Question

The return on the Rush Corporation in the state of recession is estimated to be -20% and the return on Rush in the state of boom is estimated to be 35%. The return on the Oberman Corporation in the state of recession is estimated to be 40% 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 0.70 probability that the economy will be in the state of boom and a 0.30 probability that the economy will be in the state of recession.

Answer 1

Expected Return for Rush Corporation = 0.7*35% + 0.3* -20% = 18.5%
Expected Return for Oberman Corporation = 0.7*-20%+0.3*40% = -2%

Covariance formula = Probability of Boom *(Return of Rush Corporation in boom - Expected return of Rush)*(Return of Oberman Corporation in boom - Expected return of Oberman )+ Probability of Recession*(Return of Rush Corporation in boom - Expected return of Rush)*(Return of Oberman Corporation in boom - Expected return of Oberman ) = 0.7*(35%-18.5%)*(-20%+2%)+0.3*(-20%-18.5%)*(40%+2%) = -0.0693

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