Chapter 11 Risk and Return

11.1 Expected Returns and Variances

Remember from the Prior Chapter: We calculated average returns and variances using historical data We now begin to discuss how to analyze returns and variances when the information we have concerns future possible returns and their probabilities.

Expected Returns Expected Return: return on a risky asset “expected” in the future. based on the probabilities of possible outcomes in this context, “expected” means average if the process is repeated many times The expected return is equal to: The sum of: the possible returns multiplied by their probabilities Simply multiply the possibilities by the probabilities and add up the results: Use the following example to illustrate the mathematical nature of expected returns: Consider a game where you toss a fair coin: If it is Heads then student A pays student B $1. If it is Tails then student B pays student A $1. Most students will remember from their statistics that the expected value is $0 (=.5(1) + .5(-1)). That means that if the game is played over and over then each student should expect to break-even. However, if the game is only played once, then one student will win $1 and one will lose $1.

Variance and Standard Deviation In Chapter 10 we were examining actual historical returns We estimated the average return and variance based on actual events It’s important to point out that these formulas are for populations, unlike the formulas in chapter 10 that were for samples (dividing by n-1 instead of n). Remind the students that standard deviation is the square root of the variance

Deviation from the Mean (Average) Remember This Example from the Previous Chapter Historical Variance and Standard Deviation Year Actual Return Average Return Deviation from the Mean (Average) Squared Deviation 1 .15 .105 .045 .002025 2 .09 -.015 .000225 3 .06 -.045 4 .12 .015 Totals .42 / 4 = .105 .000 .0045 Remind students that the variance for a sample is computed by dividing by the number of observations – 1 The standard deviation is just the square root (2) Variance = .0045 / (4-1) = .0015 () Standard Deviation = .03873 (Positive Square Root of the Variance)

Variance and Standard Deviation Now we’ll “project” future returns and their associated probabilities Variance and standard deviation still measure the volatility of returns Therefore, we’ll calculate “expected returns” and variances somewhat different from the previous chapter

Variance and Standard Deviation Calculating Expected Return, Variance, and Standard Deviation for an individual stock – go to: www.uta.edu/faculty/tjearp Chap 11 Self Test Problem Click on: Individual Stocks tab Demonstrates Calculations for: Individual Stock - Expected Return Variance Standard Deviation

11.2 Portfolios

Portfolios A portfolio is a group of assets such as stocks and bonds held by an investor An asset’s risk and return is important in how it affects 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

Portfolio Expected Returns The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio

Portfolios Calculating Portfolio Expected Return, Variance, and Standard Deviation – go to: www.uta.edu/faculty/tjearp Chap 11 Self Test Problem Click on: Portfolio tab Demonstrates Calculations for: Portfolio Weights Expected Return Variance Standard Deviation

11.3 Announcements, Surprises, and Expected Returns

Expected versus Unexpected Returns Realized returns are generally not = to expected returns There’s the expected component and the unexpected component Total return = Expected return + Unexpected return The unexpected return comes about because of unanticipated events. The risk from investing stems from the possibility of an unanticipated event. (i.e. a sudden unexpected change in interest rates)

Announcements and News Announcements and news contain both an expected component and a surprise component It’s the surprise component that affects a stock’s price and therefore its return This is very obvious when we watch how stock prices move when an unexpected announcement is made or earnings are different than anticipated

Efficient Markets We assume that relevant information known today is already reflected in the expected return That is the current stock price reflects relevant publicly available information This assumes that markets are at least reasonably efficient in the Semistrong form – all public information is reflected in the stock price

Efficient Markets Efficient markets are a result of investors trading on the unexpected portion of announcements The easier it is to trade on surprises, the more efficient markets should be Efficient markets involve random price changes because we cannot predict surprises

11.4 Risk: Systematic and Unsystematic

Systematic Risk Systematic Risk: a risk that affects a large number of assets Also known as non-diversifiable risk or market risk Has market-wide effects Economywide. Affects nearly all companies to some degree Includes such things as changes in GDP, inflation, interest rates, etc.

Unsystematic Risk Unsystematic Risk: a risk that affects at most a small number of assets. Also known as unique or asset-specific risk Unique to individual companies or assets Includes such things as labor strikes, part shortages, etc. Firm-Specific Example: the stock price of a gold-mining firm drops when it’s discovered the firm’s chairman has overstated minable gold reserves

Systematic and Unsystematic Components of Return Total Return = expected return + unexpected return: R = E(R) + U Unexpected return = systematic portion + unsystematic portion Therefore: Total Return = expected return + systematic portion + unsystematic portion: R = E(R) + Systematic portion + Unsystematic portion

11.5 Diversification and Portfolio Risk

Diversification Principle of diversification: Spreading an investment across a number of assets will eliminate some, but not all, of the risk. Portfolio diversification is the investment in several different asset classes or sectors Diversification is not just holding a lot of assets For example: if you own 50 internet stocks, you’re not diversified However: if you own 50 stocks that span 20 different industries, then you are diversified Video Note: “Portfolio Management” looks at the value of diversification using Tower Records

Diversifiable Risk The risk that can be eliminated by combining assets into a portfolio Often considered the same as unsystematic, unique, or asset-specific risk If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away

The Principle of Diversification 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 – market risk!

