1. Managing Portfolios: Theory
Chapter 3
Managing Portfolios: Theory

2. Overview World of two risky assets Indifference curves
Determine the efficient frontier
Indifference curves
Critical to determine which portfolio should be held
World of three risky assets
World of N-risky assets
World of N-risky assets + a risk-free asset
Multifactor index models

3. Parameters for a Two-Security Portfolio
Where Wi = portfolio weight of asset i
Wj = portfolio weight of asset j
Wi + Wj = 1

4. Variances & Covariance
= variance of the rate of return on asset i
= variance of the rate of return on asset j
= covariance of the rate of return on asset i with the rate of return on asset j 4

5. Correlation Coefficient
Measure of co-movement tendency of two variables, such as returns on two securities 5

6. Examples of Correlation Coefficients

7. Three Special Cases Correlation coefficient = +1

8. Correlation Coefficient = +1

9. Correlation Coefficient = -1

10. Correlation Coefficient = -1

11. Correlation Coefficient = 0

12. Portfolio Risk: The Two-Asset Case

13. Efficient Frontier Set of risk - expected return Tradeoffs
Each Offers Highest Expected Return for a Given Risk and Least Risk for a Given Expected Return

14. Portfolio Standard Deviation: The General Case with Two Assets

15. Indifference Curves
Investor indifferent between any two portfolios on the same indifference curve
Investor prefers ANY portfolio on higher indifference curve to one on lower one
In theory, each investor could have a unique set of indifference curves
Cannot be scientifically measured, but critical to all investment decision making

16. Indifference Curves

17. Indiff. Curves: Four Examples

18. Optimal Portfolio to Hold When Correlation Coefficient = –1

19. Why Low Correlation Coefficients Are Desirable
NOT because they produce portfolios with least risk (or potentially no risk)
Because they allow an investor to achieve highest possible indifference curve

20. Three-Asset Portfolios: Looking Only at Combinations of Two Securities

21. Three-Asset Portfolios: Looking Only at Pairs of Pairs

22. N-Asset Portfolio E(Rp) = W1[E(R1)] + W2[E(R2)] + … + Wn[E(Rn)]
(continued)

23. N-Asset Portfolio (continued)

24. Optimal Portfolio to Hold: Risk Averse Investor

25. Optimal Portfolio to Hold: Aggressive Investor

26. Adding the Risk-free Rate26

27. Market Portfolio
Hypothetical portfolio representing each investment asset in the world in proportion to its relative weight in the universe of investment assets

28. Separation Theorem
Return to any efficient portfolio and its risk can be completely described by appropriate weighted average of two assets
the risk-free asset
the market portfolio
Two separate decisions
What risky investments to include in the market portfolio
How one should divide one’s money between the market portfolio and risk-free asset

29. Capital Market Line: Better Efficient Frontier

30. Capital Asset Pricing Model
Theoretical relationship that explains returns as function of risk-free rate, market risk premium, and beta

31. Beta
Parameter that relates stock or portfolio performance to market performance
Example: with x percent change in market, stock or portfolio will tend to change by x percent times its beta

32. Implications of Beta Value
Beta < 0 => opposite of the market
Beta = 0 => independent of the market
0 < Beta < 1 => same as market, but less volatile
Beta = 1 => identical to the market
Beta > 1 => same as market, but more volatile

33. Portfolio Beta

34. Market Model Where Ri = return to asset i
Rm = return to the market in the same period
alpha = y-intercept value
beta = slope of the line
eta = random error term

35. Market Risk vs. Nonmarket Risk
i2 = (beta2 x M2 ) + eta2
Total risk = market risk + nonmarket risk

36. Nonmarket Risk Not related to general market movements Diversifiable
Total risk of investment may be decomposed into that associated with market and that which is not
Nonsystematic risk

37. Coefficient of Determination
Statistic that measures how much of variance of particular time series or sample of dependent variable is explained by movement of the independent variable(s) in a regression analysis
Measure of diversification with respect to portfolios

38. Multifactor Asset Pricing Model
Model of stock pricing
Relies on arbitrage pricing multifactor model rather than the capital asset pricing model

39. Arbitrage Pricing Model
Model used to explain stock pricing and expected return
Introduces more than one factor in place of (or in addition to) the capital asset pricing model’s market index

40. Does MPT Matter? Uniform Principal and Income Act
Prudent man has evolved to prudent investor
A model is better than no model
Departure point for how we think about what is happening in security markets