1. a) The return on shares of the Orange Company are predicted under the following states of nature. The states of nature are all equally likely, and because there are a total of three states, each state has a 33.333% chance of occurring.

Recession -0.11

Normal +0.05

Boom +0.24

What is the standard deviation of Orange?

b) Toyota Corp.'s stock is $25 per share. Its expected return is 21% and variance is 10%. Honda Corp.'s stock is $23 per share. Its expected return is 20% and variance is 5%. Benz Corp.'s stock is $45 per share. Its expected return is 11% and variance 4%. What would be the expected return of a portfolio consisting of 50% Toyota and 50% Honda?

c) Toyota has an expected return of 24%, and a variance of 0.010. Honda has an expected return of 20%, and a variance of 0.008. The covariance between Toyota and Honda is 0.03. Using these data, calculate the variance of a portfolio consisting of 50% Toyota and 50% Honda.

d) The return on the Rush Corporation in the state of recession is estimated to be -24% and the return on Rush in the state of boom is estimated to be 34%. The return on the Oberman Corporation in the state of recession is estimated to be 44% 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 0.60 probability that the economy will be in the state of boom and a 0.40 probability that the economy will be in the state of recession.