Markowitz Portfolio Theory教学讲义.pptVIP

RMIT University Efficient set Efficient set – the set of mean-variance choices from the investment opportunity set where for a given variance (or standard deviation) no other investment opportunity offers a higher mean return. E(rp) σp RMIT University RMIT University Slide * Efficient Frontier Curve Decreases steadily as we move upward the curves implication: adding increments of risk as we move up the frontier gives diminishing increments of expected return Slope of efficient frontier Selection of the Optimal Portfolio How will the investor go about selecting the optimal portfolio? Investors will have to consider their indifference curves…. Put the investor’s indifference curves and the efficient frontier and go for the portfolio on the farthest northwest indifference curve, where the indifference curve is tangent to the efficient frontier. Minimum Variance Portfolio One way to understand the benefits of diversification is to look at the portfolio that provides the investor with the smallest possible variance: the global minimum-variance portfolio. In the case of a two stock portfolio (security 1 and 2), the weights in such a portfolio are given by the following: Perfect Negative Correlation With perfect negative correlation, , we face a situation where we can reduce portfolio risk to zero. In this case, the global minimum variance portfolio will have a variance of zero. The weights for security 1 and 2 in the global minimum variance portfolio are given by: Perfectly Negative Correlation E(R) Asset 1 Asset 2 Zero-Variance Portfolio Perfectly Positive Correlation When there are perfectly positive correlation, , the investor can ONLY reduce portfolio risk to zero if short-selling is available. When one of the assets has a low risk and low return, portfolio returns will be less than the return offered by the low return asset. In the case when short-selling is not available: The investor has to put his/her wealth in the lower risk as