1. Modern Portfolio Concepts
Chapter 5
Modern Portfolio Concepts

2. Required computations (10-12)
Various return concepts (HPR, IRR, realized return, expected return)
Compute the average return and standard deviation on a time series using excel.
Compute the mean/expected return and standard deviation given scenarios with probabilities.
Compute the mean return, beta of a portfolio of multiple assets
Compute the standard deviation of a two-asset portfolio
Apply CAPM to compute required rate of return, return sensitivity to market moves, and market risk premium.

3. What is a Portfolio?
Portfolio is a collection of investments assembled to meet one or more investment goals.
Efficient portfolio
A portfolio that provides the highest return for a given level of risk
Requires search for investment alternatives to get the best combinations of risk and return

4. Portfolio Return and Risk Measures
The return on a portfolio is simply the weighted average of the individual assets’ returns in the portfolio
The standard deviation of a portfolio’s returns is more complicated, and is a function of the portfolio’s individual assets’ weights, standard deviations, and correlations with all other assets

5. Return on Portfolio

6. Correlation: Why Diversification Works!
Correlation is a statistical measure of the relationship between two series of numbers representing data
Positively Correlated items tend to move in the same direction
Negatively Correlated items tend to move in opposite directions
Correlation Coefficient is a measure of the degree of correlation between two series of numbers representing data

7. Correlation Coefficients
Perfectly Positively Correlated describes two positively correlated series having a correlation coefficient of +1
Perfectly Negatively Correlated describes two negatively correlated series having a correlation coefficient of -1
Uncorrelated describes two series that lack any relationship and have a correlation coefficient of nearly zero

8. Figure 5.1 The Correlation Between Series M, N, and P

9. Correlation: Why Diversification Works!
Assets that are less than perfectly positively correlated tend to offset each others movements, thus reducing the overall risk in a portfolio
The lower the correlation the more the overall risk in a portfolio is reduced
Assets with +1 correlation eliminate no risk
Assets with less than +1 correlation eliminate some risk
Assets with less than 0 correlation eliminate more risk
Assets with -1 correlation eliminate all risk

10. Figure 5.2 Combining Negatively Correlated Assets to Diversify Risk

11. Figure 5.3 Portfolios of IBM and Celgene

12. Figure 5.4 Risk and Return for Combinations of Two Assets with Various Correlation Coefficients

13. Why Use International Diversification?
Offers more diverse investment alternatives than U.S.-only based investing
Foreign economic cycles may move independently from U.S. economic cycle
Foreign markets may not be as “efficient” as U.S. markets, allowing true gains from superior research

14. International Diversification
Advantages of International Diversification
Broader investment choices
Potentially greater returns than in U.S.
Reduction of overall portfolio risk
Disadvantages of International Diversification
Currency exchange risk
Less convenient to invest than U.S. stocks
More expensive to invest
Riskier than investing in U.S.

15. Methods of International Diversification
Foreign company stocks listed on U.S. stock exchanges
Yankee Bonds
American Depository Shares (ADS’s)
Mutual funds investing in foreign stocks
U.S. multinational companies (typically not considered a true international investment for diversification purposes)

16. Components of Risk Diversifiable (Unsystematic) Risk
Results from uncontrollable or random events that are firm-specific
Can be eliminated through diversification
Examples: labor strikes, lawsuits
Nondiversifiable (Systematic) Risk
Attributable to forces that affect all similar investments
Cannot be eliminated through diversification
Examples: war, inflation, political events

17. Components of Risk

18. Beta: A Popular Measure of Risk
A measure of undiversifiable risk
Indicates how the price of a security responds to market forces
Compares historical return of an investment to the market return (the S&P 500 Index)
The beta for the market is 1.0
Stocks may have positive or negative betas. Nearly all are positive.
Stocks with betas greater than 1.0 are more risky than the overall market.
Stocks with betas less than 1.0 are less risky than the overall market.

19. Figure 5.5 Graphical Derivation of Beta for Securities C and D*

20. Beta as a Measure of Risk
Table 5.4 Selected Betas and Associated Interpretations

21. Interpreting Beta
Higher stock betas should result in higher expected returns due to greater risk
If the market is expected to increase 10%, a stock with a beta of 1.50 is expected to increase 15%
If the market went down 8%, then a stock with a beta of 0.50 should only decrease by about 4%
Beta values for specific stocks can be obtained from Value Line reports or websites such as yahoo.com

22. Interpreting Beta

23. Capital Asset Pricing Model (CAPM)
Model that links the notions of risk and return
Helps investors define the required return on an investment
As beta increases, the required return for a given investment increases

24. Capital Asset Pricing Model (CAPM) (cont’d)
Uses beta, the risk-free rate and the market return to define the required return on an investment

25. Capital Asset Pricing Model (CAPM) (cont’d)
CAPM can also be shown as a graph
Security Market Line (SML) is the “picture” of the CAPM
Find the SML by calculating the required return for a number of betas, then plotting them on a graph

26. Figure 5.6 The Security Market Line (SML)

27. Two Approaches to Constructing Portfolios
Traditional Approach versus Modern Portfolio Theory

28. Traditional Approach
Emphasizes “balancing” the portfolio using a wide variety of stocks and/or bonds
Uses a broad range of industries to diversify the portfolio
Tends to focus on well-known companies
Perceived as less risky
Stocks are more liquid and available
Familiarity provides higher “comfort” levels for investors

29. Modern Portfolio Theory (MPT)
Emphasizes statistical measures to develop a portfolio plan
Focus is on:
Expected returns
Standard deviation of returns
Correlation between returns
Combines securities that have negative (or low-positive) correlations between each other’s rates of return

30. Key Aspects of MPT: Efficient Frontier
The leftmost boundary of the feasible set of portfolios that include all efficient portfolios: those providing the best attainable tradeoff between risk and return
Portfolios that fall to the right of the efficient frontier are not desirable because their risk return tradeoffs are inferior
Portfolios that fall to the left of the efficient frontier are not available for investments

31. Figure 5.7 The Feasible or Attainable Set and the Efficient Frontier

32. Key Aspects of MPT: Portfolio Betas
The beta of a portfolio; calculated as the weighted average of the betas of the individual assets the portfolio includes
To earn more return, one must bear more risk
Only nondiversifiable risk (relevant risk) provides a positive risk-return relationship

33. Figure 5.8 Portfolio Risk and Diversification

34. Key Aspects of MPT: Portfolio Betas
Table 5.6 Austin Fund’s Portfolios V and W

35. Interpreting Portfolio Betas
Portfolio betas are interpreted exactly the same way as individual stock betas.
Portfolio beta of 1.00 will experience a 10% increase when the market increase is 10%
Portfolio beta of 0.75 will experience a 7.5% increase when the market increase is 10%
Portfolio beta of 1.25 will experience a 12.5% increase when the market increase is 10%
Low-beta portfolios are less responsive and less risky than high-beta portfolios.
A portfolio containing low-beta assets will have a low beta, and vice versa.

36. Interpreting Portfolio Betas
Table 5.7 Portfolio Betas and Associated Changes in Returns

37. Reconciling the Traditional Approach and MPT
Recommended portfolio management policy uses aspects of both approaches:
Determine how much risk you are willing to bear
Seek diversification between different types of securities and industry lines
Pay attention to correlation of return between securities
Use beta to keep portfolio at acceptable level of risk
Evaluate alternative portfolios to select highest return for the given level of acceptable risk

38. Figure 5.9 The Portfolio Risk-Return Tradeoff