Chapter 13—Risk and Return- Recap on Chapter 12—Historical Informationo Dividend yield= income/beginning price (can’t be negative)o Capital yield (percent return) = (ending price—beginning price)/beginningpriceo Total percentage return= dividend yield + capital yieldo Variance standard deviation (calculate risk) Historical variance = sum of squared deviations from mean/ (number of observations -1) Standard deviation = squared root of variance - How to quantify return and how spread out risk can be- Expected returnso Based on probability of possible outcomes Since stock value is based on present value of future cash flows Expected means average in the process is repeated many times- Expected does not even have to be a possible return, any other outcome is possible- Example:State Probability (alwaysneeds to equal 1)C TBoom 0.3 15 25Normal 0.5 10 20Recession 0.2 2 1- What is the probability of recession?o Expected returns RC =. 3(15)+. 5(10)+. 2(2) = 9.9% RT =. 3(25)+. 5(20)+. 2(1) = 17.7%- Weighted based off expected probability- If the risk-free rate (ch. 12) is 4.15%, what is the premium for C&T?o Risk premium = expected-risk free rate C: 9.9%-4.15% = 5.75% T: 17.7% -4.15% = 13.55%- Variance and Standard deviationo Needed to compare risk premiums- Variance and standard deviation measure volatile of returns (how broad)o Given the weight to each one/ allowing weight to be assigned to possible outcomeso From example: C=9.9%, T=17.7% Variance C= .3 (15-9.9) 2 + .5 (10-9.9) 2 + .2 (2-9.9) 2 = 20.29%- Standard deviation: √20.29 = 4.5% Variance T= .3 (25-17.7) 2 + .5 (20-17.7) 2 + .2 (1-17.7) 2 = 74.41- Standard deviation: √74.41 = 8.62%- Example 2o Expected Return: .25 (15) + .5 (8) + .15(4) + .10(-3) =8.05%o Variance: .25(15-18.05) 2 +. 5 (8-8.05) 2 +. 15 (4-8.05) 2 +. 10(-3-8.05) 2 =26.7476 Standard deviation: √26.7478 = 5.1718- Portfolios—collection of assetso An asset’s risk and return are important in how they affect the risk and return of the portfolio Weight in portfolio sum to oneo Example Suppose you have $15,000 to invest and youhave purchased securities in following amounts- $2000 of DCLK: 13.3% (2000/15000)- $3000 of KO: 20% (3000/15000)- $4000 of INTC: 26.71% (4000/15000)- $6000 of KEI: 40% (6000/15000)Chapter 13—Risk and Return- Portfolio Varianceo Use same formula for an individual asseto ExampleState Probability A BBoom .4 .30 (30%) -.05 (-5%)Bust .6 -.10 (-10%) .25 (25)o Expected Return for Asset A .4 (30) +. 6 (-10) =6%o Expected Return for Asset B .4 (-5) +. 6 (25) =13%o Variance Standard A .4(30-6) 2 + .6(-10-6) 2 =384 Standard deviation = √384 = 19.59o Variance Standard B .4 (-5-13) 2 +. 6 (25-13) 2 = 216 Standard deviation = √216 = 14.69- Portfolio Varianceo Calculate: You invest 50% of money in asset A, what is expected return for the portfolio in each state of the economy Expected = weight of A (percentage A) + weight of B (percentage B) Boom (E) = .5(30) + .5(-5) =12.5% Bust (E) = .5(-10) +. 5(25) = 7.5%o Expected return for the portfolio as a whole (considering both states of an economy)? Portfolio return = boom probability (return of given boom) + bust probability (return of given bust) Portfolio return = .4 (12.5) + .6 (7.5) = 9.5% What is the variance of portfolio?- .4 (12.5-9.5) 2 + .6 (7.5-9.5) 2 = 6- Standard deviation = √6 = 2.45- Expected vs. unexpected returnso Realized returns are generally not equal to expected returnso There is the expected component and the unexpected component At any point in time, unexpected return can be either positive or negative Overtime, the average of component is zero o Unexpected returns = expected—realized return Can be either positive or negativeo It’s the surprise component that affects the stock price and therefore its return- Efficient marketso How fast information is included in priceo Result of investors trading on the unexpected portion of a announcementso Easier to trade on surprises, more efficient markets should beo Efficient markets involve random price changes because we cannot predictsurprises- Systematic Risk (Affects market as whole)o Risk factors that affect large number of assetso Known as non-diversable risk or market risk (can’t get rid of)o Includes such things like changes in GDP, inflation, interest rates, etc.o Chance we will go in recession or get out of recessiono Overarching factors- Unsystematic Risko Risk factors that affect a limited number of assetso Known as unique risk and asset-specific risko Includes such things as labor strikes, part shortages, etc. (specific factors)o Can affect only on firm, one industry, etc. Vastly different outcomes of two companies in the same industryChapter 13—Risk and Return continued- Risk possibility of earning more or less than what we expected (deviations from what we expect)o Random movement of stock prices (don’t meet expectations)- Measuring systematic Risko Not compensated for having more firm specific risk Unnecessary risk that your taking- Beat coefficiento How sensitive is firm to economic conditions Beta of 1 implies the asset has same systematic risk as overall market Beta less than 1 implies the asset has less systematic risk than overall market (less exposure)- Exposure—utility stock- Movements not as large Beta greater than 1 implies that asset has more systematic risk than overall market (more exposure)- More sensitive than overall market- Example: luxury stocks (Tiffany’s co)- Larger movements- Total vs. Systematic RiskSecurities Standard deviation (totalrisk)Beta (measure of systematicrisk)C 20% 1.25K 30% .95- Which has more total risk?o K; standard deviation is greater than C- Which has more systematic risk?o C; Beta is greater than K- Which security should have higher expected returno C; beta measures risk and it’s expected return- Portfolio Beta ExampleSecurities Weight BetaDCLK .133 2.685KO .2 0.195INTC .267 2.161KEI .4 2.434o Portfolio Beta .133(2.685) +.2 (0.195) + .267 (2.161) + .4 (2.434) = 1.947- Security Market Lineo Represents market equilibriumo Slope of SML is reward-to-risk ratio (E(RM) –Rf) /Bm- RM – return on the market- Rf –risk free rate- Bm—market beta (always 1)o Since B is market is always 1; formula can be E(RM) –Rf = market risk premium- Capital Asset Pricing (CAPM)o Capital asset pricing model defines the relationship between risk and returno E(RA) = RF +
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