Risk and Rates of Return Chapter 8

Historical Risk and Return Info. Based on annual returns from Based on annual returns from Avg. ReturnStd Dev. Small Stocks17.5%33.1% Large Co. Stocks12.4%20.3% L-T Corp Bonds6.2%8.6% L-T Govt. Bonds5.8%9.3% U.S. T-Bills3.8%3.1%

Chapter 8 Risk & Rates of Return Risk: The Big Picture Risk: The Big Picture Expected Return Expected Return Stand Alone Risk Stand Alone Risk Portfolio Return and Risk Portfolio Return and Risk Risk Diversification Risk Diversification Market Risk Market Risk – Beta CAPM/Security Market Line Equation (SML) CAPM/Security Market Line Equation (SML)

What is Risk? The big picture. Risk is an uncertain outcome or chance of an adverse outcome. Risk is an uncertain outcome or chance of an adverse outcome. Concerned with the riskiness of cash flows from financial assets. Concerned with the riskiness of cash flows from financial assets. Stand Alone Risk: Single Asset Stand Alone Risk: Single Asset – relevant risk measure is the total risk of expected cash flows measured by standard deviation.

Risk: The Big Picture (cont.) Portfolio Context: A group of assets. Total risk consists of: Portfolio Context: A group of assets. Total risk consists of: – Diversifiable Risk (company-specific, unsystematic) – Market Risk (non-diversifiable, systematic) Small group of assets with Diversifiable Risk remaining: interested in portfolio standard deviation. Small group of assets with Diversifiable Risk remaining: interested in portfolio standard deviation. – correlation (  or r) between asset returns which affects portfolio standard deviation

finishing the Big Picture on Risk Well-diversified Portfolio Large Portfolio (10-15 assets) eliminates diversifiable risk for the most part. Large Portfolio (10-15 assets) eliminates diversifiable risk for the most part. Interested in Market Risk which is the risk that cannot be diversified away. Interested in Market Risk which is the risk that cannot be diversified away. The relevant risk measure is Beta which measures the riskiness of an individual asset in relation to the market portfolio. The relevant risk measure is Beta which measures the riskiness of an individual asset in relation to the market portfolio.

Holding Period (Realized) Return HPR = (End of Period Price - Beginning Price + Dividends)/Beginning Price HPR = Capital Gains Yield + Dividend Yield HPR = (P1-P0)/P0 + D/P0 Example: Bought at $50, Receive $3 in dividends, current price is $54 HPR = ( )/50 =.14 or 14% CGY = 4/50 = 8%, DY = 3/50 = 6%

Expected Return: Single Asset Expected Rate of Return given a probability distribution of possible returns(r i ): E(r) Expected Rate of Return given a probability distribution of possible returns(r i ): E(r) n n E(r) =  P i r i i=1 i=1 Realized or Average Return on Historical Data: Realized or Average Return on Historical Data: - n - n r = 1/n  r i r = 1/n  r i i=1 i=1

Standard Deviation Relevant Risk Measure for single asset Relevant Risk Measure for single asset Variance =  2 =  ( r i - E(r)) 2 P i Standard Deviation = Square Root of Variance Standard Deviation = Square Root of Variance Historical Variance =  2 = 1/n  (r i – r AVG ) 2 Historical Variance =  2 = 1/n  (r i – r AVG ) 2 Sample Variance = s 2 = 1/(n-1)  (r i – r AVG ) 2 Sample Variance = s 2 = 1/(n-1)  (r i – r AVG ) 2

Example: Exp. Return and 

Example: Standard Deviation

Decision Time: Coefficient of Variation Most investors are Risk Averse, meaning they don’t like risk and demand a higher return for bearing more risk. Most investors are Risk Averse, meaning they don’t like risk and demand a higher return for bearing more risk. The Coefficient of Variation (CV) scales risk per unit of expected return. The Coefficient of Variation (CV) scales risk per unit of expected return. CV =  /E(r) CV =  /E(r) CV is a measure of relative risk, where standard deviation measures absolute risk. CV is a measure of relative risk, where standard deviation measures absolute risk.

