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

The covariance between Goldday Corporation and the market portfolio can be calculated using the given returns under different economic states and their associated probabilities. The expected returns are computed for each and then used to find the covariance, which is found to be 0.007 for the given conditions.

Step-by-step explanation:

The computation of the covariance between the returns on shares of Goldday Corporation and the overall market portfolio involves measuring how the returns on Goldday shares move in relation to the market portfolio. Using the given state-dependent returns for each economic state (recession and boom) and their associated probabilities, we can calculate the expected returns and then find the covariance.

First, calculate the expected returns (ER) for Goldday (ER_G) and the market (ER_M):
ER_G = (Probability of Recession * Return in Recession) + (Probability of Boom * Return in Boom)
ER_M = (Probability of Recession * Return in Recession) + (Probability of Boom * Return in Boom)

Next, calculate the products of deviation scores for corresponding states of the economy and their probabilities to find the covariance:
Covariance = Σ(Probability(i) * (Return of Goldday in state i - ER_G) * (Return of Market in state i - ER_M))

Applying these steps with the provided numbers:

• ER_G = (0.50 * -0.04) + (0.50 * 0.10) = 0.03
• ER_M = (0.50 * -0.06) + (0.50 * 0.14) = 0.04

Then we calculate the covariance:

• Covariance = (0.50 * (-0.04 - 0.03) * (-0.06 - 0.04)) + (0.50 * (0.10 - 0.03) * (0.14 - 0.04)) = 0.50 * (0.07 * 0.10) + 0.50 * (0.07 * 0.10) = 0.007

The covariance between Goldday and the market under the given conditions is 0.007.

Answer 2

covariance = 0.0070

Step-by-step 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