Are the following statements true or false? Given your reasons.

a$)$ In a portfolio of two assets, diversification will not work if the two assets are positively correlated.

b$)$ The volatility of a stock index depends exclusively on the volatilities of the assets included in the index.

c$)$ For mean$-$variance analysis to hold we need to make two assumptions: quadratic utility for investors and normality for returns.

d$)$ Along the mean$-$variance frontier, higher risk is always associated with higher return.

e$)$ Along the efficient frontier, higher risk is always associated with higher return.

f$)$ Along the capital market line, an additional unit of risk always provides the same additional excess return.

g$)$ Along the capital market line, no matter what your risk aversion is$,$ your optimal portfolio always achieves the same Sharpe ratio.

h$)$ For the maximum expected utility strategy, investors with low risk aversion will put more weight on the riskless asset.

i$)$ For the maximum expected return strategy, investors who set a high target portfolio volatility will put less weight on the riskless asset.

j$)$ For the minimum volatility strategy, investors who set a high target portfolio expected return will form a portfolio with high volatility and high Sharpe ratio.