Back to our Example: CV MAD Inc. MAD Inc. E(r) = 33.5% E(r) = 33.5%  = 34.0%  = 34.0% CV = 34%/33.5% CV = 34%/33.5% CV = CV = Contrary Co. Contrary Co. E(r) = 7.5% E(r) = 7.5%  = 8.9%  = 8.9% CV = 8.9%/7.5% CV = 8.9%/7.5% CV = CV = 1.187

Portfolio Risk and Return E(r p ) =  w i E(r i ) = weighted average of the expected return of each asset in the portfolio E(r p ) =  w i E(r i ) = weighted average of the expected return of each asset in the portfolio In our example, MAD E(r) = 33.5% and CON E(r) = 7.5% In our example, MAD E(r) = 33.5% and CON E(r) = 7.5% What is the expected return of a portfolio consisting of 60% MAD and 40% CON? What is the expected return of a portfolio consisting of 60% MAD and 40% CON? E(r p ) =  w i E(r i ) =.6(33.5%) +.4(7.5%) = 23.1% E(r p ) =  w i E(r i ) =.6(33.5%) +.4(7.5%) = 23.1%

Portfolio Risk Looking at a 2-asset portfolio for simplicity, the riskiness of a portfolio is determined by the relationship between the returns of each asset over different states of nature or over time. Looking at a 2-asset portfolio for simplicity, the riskiness of a portfolio is determined by the relationship between the returns of each asset over different states of nature or over time. This relationship is measured by the correlation coefficient( r ): -1<= r < =+1 This relationship is measured by the correlation coefficient( r ): -1<= r < =+1 All else constant: Lower r = less portfolio risk All else constant: Lower r = less portfolio risk

Example Portfolio  Each MAD-CON r i =.6(MAD)+.4(CON); Each MAD-CON r i =.6(MAD)+.4(CON); E(R p ) = 23.1% E(R p ) = 23.1%

Market Risk As more and more assets are added to a portfolio, risk measured by  decreases. As more and more assets are added to a portfolio, risk measured by  decreases. However, we could put every conceivable asset in the world into our portfolio and still have risk remaining. (See Fig. 8-8, pg. 265) However, we could put every conceivable asset in the world into our portfolio and still have risk remaining. (See Fig. 8-8, pg. 265) This remaining risk is called Market Risk and is measured by Beta. This remaining risk is called Market Risk and is measured by Beta.

As you add stocks to your portfolio, diversifiable risk is reduced.

The Concept of Beta Beta(b) measures how the return of an individual asset (or even a portfolio) varies with the market. Beta(b) measures how the return of an individual asset (or even a portfolio) varies with the market. b = 1.0 : same risk as the market b = 1.0 : same risk as the market b < 1.0 : less risky than the market b < 1.0 : less risky than the market b > 1.0 : more risky than the market b > 1.0 : more risky than the market Beta is the slope of the regression line (y = a + bx) between a stock’s return(y) and the market return(x) over time, b from simple linear regression. Beta is the slope of the regression line (y = a + bx) between a stock’s return(y) and the market return(x) over time, b from simple linear regression. Sources for stock betas: ValueLine Investment Survey (at BEL), Yahoo Finance, MSN Money, Standard & Poors Sources for stock betas: ValueLine Investment Survey (at BEL), Yahoo Finance, MSN Money, Standard & Poors

Relating Market Risk and Return: the CAPM and SML equation The story is the same as Chapter 6: a stock’s required rate of return = nominal risk-free rate + the stock’s risk premium. The story is the same as Chapter 6: a stock’s required rate of return = nominal risk-free rate + the stock’s risk premium. The main assumption is investors hold well diversified portfolios = only concerned with market risk. The main assumption is investors hold well diversified portfolios = only concerned with market risk. A stock’s risk premium = measure of market risk X market risk premium. A stock’s risk premium = measure of market risk X market risk premium.

