1. McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Efficient Diversification Module 5.3

2. 11-1 Motivation  Note that in the prior module, we measured portfolio risk and return using an equally- weighted portfolio (50% in each asset).  We didn’t have any particular reason to choose equal weights.  Ideally, we want to choose weights such that the ratio of expected return per unit risk is the highest.

3. 11-2 11.4 Expected Return and Risk at various weights: We can consider other portfolio weights besides 50% in stocks and 50% in bonds. 100% bonds 100% stocks

4. 11-3 The Efficient Set for Two Assets 100% stocks 100% bonds Note that some portfolios are “better” than others. They have higher returns for the same level of risk or less.

5. 11-4 Portfolios with Various Correlations 100% bonds expected return  100% stocks  = 0.2  = 1.0  = -1.0  Relationship depends on correlation coefficient!! -1.0 <  < +1.0  If  = +1.0, no risk reduction is possible  If  = –1.0, complete risk reduction is possible

6. 11-5 Increasing portfolio size  Now, let’s see what happens as we increase portfolio size.  Basic principle stays the same: It is rational for us to choose portfolios that are efficient – that offer the highest expected return per unit risk.

7. 11-6 11.5 The Efficient Set for Many Securities Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios as shown on red curve. expected return PP Individual Assets

8. 11-7 The Efficient Set for Many Securities The section of the opportunity set above the minimum variance portfolio is the efficient frontier. We want to invest in portfolios on the efficient frontier. expected return PP minimum variance portfolio efficient frontier Individual Assets

9. 11-8 Announcements, Surprises, and Expected Returns  The return on any security can be decomposed into two components. First, the expected return component Second, the unexpected component  A way to write the return on a stock in the coming month is:

10. 11-9 Announcements, Surprises, and Expected Returns  Any announcement can be broken down into two parts, the anticipated (or expected) part and the surprise (or innovation): Announcement = Expected part + Surprise.  The expected part of any announcement is the part of the information the market uses to form the expectation, R, of the return on the stock.  The surprise is the news that influences the unanticipated return on the stock, U.

11. 11-10 Diversification and Portfolio Risk  Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns.  This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another.  However, there is a minimum level of risk that cannot be diversified away, and that is the systematic portion.

12. 11-11 Portfolio Risk and Number of Stocks Nondiversifiable risk; Systematic Risk; Market Risk Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk n  In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. Portfolio risk

13. 11-12 Risk: Systematic and Unsystematic  A systematic risk is any risk that affects a large number of assets, each to a greater or lesser degree.  An unsystematic risk is a risk that specifically affects a single asset or small group of assets. Unsystematic risk can be diversified away.  Examples of systematic risk include uncertainty about general economic conditions, such as GNP, interest rates or inflation.  On the other hand, announcements specific to a single company are examples of unsystematic risk.

14. 11-13 Total Risk  Total risk = systematic risk + unsystematic risk  The standard deviation of returns is a measure of total risk.  For well-diversified portfolios, the amount of unsystematic risk remaining approaches zero.  Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk.

15. 11-14 Optimal Portfolio with a Risk-Free Asset In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills. 100% bonds 100% stocks rfrf return 

16. 11-15 11.7 Riskless Borrowing and Lending Now investors can allocate their money across the T-bills and a balanced mutual fund. 100% bonds 100% stocks rfrf return  Balanced fund CML

17. 11-16 Riskless Borrowing and Lending With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope. return PP efficient frontier rfrf CML

18. 11-17 Portfolio selection with riskless borrowing and lending  Why do we choose the portfolio that gives the capital allocation line with the steepest slope?  The slope of the capital allocation line IS the ratio of expected return per unit of risk, and this is what we would ideally like to maximize.