Modern Portfolio Theory (MPT)

1. Modern Portfolio Theory (MPT)

2. 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. • Emphasizes statistical measures to develop a portfolio plan • Focus is on: • Expected returns • Standard deviation of returns • Correlation between returns

3. A A B B Expected Returns Investment A is the obvious choice… … but add risk, is the choice still obvious? B would die out through lack of takers

4. Correlation between Returns • Correlations can range from -1 (perfectly negatively correlated) through to +1 (perfectly positively correlated). • If asset B tends to move in the opposite direction to asset A then these two assets are said to have “negative correlation”, and they can be highly effective at cancelling out each other’s volatility. • If the assets both trend upwards over the longer term a combination of them will have a return equal to the average of the two assets’ returns but with substantially reduced volatility.

5. Correlation between Returns Negatively correlated assets cancel the greatest amount of each other’s volatility.

6. Types of Correlation • Positive Correlation • Perfect Positive Correlation • Zero Correlation • Negative Correlation • Perfect Negative Correlation

7. Portfolio Return and Risk • Portfolio Expected Return where 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.

8. Portfolio Risk 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?

9. Coefficient of Correlation • where • r12 = the correlation coefficient between the returns on stocks 1 and 2, • s12 = the covariance between the returns on stocks 1 and 2, • s1 = the standard deviation on stock 1, and • s2 = the standard deviation on stock 2.

10. Coefficient of Correlation 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?

11. Return Efficient portfolios on or near the efficient frontier Risk Inefficient portfolios below efficient frontier Efficient Frontier

12. Efficient Frontier • The “efficient frontier” is the name of the line that joins all portfolios that have achieved a maximum return for a given level of risk (portfolios that are “efficient”). • The top of the curve and anything actually on the curve, or close to it, is an “efficient” frontier or portfolio, anything below that curve is an “inefficient” portfolio.

13. Optimal Portfolio • The optimal portfolio is found at the point of tangency between the efficient frontier and a utility indifference curve. • The point represents the highest level of utility the investor can reach.