Chapter 13 Risk and Return Recap on Chapter 12 Historical Information o Dividend yield income beginning price can t be negative o Capital yield percent return ending price beginning price beginning price o Total percentage return dividend yield capital yield o 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 returns o 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 always needs to equal 1 C T Boom Normal Recession 0 3 0 5 0 2 15 10 2 25 20 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 deviation o 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 outcomes o 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 2 o 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 assets o An asset s risk and return are important in how they affect the risk and return of the portfolio Weight in portfolio sum to one o Example Suppose you have 15 000 to invest and you have 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 Variance o Use same formula for an individual asset o Example State Boom Bust Probability A B 4 6 30 30 05 5 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 59 o Variance Standard B 4 5 13 2 6 25 13 2 216 Standard deviation 216 14 69 Portfolio Variance o 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 returns o Realized returns are generally not equal to expected returns o 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 negative o It s the surprise component that affects the stock price and therefore its return Efficient markets o How fast information is included in price o Result of investors trading on the unexpected portion of a announcements o Easier to trade on surprises more efficient markets should be o Efficient markets involve random price changes because we cannot predict surprises Systematic Risk Affects market as whole o Risk factors that affect large number of assets o 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 recession o Overarching factors Unsystematic Risk o Risk factors that affect a limited number of assets o Known as unique risk and asset specific risk o 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 industry Chapter 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 Risk o Not compensated for having more firm specific risk Unnecessary risk that your taking Beat coefficient o 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 Risk Securities Standard deviation total risk Beta measure of systematic risk C K 20 30 1 25 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 return o C beta measures risk and it s expected return Portfolio Beta Example Securities Weight Beta 133 267 2 4 2 685 0 195 2 161 2 434 133 2 685 2 0 195 267 2 161 4 2 434 1 947 DCLK KO INTC KEI o Portfolio Beta Security Market Line o Represents market equilibrium o 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 return o E RA RF BA E RM Rf E RA expected compensation of market BA sensitivity of stock to market factors E RM Rf risk premium on market how much compensation for being on market If we know an asset s systematic risk we can use the CAPM to …
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