Total Risk Total risk (as measured by the standard deviation of return) = systematic risk + unsystematic risk Systematic Risk - nondiversifiable risk or market risk Unsystematic Risk - is diversifiable risk, unique risk, or asset-specific risk. The standard deviation of returns is a measure of total risk For well diversified portfolios, unsystematic risk is very small Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk

Table 11.7 – Std Dev declines as the number of securities increases %

Figure 11.1 Average annual standard deviation (%) Diversifiable risk Nondiversifiable risk Number of stocks in portfolio 49.2 23.9 19.2 1 10 20 30 40 1,000

11.6 Systematic Risk and Beta

Systematic Risk Principle Systematic Risk Principle: the expected return on a risky asset depends only on that asset’s systematic (market) risk There is a reward for bearing risk There is not a reward for bearing risk unnecessarily Unsystematic (firm specific) risk can be eliminated at virtually no cost (by diversifying)

Measuring Systematic Risk Beta Coefficient: Amount of systematic (market) risk present in a particular risky asset relative to that in an average risky asset We use the beta coefficient to measure systematic (market) risk 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 Since assets with larger betas have greater systematic risks, they will have greater expected returns

Table 11.8 (I) www: Click on the web surfer icon to go to www.stockscreener.com where you can do searches for various betas. Students are often interested to see the range of betas that are out there.

Portfolio Betas Example: 11.6 – Page 323 Security Amt Inv Exp Rtn Beta Weight Stock A $ 1,000 8% .80 .10 Stock B 2,000 12 .95 .20 Stock C 3,000 15 1.10 .30 Stock D 4,000 18 1.40 .40 10,000 1.00 What is the expected return on this portfolio? E(Rp) = .10(.08) + .20(.12) + .30(.15) + .40(.18) = .149 or 14.9% What is the beta of this portfolio? Bp = .10(.80) + .20(.95) + .30(1.10) + .40(1.40) = 1.16 Which security has the highest systematic risk? DCLK Which security has the lowest systematic risk? KEI Is the systematic risk of the portfolio more or less than the market? more

11.7 The Security Market Line

Beta and the Risk Premium Remember that the risk premium = expected return – risk-free rate The higher the beta, the greater the risk premium

Security Market Line The security market line (SML): Positively sloped straight line displaying the relationship between expected return and beta. Figure 11.4, Page 330 The slope of the SML is: (E(RM) – Rf) / M But since the beta for the market is ALWAYS equal to one, the slope can be rewritten: E(RM) – Rf Based on the discussion earlier, we now have all the components of the line: E(R) = [E(RM) – Rf] + Rf

Example: Portfolio Expected Returns and Betas (SML) E(RA) Rf Based on the example in the book. Point out that there is a linear relationship between beta and expected return. Ask if the students remember the form of the equation for a line. Y = mx + b E(R) = slope (Beta) + y-intercept The y-intercept is = the risk-free rate, so all we need is the slope A

Capital Asset Pricing Model Market Risk Premium: The slope of the Security Market Line (SML), the difference between the expected return on a market portfolio and the risk-free rate. E(RM) - Rf the reward for bearing an average amount of systematic risk Capital Asset Pricing Model (CAPM): The equation of the SML showing the relationship between expected return and beta: E(RA) = Rf + [E(RM) – Rf] x A

Capital Asset Pricing Model If we know an asset’s systematic (market) risk, we can use the CAPM to determine its expected return Example: A stock has a beta of 1.2, the expected return on the market is 12 percent, and the risk-free rate is 6 percent. What must the expected return on this stock be? E(RA) = Rf + [E(RM) – Rf] x A E(RA) = .06 + (.12 - .06) x 1.2 = .132

The CAPM shows that the expected return for a particular asset depends on three things: The Pure time value of money – measured by the risk-free rate The reward for merely waiting for your money, without taking any risk The Reward for bearing systematic risk – measured by the market risk premium: (E(RM) – Rf) The reward for bearing an average amount of systematic risk in addition to waiting. The Amount of systematic risk – measured by beta Market risk

Chapter 11: Suggested Homework and Test Review Chapter Review and Self-Test Problem 11.1 and 11.2 Critical Thinking and Concepts Review: 1 & 4 Questions and Problems: 5, 6, 7, 9, 10, 11, 13, 15, 25 Know how to calculate the following for individual stocks and a portfolio: Expected Return Variance Standard Deviation Know how to calculate: Portfolio Beta CAPM Equation Risk Premium Know chapter theories, concepts, and definitions