The Pricing of Risky Financial Assets Risk and Return

2 Introduction Risk is a double-edged sword—It complicates decision making but makes things interesting Risk is a double-edged sword—It complicates decision making but makes things interesting Understand how investors are compensated for holding risky securities and how portfolio decisions impact the outcome Understand how investors are compensated for holding risky securities and how portfolio decisions impact the outcome A financial asset is a contractual agreement that entitles the investor to a series of future cash payments from the issuer A financial asset is a contractual agreement that entitles the investor to a series of future cash payments from the issuer Value of a security is dependent on nature of the future cash payments and credibility of the issuer in making those payments Value of a security is dependent on nature of the future cash payments and credibility of the issuer in making those payments

3 A World of Certainty Individuals are predictable and live up to contractual agreements on financial securities Individuals are predictable and live up to contractual agreements on financial securities In this case, the same interest rate is applicable to each and every loan In this case, the same interest rate is applicable to each and every loan Charge more—people would not borrow Charge more—people would not borrow Charge less—lenders would be deluged with requests for funds Charge less—lenders would be deluged with requests for funds All securities are prefect substitutes for each other—sell at the same price and yield the same return All securities are prefect substitutes for each other—sell at the same price and yield the same return

4 A World of Certainty Consumption versus saving Consumption versus saving The individual investor would forgo consumption for a minimum riskless rate of return The individual investor would forgo consumption for a minimum riskless rate of return Depends on the individual’s preference between current and future consumption Depends on the individual’s preference between current and future consumption Is the rate high enough to persuade individual to forgo consumption in favor of saving Is the rate high enough to persuade individual to forgo consumption in favor of saving The higher the rate, the more people will elect to save for future consumption The higher the rate, the more people will elect to save for future consumption

5 Consequences of Uncertainty In contrast to a “perfect world,” investors face uncertainty In contrast to a “perfect world,” investors face uncertainty Outcome may be better or worse than expected Outcome may be better or worse than expected

6 Risk Aversion Investors must be compensated for risk Investors must be compensated for risk Will hold risky securities if higher expected returns will offset the undesirable uncertainty Will hold risky securities if higher expected returns will offset the undesirable uncertainty Trade-off of higher return versus risk is subjective and different for every individual Trade-off of higher return versus risk is subjective and different for every individual

7 Portfolio Diversification A strategy employed by investors to reduce risk A strategy employed by investors to reduce risk Holding many different securities rather than just one Holding many different securities rather than just one

8 Risk and Return Probability Distribution Probability Distribution A listing of the various outcomes and the probability of each outcome occurring A listing of the various outcomes and the probability of each outcome occurring Expected return Expected return A weighted average of the different outcomes multiplied by their respective probability A weighted average of the different outcomes multiplied by their respective probability

9 Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns? Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns? StateProbabilityCT StateProbabilityCT Boom Boom Normal Normal Recession Recession R C =.3(.15) +.5(.10) +.2(.02) =.099 = 9.99% R C =.3(.15) +.5(.10) +.2(.02) =.099 = 9.99% R T =.3(.25) +.5(.20) +.2(.01) =.177 = 17.7% R T =.3(.25) +.5(.20) +.2(.01) =.177 = 17.7%

10 Variance and Standard Deviation Variance and standard deviation measure the volatility of returns Variance and standard deviation measure the volatility of returns Weighted average of squared deviations Weighted average of squared deviations

11 Example: Variance and Standard Deviation Consider the previous example. What are the variance and standard deviation for each stock? Consider the previous example. What are the variance and standard deviation for each stock? Stock C Stock C  2 =.3( ) 2 +.5( ) 2 +.2( ) 2 =  2 =.3( ) 2 +.5( ) 2 +.2( ) 2 =  =.045  =.045 Stock T Stock T  2 =.3( ) 2 +.5( ) 2 +.2( ) 2 =  2 =.3( ) 2 +.5( ) 2 +.2( ) 2 =  =.0863  =.0863

12 Standard Deviation When comparing securities, the one with the largest standard deviation is the riskier When comparing securities, the one with the largest standard deviation is the riskier If returns and standard deviations between two securities are different, the investor must make a decision between the tradeoff of the expected return and the standard deviation of each If returns and standard deviations between two securities are different, the investor must make a decision between the tradeoff of the expected return and the standard deviation of each

13 Modern Portfolio Theory Asset may seem very risky in isolation, but when combined with other assets, risk of portfolio may be substantially less—even zero Asset may seem very risky in isolation, but when combined with other assets, risk of portfolio may be substantially less—even zero When combining different securities, it is important to understand how outcomes are related to each other When combining different securities, it is important to understand how outcomes are related to each other Procyclical—Returns of two or more securities are positively correlated indicating they move in same direction Procyclical—Returns of two or more securities are positively correlated indicating they move in same direction Countercyclical—Returns of two or more securities are negatively correlated-move in opposite directions Countercyclical—Returns of two or more securities are negatively correlated-move in opposite directions Combining a procyclical and countercyclical securities would greatly reduce the risk of the portfolio Combining a procyclical and countercyclical securities would greatly reduce the risk of the portfolio

