# Covariances Between Asset Classes

Equities: Std Dev = 15; Corr w/ GIM = .85

Bonds: Std Dev = 8; Corr w/ GIM = .5

GIM: Std Dev = 10; Corr w/ GIM = 1

What is the covariance between Bonds and equities?

beta equities = cov (e,market)/var(market) = corr with GIM * std equity / std market = 0.85 * 15 / 10 = 1.275

beta bonds = .5 * 8 / 10 = 0.4

cov bond, equities = 1.275 * 0.4 * 10^2 = 51

Correct, Did you have to look it up? I would have before yesterday.

Try this:

The GIM is composed of 2 markets (Mkt 1 and Mt 2)

Equities: Std Dev = 15; Corr w/ Mkt 1 = .9; Corr w/ Mkt 2 = .7

Bonds: Std Dev = 8; Corr w/ Mkt 1 = .3; Corr w/ Mkt 2 = .6

Mkt 1: Std Dev = 12; Corr w/ Mkt 2 = .75

Mkt 2: Std Dev = 9; Corr w/ Mkt 1 = .75

Now what is the covariance b/w Equities and Bonds?

[original post removed]

wouldn’t we need the weights of the two markets in order to calculate the 2 asset portfolio SD?

you don’t need to use weightings of the 2 markets to find the answer. A hint on how to find the answer is to contemplate the use of a multi-factor model like:

R(GIM) = a + B1*F1 + B2*F2 + e

Where F1 & F2 are the respective markets and B1 and B2 are the Factor Beta’s corresponding to Equities and Bonds.

COV (eq,bond) =[BETA (eq, mkt 1) BETA (bond, mkt 1) Variance of mkt 1] + [BETA (eq, mkt 2) BETA (bond, mkt 2) Variance of mkt 2] + {[BETA (eq, mkt 1) BETA (bond, mkt 2) + BETA (eq, mkt 2) BETA (bond, mkt 1)]* COV (mkt 1, mkt 2}

So

BETA (eq, mkt 1) = [COR (eq, mkt 1) * STD DEV (eq)] divide by STD DEV (mkt 1)

= (0.9 X 15) / 12 = 1.125

BETA (eq, mkt 2) = [COR (eq, mkt 2) * STD DEV (eq)] divide by STD DEV (mkt 2)

= ( 0.7 X 15) / 9 = 1.17

BETA (bond, mkt 1) = [COR (bond, mkt 1) * STD DEV (bond)] divide by STD DEV (mkt 1)

= ( 0.3 X 8) / 12 = 0.2

BETA (bond, mkt 2) = [COR (bond, mkt 2) * STD DEV (bond)] divide by STD DEV (mkt 2)

= ( 0.6 x 8) / 9 = 0.533

COV (mkt 1, mkt 2) = COR (mkt 1, mkt 2) x STD DEV (mkt 1) x STD DEV (mkt 2)

= 0.75 x 12 x 9 = 81

COV (eq,bond) =[1.125 x 0.2 x 12^2] + [1.17 x 0.533 x 9^2] + {[1.25 x 0.533) + 1.17 x 0.2)] x 81

= 155.324

This is a Multifactor Model.

SCH says :

For the Exam: The odds of this particular calculation showing up on the exam are quite low. I would not place it on the high priority list, so don’t take time away from more important topics to memorize it.

100% correct! Although I got 151.39 due to rounding the Beta (eq,Mkt2) to 1.67.

I agree the second question is probably a low probability question, but it’s good practice. I think the first question posted is more probable since it shows up in example 19 of the reading, I wouldn’t be surprised to see something like that on the test.

I don’t know how many time’s I’ve gone over this reading and never paid any attention to it before. I’ve gone over a lot of the larger topics, so now I’m going through to find those smaller intricacies and the things that I’ve missed. This was one I found.

same like Volatility clustering one…

How do you move from “cov (e,market)/var(market)” to “corr with GIM * std equity / std market”

COV(a,b) = Corr(a,b)*Std Dev(a)*Std Dev(b)

so COV(a,b)/Var(b) = Corr(a,b)*Std Dev(a)/Std Dev(b).