Answer:
covariance = 0.0070
Explanation:
Given data :
probability of recession = 0.5 , probability of economic boom = 0.5
<u>For Goldday corporation</u>
<em>During Recession </em>
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
<em>During Economic boom</em>
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%
<u>Determine the covariance between Goldday and the MARKET </u>
= ∑ ( deviation 1 * deviation 2 * probability )
= recession + economic boom
= ( - 7% * - 10% * 0.5 ) + ( 7% * 10% * 0.5 )
= 0.0035 + 0.0035 = 0.0070 ---------> answer
