Question

The return on the Rush Corporation in the state of recession is estimated to be -25% and the return on Rush in the state of boom is estimated to be 32%. The return on the Oberman Corporation in the state of recession is estimated to be 42% and the return on Oberman in the state of boom is estimated to be -20%. Given this information, what is the covariance between Rush and Oberman if there is a 0.50 probability that the economy will be in the state of boom and a 0.50 probability that the economy will be in the state of recession.

Answer 1

Calculation of Covariance between Rush Corporation and Oberman Corporation:

State	Probability	Rush Corp	Oberman Corp	Deviation of Rush	Deviation of Oberman	Deviation of Rush* Deviation of Oberman
Recession	0.5	-25	42	-28.5	31	-883.5
Boom	0.5	32	-20	28.5	-31	-883.5
		3.5	11			-883.5

Expected returns of Rush Corp = 0.5*(-25)+0.5*32

= 3.5%

Expected returns of Oberman Corp = 0.5*42+0.5*(-20)

= 11%

Covariance = Σ(Deviation of Return of Rush*Deviation of Return of Oberman)*Probability

= - 0.50*883.50-0.50*883.50

= - 883.50