Agenda for 29 July (Chapter 13) Expected Returns, Variances, and Standard Deviations for individual securities Expected Returns, Variances, and Standard Deviations for portfolios Announcements, Surprises, and Expected Returns Risk: Systematic and Unsystematic Capital Asset Pricing Model 13-1

Expected Returns Expected returns are based on the probabilities of possible outcomes In this context, “expected” means average if the process is repeated many times 13-2

Variance and Standard Deviation Variance and standard deviation measure the volatility of returns Weighted average of squared deviations 13-3

Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of the economy. What are the expected returns? State Probability C T___ Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession 0.2 0.02 0.01 E(RC) = .3(15) + .5(10) + .2(2) = 9.9% E(RT) = .3(25) + .5(20) + .2(1) = 17.7% 13-4

Example: Variance & Standard Deviation What are the variance and standard deviation for each stock? Stock C 2 = .3(0.15-0.099)2 + .5(0.10-0.099)2 + .2(0.02-0.099)2 = 0.002029  = 4.50% Stock T 2 = .3(0.25-0.177)2 + .5(0.20-0.177)2 + .2(0.01-0.177)2 = 0.007441  = 8.63% 13-5

Portfolios A portfolio is a collection of assets An asset’s risk and return are important in how they affect the risk and return of the portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets 13-6

Portfolio Expected Return The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities Here, w(j) is the % of the portfolio invested in security j. 13-7

Portfolio Variance Compute the portfolio return for each state: RP = w1R1 + w2R2 + … + wmRm Compute the expected portfolio return using the same formula as for an individual asset Compute the portfolio variance and standard deviation using the same formulas as for an individual asset 13-8

Example: Portfolio Expected Return and Standard Deviation Consider the following information on returns and probabilities: Invest 50% of your money in Asset A and 50% in B State Probability A B Portfolio Boom .5 30% -5% 12.5% Bust .5 -10% 25% 7.5% What are the expected return and standard deviation for each asset? What are the expected return and standard deviation for the portfolio? Download the portfolio problem spreadsheet. Note – the returns on these two securities are perfectly negatively correlated: Calculate covariance Correlation = covariance/product of standard deviations. 13-9

Expected vs. Unexpected Returns Realized returns are generally not equal to expected returns There is the expected component and the unexpected component At any point in time, the unexpected return can be either positive or negative Over time, the average of the unexpected component is zero; by definition, something that is unexpected is purely random! 13-10

Announcements and News Announcements and news contain both an expected component and a surprise component It is the surprise component that affects a stock’s price and therefore its return (positively or negatively) This is apparent when we watch how stock prices move in response to news about the firm that is not anticipated; e.g., a better or worse than expected earnings announcement Lecture Tip: It is easy to see the effect of unexpected news on stock prices and returns. Consider the following two cases: (1) On November 17, 2004 it was announced that K-Mart would acquire Sears in an $11 billion deal. Sears’ stock price jumped from a closing price of $45.20 on November 16 to a closing price of $52.99 (a 7.79% increase) and K-Mart’s stock price jumped from $101.22 on November 16 to a closing price of $109.00 on November 17 (a 7.69% increase). Both stocks traded even higher during the day. Why the jump in price? Unexpected news, of course. (2) On November 18, 2004, Williams-Sonoma cut its sales and earnings estimates for the fourth quarter of 2004 and its share price dropped by 6%. There are plenty of other examples where unexpected news causes a change in price and expected returns. 13-11

Systematic Risk Also known as non-diversifiable risk or market risk Includes risk factors that affect firms generally; e.g., macroeconomic factors such as GDP, inflation, interest rates, demographic change, changes in consumer preferences, and so forth. 13-12

Unsystematic Risk Also known as diversifiable or unique risk Includes risk factors that are firm-specific; e.g., property damage, lawsuits, product recalls, labor strikes, theft of intellectual property by hackers, and so forth. Lecture Tip: You can expand the discussion of the difference between systematic and unsystematic risk by using the example of a strike by employees. Students will generally agree that this is unique or unsystematic risk for one company. However, what if the UAW stages the strike against the entire auto industry. Will this action impact other industries or the entire economy? If the answer to this question is yes, then this becomes a systematic risk factor. The important point is that it is not the event that determines whether it is systematic or unsystematic risk; it is the impact of the event. 13-13

Returns Total Return = expected return + unexpected return Unexpected return = systematic portion + unsystematic portion Therefore, total return can be expressed as follows: Total Return = expected return + systematic portion + unsystematic portion 13-14

Systematic and Unsystematic Risk Non-zero correlation occurs naturally since stocks tend to be positively correlated with each other Note that according to the combinatorial equation, the number of unique pairs in a group of n securities is equal (n-1)/n. In the portfolio variance formula shown here, we have the (quite familiar) expression which decomposes risk into its unique and systematic components. Changing the composition of the risk pool (by varying n) does not affect expected return, but it does affect variance!

Systematic and Unsystematic Risk Draw the familiar diagram which decomposes risk into its systematic and unsystematic components.

Systematic Risk Principle There is a reward for bearing risk There is not a reward for bearing risk unnecessarily The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away A discussion of diversification via mutual funds and ETFs may add to the students’ understanding. 13-17

Measuring Systematic Risk How do we measure systematic risk? We use the beta coefficient What does beta tell us? A beta of 1 implies the asset has the same systematic risk as the overall market A beta < 1 implies the asset has less systematic risk than the overall market A beta > 1 implies the asset has more systematic risk than the overall market Note that Beta is a standardized covariance – it is equal to the ratio of the covariance between an individual security and the overall market divided by the variance of the overall market; it indicates how much systematic risk a security has compared with the overall market. 13-18

Total vs. Systematic Risk Consider the following information: Standard Deviation Beta Security C 20% 1.25 Security K 30% 0.95 Which security has more total risk? Which security has more systematic risk? Which security should have the higher expected return? Security K has the higher total risk Security C has the higher systematic risk Security C should have the higher expected return 13-19

The Risk Reward Ratio for the Overall Market A Graphical Illustration Note: the equation for the line in this graph is E(RM) = Rf + M[E(RM) – Rf]; the slope of the line is (E(RM) – Rf)/M Lecture 13: Capital Market Theory 17 17

The Capital Asset Pricing Model (CAPM) In equilibrium, all assets and portfolios must have the same reward-to-risk ratio, and they all must equal the reward-to-risk ratio for the market; i.e., Since the beta of the market is (by definition) equal to 1, this implies that Discuss the economics of this – if you receive a higher reward-to-risk ratio with A than with the market, this means that A is undervalued, so people bid the price of A up, which reduces its reward-to-risk ratio. If A gets too expensive relative to the overall market, then it’s reward-to-risk ratio is too low relative to the market. This encourages investors to sell A until it’s reward-to-risk ratio is on par with the overall market. The 13-21

Factors Affecting Expected Return Pure time value of money: measured by the risk-free rate Reward for bearing systematic risk: measured by the market risk premium Amount of systematic risk: measured by beta 13-22

The Capital Asset Pricing Model (CAPM) The capital asset pricing model defines the relationship between risk and return If we know an asset’s systematic risk, we can use the CAPM to determine its expected return This is true whether we are talking about financial assets or physical assets 13-23

Field Research – look up betas for publicly traded companies Apple Google JP Morgan Chase Ford Walmart Amazon Facebook Assuming that the MRP is 8% and Rf is 2%, what is the expected return for each of these companies? Calculate the beta of an equally weighted portfolio consisting of these companies. What is the expected return on this portfolio?\ Syntax for finding beta is http://finance.yahoo.com/q?s=<ticker symbol> 13-24