Covariance question

CFA Level III
#1

I have seen a question that asks for covariance between market 1 and market 2 given: Covariance matrix Global Equity Global Bonds Global Equity 0.225 0.0022 Global Bonds 0.0022 0.0025 Factor sensitivities Global Equity Global Bonds Market 1 1.2 0 Market 2 0.9 0

Answer is given as: M12 = (1.20 × 0.90 × 0.0225) + (0 × 0 × 0.0025) + [(1.20 × 0) + (0 × 0.90)] × 0.0022 = 0.0243. Can someone explain their formula and whatever happened to our covariance between two markets formula of B1 x B2 x variance of return to market?

#2

This is based on market factor model. Not based on historical estimate of covariance.

#3

Thanks, 1. What reading is market factor models in?

  1. Why can’t we use the Beta x Beta x variance of market returns formula?
#4

Reading is on capital market expectation. I guess the number given here is not the same as your beta x beta x variance marker formula. Also this is a 2 factor model. It just a different model to use to find covariance. I not an expert on this btw

#5

it would be a bit harsh if this came up…

#6

This is the factor covariance matrix formula. It’s the hardest formula to remember, and I am not going to bother. They can have the 3 points if they put it in the PM exam. If it’s 8 marks in the AM, I’ll start weeping in the exam.

#7

Where in the curriculum is this equation?

#8

it’s in Applications of Economic Analysis to PM under statistical forecasting tools

#9

Mij=bi1bj1Var(F1)+bi2bj2Var(F2)+(bi1bj2+bi2bj1)Cov(F1,F2) + Var(εi)

#10

I think it’s easier to memorize the example they provide in the curriculum than that formula…

#11

it’s actually very similar to the variance of a 2-asset portfolio formula…

just with b1 x b2 instead of b1^2 = (b1 x b1)