Suppose you group all the stocks in the world into mutually exclusive portfolios (each stock is in only one portfolio): growth stocks and value stocks. Suppose the two portfolios have equal size (in terms of total value), a correlation of 0.5, and the following characteristics:

The risk free-rate is 2%.

a. What is the expected return and volatility of the market portfolio (which is a 5050 combination of the two portfolios)?

b. Calculate the Sharpe ratios of the value stock, growth stock, and market portfolio.

c. Does the CAPM hold in this economy?

(Hint:Is the market portfolio efficient?)

Could you kindly include the formulas? I found different formulas to solve this problem in different resources, and I am not sure which one is the right one to use in this case.

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