All else equal, people dislike risk.

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Melanie Woods
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1 All else equal, people like returns. All else equal, people dislike risk.

2 On October 7, 07, Home Depot stock closed at $64.. It paid dividends of $0.89 per share on November 9, 07, and $.03 per share on March 7,, and, 08. It is currently trading at $. What is your dollar return over this period? What is your percent return?

3 The stock of Home Depot has had the following annual returns: 07: 44.6% 06:.38% 05:.04% 04: 38.8% Arithmetic Mean:... T T

4 The variance ( ) of returns tells us how much the actual returns each year vary from the average return. In other words, it is a measure of the volatility of returns.... T T T t t T

5 The standard deviation () is just the square root of the variance and explains the deviation from expected returns as a percentage. 68.6% 95.46% 99.74%

6 There are four possible states of the world: severe recession with a probability of 0%, slow growth with a probability of 30%, recovery with a probability of 40%, and boom with a probability of 0%. Big Maui, Inc. stock will have a return of -3% in the severe recession state, 3% in the slow growth state, 7% in the recovery state, and 0% in the boom state. What is the expected return on this stock? Little Gulf, Inc. stock will have a return of % in the severe recession state, 4% in the slow growth state, 0% in the recovery state, and 0% in the boom state. What is the expected return on this stock?

7 ... P P P T T T t t t P

8 Calculate the variance and standard deviation of the expected returns for Big Maui, Inc. and Little Gulf, Inc.

9 The return on a portfolio is simply a weighted sum of the returns of the securities in the portfolio. Assume Papa John s Pizza had a return of 30% last year and the Boston Beer Company had a return of 0% last year. If we had a $00 portfolio with $50 invested in Papa John s Pizza and $50 invested in the Boston Beer Company, what is the return on our beer and pizza portfolio?

10 The expected return on a portfolio is simply a weighted sum of the expected returns of the securities in the portfolio. What is the expected return on an equally-weighted portfolio of Big Maui, Inc. and Little Gulf, Inc.? Cov The covariance of returns tells us how returns of different securities move together. X X Y Y P X X Y Y... ( X, Y ) P Cov ( X, Y ) T t P t X X Y Y t t

11 Like variance, covariance is unbounded. The correlation coefficient is a standardized measure of how returns move together. The correlation coefficient is always between and +. Corr X Y (, ) X, Y COV X ( X, Y Y ) Cov ( X, Y ) X, Y X Y

12 Calculate the covariance and correlation coefficient of the expected returns for Big Maui, Inc. and Little Gulf, Inc.

13 For a portfolio containing two securities, with weights w and w, variances and, and covariance Cov(, ): ), ( Cov w w w w p, w w w w p What if there are more than assets?

14 What are the variance and standard deviation of an equally-weighted portfolio of Big Maui, Inc. and Little Gulf, Inc.?

15 What is risk? Systematic and Unsystematic isk What is diversification? What does diversification do? What does it measure? What is the market portfolio s beta? What is the beta of a risk-free asset? How do we calculate a beta coefficient?

16 The CAPM: An equilibrium asset pricing model showing that the expected return for a particular asset depends on the pure time value of money plus a reward for bearing systematic risk. CAPM E i f i M f

17 What is the expected return on a share of stock whose beta is.5 if the risk-free rate is 4% and the expected return on the market is 0%? An Example: We have $00 invested in stock A, which has an expected return of 7% and a beta of 0.5. We have $50 invested in stock B, which has an expected return of.% and a beta of.. We also have $50 invested in stock C, which has an expected return of 0% and a beta of.0. What is the expected return of this portfolio? What is the portfolio beta?

18 Strengths: Weaknesses: Concept Questions Chapter 0: 3, 4, 6, and 7 Chapter :, 3, 4, 5, and 8 Questions and Problems Chapter 0:,, 3, 4 (part a only), 9, 3, and 4 Chapter :, 5, 0,,, 3, 5, 6, and 7

19 There are three possible states of the world: recession (0% of the time), growth (60% of the time), and boom (0% of the time). Catwoman Cruiselines, Inc. earns 5%, 3%, and 5% in the recession, growth, and boom states, respectively. Batman epossessions, Inc. earns 5%, -3%, and 6% in the recession, growth, and boom states, respectively. What is the expected return of Catwoman Cruiselines, Inc.? E( C ) = 3.8% What is the variance and standard deviation of the expected returns of Catwoman? C = 0.06 C = 0.69

20 What is the expected return of Batman epossessions, Inc.? E( B ) = 0.0% What is the variance and standard deviation of the expected returns of Batman? B = B = What are the covariance and correlation coefficient of the expected returns of Catwoman and Batman? Cov(C,B) = Corr(C,B) =

21 What is the expected return of an equallyweighted portfolio of Catwoman and Batman? E( P ) =.9% What is the standard deviation of the equally-weighted portfolio? P =

Portfolio Management

Portfolio Management Risk & Return Return Income received on an investment (Dividend) plus any change in market price( Capital gain), usually expressed as a percent of the beginning market price of the