SML Equation RP M = market risk premium = r M - r RF RP M = market risk premium = r M - r RF RP i = stock risk premium = (RP M )b i RP i = stock risk premium = (RP M )b i r i = r RF + (r M - r RF )b i r i = r RF + (r M - r RF )b i = r RF + (RP M )b i = r RF + (RP M )b i

CAPM Example What is Intel’s required return if its B = 1.2 (from ValueLine Investment Survey), the current 3-mo. T-bill rate is 5%, and the historical US market risk premium of 8.6% is expected? What is Intel’s required return if its B = 1.2 (from ValueLine Investment Survey), the current 3-mo. T-bill rate is 5%, and the historical US market risk premium of 8.6% is expected?

Portfolio Beta The beta of a portfolio of stocks is equal to the weighted average of their individual betas: b p =  w i b i The beta of a portfolio of stocks is equal to the weighted average of their individual betas: b p =  w i b i Example: What is the portfolio beta for a portfolio consisting of 25% Home Depot with b = 1.1, 40% Hewlett-Packard with b = 1.4, and 35% Disney with b = What is this portfolio’s required (expected) return if the risk-free rate is 5% and the market expected return is 13%? Example: What is the portfolio beta for a portfolio consisting of 25% Home Depot with b = 1.1, 40% Hewlett-Packard with b = 1.4, and 35% Disney with b = What is this portfolio’s required (expected) return if the risk-free rate is 5% and the market expected return is 13%?

Continuing our Example Coca-Cola currently sells for $44. Should we add Coca-Cola with an expected price and dividend in a year of $48.27 & $1.24 and a b = 0.6 to our portfolio? Coca-Cola currently sells for $44. Should we add Coca-Cola with an expected price and dividend in a year of $48.27 & $1.24 and a b = 0.6 to our portfolio? To make our decision find Coke’s expected return using the holding period return formula and compare to Coke’s SML return. To make our decision find Coke’s expected return using the holding period return formula and compare to Coke’s SML return. Recall that r RF = 5% and r M = 13% Recall that r RF = 5% and r M = 13%

Drink Coke?

The Security Market Line (SML) A graphical representation of the CAPM/SML equation. A graphical representation of the CAPM/SML equation. Gives required (expected) returns for investments with different betas. Gives required (expected) returns for investments with different betas. Y axis = expected return, X axis = beta Y axis = expected return, X axis = beta Intercept = risk-free rate = 3-month T-bill rate (B = 0) Intercept = risk-free rate = 3-month T-bill rate (B = 0) Slope of SML = market risk premium Slope of SML = market risk premium For the following SML graph, let’s use a 3-month T-bill rate of 5% and assume investors require a market return of 13%. For the following SML graph, let’s use a 3-month T-bill rate of 5% and assume investors require a market return of 13%. Graph r = 5% + B(13%-5%) Graph r = 5% + B(13%-5%) Market risk premium = 13% - 5% = 8% Market risk premium = 13% - 5% = 8%

Our SML and Coke: r RF = 5%, r M = 13%

Changes to SML Equation What happens if inflation increases? What happens if inflation increases? What happens if investors become more risk averse about the stock market? What happens if investors become more risk averse about the stock market? Check out the following graphs with our base SML = 5% + (13%-5%)b Check out the following graphs with our base SML = 5% + (13%-5%)b

SML change, increase in inflation and r RF : r RF = 7%, r M = 15%

SML increase in risk aversion (market risk premium: r RF = 5%, r M = 16%

Finding Beta using Excel. There are two functions in Excel that will find the X coefficient (beta). There are two functions in Excel that will find the X coefficient (beta). The functions are LINEST and SLOPE. The functions are LINEST and SLOPE. The format is =LINEST(y range,x range) The format is =LINEST(y range,x range) The above format is the same for SLOPE. The above format is the same for SLOPE. Remember the stock’s returns is the y range, and the market’s returns is the x range. Remember the stock’s returns is the y range, and the market’s returns is the x range.