Question

6，The return on the Rush Corporation in the state of recession is estimated to be -23% 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 42% and the return on Oberman in the state of boom is estimated to be -18%. 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.

——————Place your answer in decimal form and not as a percentage.

7，Toyota Corp.'s stock price has a variance of returns of 0.0325. Honda Corp.'s stock has a variance of returns of 0.0475. The covariance between Toyota and Honda is 0.0285. What is the correlation coefficient between Toyota and Honda?

———————Use at least four decimal places in your answer.

Answer 1

Answer 6)

Average return on Rush corporation = probability of boom x return on boom + probability of recession x return during recession
=  0.70 x 35 % + 0.30 x - 23 %
= 24.4 % - 6.9 %
Average return on Rush corporation = 17.3 %

Average return on Oberman corporation = probability of boom x return on boom + probability of recession x return during recession
= 0.70 x - 18 % + 0.30 x 42 %
= - 12.6 % + 12.6 %
= 0 %

Covariance between Rush and Oberman = 0.70 x[ ( 35 % - 17.3 %) x ( - 18 % - 0 %) ] + 0.3 x [ ( -23 % - 17.3 %) x ( 42 % - 0 %)

Covariance between Rush and Oberman = 070 X [17.7 % x -18 %] + 0.3 x [ - 40.3 % x 42 %]
Covariance between Rush and Oberman = 0.70 x - 318.6 % + 0.30 x - 1692.6 %
Covariance between Rush and Oberman = - 223.02 % - 507.78 %
Covariance between Rush and Oberman = - 730.80 %
Covariance between Rush and Oberman = - 7.308

Q 7)

Given

variance of Toyota Corp.'s stock price = 0.0325
variance of Honda Corp.'s stock price = 0.0475
Covariance between Toyota and Honda is = 0.0285

Standard deviation of  Toyota Corp's stock price = (0.0325)^0.5 = 0.1803
Standard deviation of Honda Corp.'s stock price = (0.0475)^0.5 = 0.2179

Correlation coefficient between Toyota and Honda = Covariance between Toyota and Honda / ( Standard deviation of  Toyota Corp's stock price x Standard deviation of Honda Corp.'s stock price )

Correlation coefficient between Toyota and Honda = 0.0285 / ( 0.1803 x 0.2179)
Correlation coefficient between Toyota and Honda = 0.0285 / 0.03928
Correlation coefficient between Toyota and Honda = 0.7256