14 Principles of Diversification As long as assets do not have precisely the same pattern of returns, then holding a group of assets can reduce risk As long as assets do not have precisely the same pattern of returns, then holding a group of assets can reduce risk If the returns of each security are totally independent of each other, combining a large number of securities tends to produce the average return of the portfolio If the returns of each security are totally independent of each other, combining a large number of securities tends to produce the average return of the portfolio

15 The Risk Premium on Risky Securities The standard deviation of returns is a good measure of risk for analyzing a security The standard deviation of returns is a good measure of risk for analyzing a security However, it is a relatively poor measure of the risk contribution of a single security to an entire portfolio However, it is a relatively poor measure of the risk contribution of a single security to an entire portfolio This depends on the covariance of returns with other securities This depends on the covariance of returns with other securities Nonsystematic Risk of a portfolio is diversified away as the number of securities held increases Nonsystematic Risk of a portfolio is diversified away as the number of securities held increases

16 Market Portfolio A widely diversified portfolio that contains virtually every security in the marketplace A widely diversified portfolio that contains virtually every security in the marketplace Investor earns a return above the risk-free rate that compensates for the co-movement of returns among all securities, rather than the risks inherent in every security Investor earns a return above the risk-free rate that compensates for the co-movement of returns among all securities, rather than the risks inherent in every security The risk of the market portfolio is less than the sum of each security’s risk because some of the individual variability tends to cancel out The risk of the market portfolio is less than the sum of each security’s risk because some of the individual variability tends to cancel out

17 Systematic Risk Relates to the risk of an individual security in relation to the movement of the entire portfolio Relates to the risk of an individual security in relation to the movement of the entire portfolio The risk premium that investors demand will be in proportion to the systematic risk of the security The risk premium that investors demand will be in proportion to the systematic risk of the security Riskier securities must offer investors higher expected returns Riskier securities must offer investors higher expected returns Extra expected return on a risky security above the risk-free rate will be proportional to the risk contribution of a security to a well-diversified portfolio Extra expected return on a risky security above the risk-free rate will be proportional to the risk contribution of a security to a well-diversified portfolio

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

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

20 Portfolio Variance Compute the portfolio return for each state: R P = w 1 R 1 + w 2 R 2 + … + w m R m Compute the portfolio return for each state: R P = w 1 R 1 + w 2 R 2 + … + w m R m Compute the expected portfolio return using the same formula as for an individual asset 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 Compute the portfolio variance and standard deviation using the same formulas as for an individual asset

21 Example Consider the following information Consider the following information StateProbabilityXZ StateProbabilityXZ Boom.2515%10% Boom.2515%10% Normal.6010%9% Normal.6010%9% Recession.155%10% Recession.155%10% What is the expected return and standard deviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Y? What is the expected return and standard deviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Y?

22 Expected versus Unexpected Returns Realized returns are generally not equal to expected returns Realized returns are generally not equal to expected returns There is the expected component and the unexpected component There is the expected component and the unexpected component At any point in time, the unexpected return can be either positive or negative At any point in time, the unexpected return can be either positive or negative Over time, the average of the unexpected component is zero Over time, the average of the unexpected component is zero

23 Announcements and News Announcements and news contain both an expected component and a surprise component 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 It is 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 This is very obvious when we watch how stock prices move when an unexpected announcement is made or earnings are different than anticipated

24 Efficient Markets Efficient markets are a result of investors trading on the unexpected portion of announcements 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 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 Efficient markets involve random price changes because we cannot predict surprises

25 Systematic Risk Risk factors that affect a large number of assets Risk factors that affect a large number of assets Also known as non-diversifiable risk or market risk Also known as non-diversifiable risk or market risk Includes such things as changes in GDP, inflation, interest rates, etc. Includes such things as changes in GDP, inflation, interest rates, etc.

26 Unsystematic Risk Risk factors that affect a limited number of assets Risk factors that affect a limited number of assets Also known as unique risk and asset- specific risk Also known as unique risk and asset- specific risk Includes such things as labor strikes, part shortages, etc. Includes such things as labor strikes, part shortages, etc.

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

28 Diversification Portfolio diversification is the investment in several different asset classes or sectors Portfolio diversification is the investment in several different asset classes or sectors Diversification is not just holding a lot of assets Diversification is not just holding a lot of assets For example, if you own 50 internet stocks, you are not diversified For example, if you own 50 internet stocks, you are not diversified However, if you own 50 stocks that span 20 different industries, then you are diversified However, if you own 50 stocks that span 20 different industries, then you are diversified

29 The Principle of Diversification Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns 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 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 However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion

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

31 Total Risk Total risk = systematic risk + unsystematic risk Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of total risk The standard deviation of returns is a measure of total risk For well diversified portfolios, unsystematic risk is very small For well diversified portfolios, unsystematic risk is very small Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk

32 Systematic Risk Principle There is a reward for bearing risk There is a reward for bearing risk There is not a reward for bearing risk unnecessarily 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 The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away