# Question: Suppose there are three states of the economy boom moderate

Suppose there are three states of the economy: boom, moderate growth, and recession. The annual return on Honda and Toyota stock in each state of the economy is shown in the file S04_66.xlsx.
a. Calculate the mean and standard deviation of the annual return on each stock, assuming the probability of each state is 1/3.
b. Calculate the mean and standard deviation of the annual return on each stock, assuming the probabilities of the three states are 1/4, 1/4, and 1/2.
c. Calculate the covariance and correlation between the annual returns of the two companies’ stocks, assuming the probability of each state is 1/3.
d. Calculate the covariance and correlation between the annual returns of the two companies’ stocks, assuming the probabilities of the three states are 1/4, 1/4, and 1/2.
e. You have invested 25% of your money in Honda and 75% in Toyota. Assuming that each state is equally likely, find the mean and variance of your portfolio’s return.
f. Now check your answer to part e by directly calculating the return on your portfolio for each state and use the formulas for mean and variance of a random variable. For example, in the boom state, your portfolio earns 0.25(0.25) + 0.75(0.32).

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