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 -0.08 in recession,and 0.16 in boom. The analyst consider each state to be equally likely.

Compute the correlation coefficient between Goldday and the Market.

Answer 1

To compute the correlation coefficient between Goldday Corporation's shares and the market portfolio, one needs to calculate the expected returns, variances, and covariance of the two and then use the formula for correlation coefficient. The expected returns, variances, and covariance are determined based on the given state-dependent returns and their equal probability.

Step-by-step explanation:

To compute the correlation coefficient between Goldday and the Market, we must first calculate the expected returns, variances, and covariance between the two sets of returns. Given that these states are equally likely, we can determine these statistical measures to further compute the correlation coefficient.

• Expected Return of Goldday = (0.5 * (-0.04)) + (0.5 * 0.10) = 0.03 or 3%
• Expected Return of the Market = (0.5 * (-0.08)) + (0.5 * 0.16) = 0.04 or 4%
• Variance of Goldday = (0.5 * (-0.04 - 0.03)^2) + (0.5 * (0.10 - 0.03)^2)
• Variance of the Market = (0.5 * (-0.08 - 0.04)^2) + (0.5 * (0.16 - 0.04)^2)
• Covariance of Goldday and the Market = (0.5 * (-0.04 - 0.03) * (-0.08 - 0.04)) + (0.5 * (0.10 - 0.03) * (0.16 - 0.04))

After calculating these values, use the formula for correlation coefficient:

\( \rho = \frac{\text{Covariance}(\text{Goldday}, \text{Market})}{\sqrt{\text{Variance}(\text{Goldday}) \times \text{Variance}(\text{Market})}} \)

Finally, divide the computed covariance by the product of the standard deviations of Goldday's and the Market's returns to obtain the correlation coefficient.