Imagine that there are two stock markets in the world, whose relative capitalization weights are \(25 \%\) and \(75 \%\), respectively. The expected returns of the two markets are \(6 \%\) and \(4 \%\), and their volatilities are \(15 \%\) and \(10 \%\), respectively. Kurtosis of return is 5 in the first market and 7 in the second one; skewness is zero for both of them.

- Consider a risk-averse investor X, with logarithmic utility function. If she wants a portfolio with expected return of \(3 \%\), is it possible to achieve her objective?

- What is the volatility of the above portfolio, assuming that the two markets are statistically independent?

- Now assume that all investors are exactly like investor X. Is investor X still able to achieve the above portfolio at market equilibrium? Why?

- Can the CAPM hold for these two markets, populated by investors like \(\mathrm{X}\) ? Why?