Modern Portfolio Theory (MPT). Introduction. Portfolio theory is about finding the balance between maximizing your return and minimizing your risk . The objective is to select your investments in such as way as to diversify your risks while not reducing your expected return.
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Investment A is the obvious choice…
… but add risk, is the choice still obvious?
B would die out through lack of takers
Negatively correlated assets cancel the greatest amount of each other’s volatility.
E[Rp] = the expected return on the portfolio,
N = the number of stocks in the portfolio,
wi = the proportion of the portfolio invested in stock i, and
E[Ri] = the expected return on stock i.
Ex - A portfolio consists of two securities 1 and 2 , in the proportions 0.6 and 0.4. The standard deviations of the returns on securities 1 and 2 are 10 and 16 respectively. The coefficient of correlation between the returns on securities 1 and 2 is 0.5. What is the standard deviation of portfolio return?
Ex - The standard deviations of the returns on asset 1 and 2 are 4% and 7.27% respectively. The covariance between the returns on assets 1 and 2 is 29. What is the coefficient of correlation between the returns on assets 1 and 2?
Efficient portfolios on or near the efficient frontier
Inefficient portfolios below efficient frontierEfficient Frontier