x beta c x corelation + ERROR TERM ( you add the error term found in step 1)

#11

Gotcha. I’ll try that one out. Thanks!

The CFAI text made it look awful.

#12

If you looked at the problem in the mock in a different way … you actually do not need to do anything at all.

2 ways that I know of:

Way 1:

  1. They gave the current variance = 0.2704 with 0 correlation -> 0.52 (or 52% std dev).

  2. they told you that correlation was now 0.25 … so std dev must go up. Only one answer choice 56.4 met that criterion.

So you have your answer right away.

Way 2:

How to calculate to make certain?

New term that gets added = 2 x SD B x SD c X beta b x beta c x corelation

= 2 * 1.02 * 1.045 * 0.0784^0.5 * 0.1024^0.5 * 0.25 = 0.04775

Add to 0.2704 = 0.3181

sqrt (0.3181) = .564 = 56.4%