Question

Financial analysts have estimated the returns on shares of the Goldday Corporation and the overall market portfolio under two economic states nature as follows. For Goldday the state dependent returns are -0.04 in recession, and 0.10 in an economic boom. For the market the state dependent returns are -0.06 in recession,and 0.14 in boom. The analyst estimates that the probability of a recession is 0.50 while the probability of an economic boom is 0.50. Compute the covariance between Goldday and the market.'

Answer 1

Answer:

covariance = 0.0070

Explanation:

Given data :

probability of recession = 0.5 , probability of economic boom = 0.5

For Goldday corporation

During Recession

probability = 0.5

return on stocks = -0.04

expected return = 0.5 * - 0.04 = - 2.00%

deviation 1 = - 7% ( -0.04 - average return )

Prob * deviation ^2 = 0.5 * (- 7% )^2 = 0.002450

During Economic boom

probability = 0.5

return on stocks = 0.10

expected return = 0.5 * 0.10 = 5%

deviation 1 = 0.10 - average return = 7%

Prob * deviation^2 = 0.5 * ( 7%)^2 = 0.002450

Hence for Goldday corporation

average return = ∑ expected returns = 3%

variance = ∑ Prob * deviation^2 = 0.0049

std = √0.0049 = 7%

Note : perform the same calculation for the  Market

For Market

average return =  ∑ expected returns  = 4%

variance = ∑ Prob * deviation^2 = 0.01000

std = √ variance = 10%

Determine the covariance between Goldday and the MARKET

= ∑ ( deviation 1 * deviation 2 * probability )

=       recession    +  economic boom

= ( - 7% * - 10% * 0.5 ) + ( 7% * 10% * 0.5 )

= 0.0035 + 0.0035 = 0.0070  --------->  answer