1. Chapter 8 1

2.  Based on annual returns from 1926-2004 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% 2

3.  Risk: The Big Picture  Expected Return  Stand Alone Risk  Portfolio Return and Risk  Risk Diversification  Market Risk  Beta  CAPM/Security Market Line Equation (SML) 3

4.  Risk is an uncertain outcome or chance of an adverse outcome.  Concerned with the riskiness of cash flows from financial assets.  Stand Alone Risk: Single Asset  relevant risk measure is the total risk of expected cash flows measured by standard deviation. 4

5.  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.  correlation (  or r) between asset returns which affects portfolio standard deviation 5

6. Well-diversified Portfolio  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.  The relevant risk measure is Beta which measures the riskiness of an individual asset in relation to the market portfolio. 6

7. 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 = (54-50+3)/50 =.14 or 14% CGY = 4/50 = 8%, DY = 3/50 = 6% 7

8.  Expected Rate of Return given a probability distribution of possible returns(r i ): E(r) n E(r) =  P i r i i=1  Realized or Average Return on Historical Data: - n r = 1/n  r i i=1 8

9.  Relevant Risk Measure for single asset Variance =  2 =  ( r i - E(r)) 2 P i  Standard Deviation = Square Root of Variance  Historical Variance =  2 = 1/n  (r i – r AVG ) 2  Sample Variance = s 2 = 1/(n-1)  (r i – r AVG ) 2 9

10. 10

11. 11

12.  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.  CV =  /E(r)  CV is a measure of relative risk, where standard deviation measures absolute risk. 12

13.  MAD Inc.  E(r) = 33.5%   = 34.0%  CV = 34%/33.5%  CV = 1.015  Contrary Co.  E(r) = 7.5%   = 8.5%  CV = 8.5%/7.5%  CV = 1.133 13

14.  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%  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% 14

15.  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  All else constant: Lower r = less portfolio risk 15

16.  Each MAD-CON r i =.6(MAD)+.4(CON);  E(R p ) = 23.1% 16

17. 17

18.  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)  This remaining risk is called Market Risk and is measured by Beta. 18

19.  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 : less 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.  Sources for stock betas: ValueLine Investment Survey (at BEL), Yahoo Finance, MSN Money, Standard & Poors 19

20.  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.  A stock’s risk premium = measure of market risk X market risk premium. 20

21.  RP M = market risk premium = r M - r RF  RP i = stock risk premium = (RP M )b i  r i = r RF + (r M - r RF )b i = r RF + (RP M )b i 21

22.  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? 22

23.  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 = 1.0, 40% Hewlett-Packard with b = 1.35, and 35% Disney with b = 1.25. What is this portfolio’s required (expected) return if the risk-free rate is 5% and the market expected return is 14%? 23

24.  AT&T currently sells for $36.50. Should we add AT&T with an expected price and dividend in a year of $39.54 & $1.42 and a b = 1.2 to our portfolio?  To make our decision find AT&T’s expected return using the holding period return formula and compare to AT&T’s SML return.  Recall that r RF = 5% and r M = 14% 24

25. 25

26.  A graphical representation of the CAPM/SML equation.  Gives required (expected) returns for investments with different betas.  Y axis = expected return, X axis = beta  Intercept = risk-free rate = 3-month T-bill rate (B = 0)  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 14%.  Graph r = 5% + B(14%-5%)  Market risk premium = 14% - 5% = 9% 26

27. 27

28.  What happens if inflation increases?  What happens if investors become more risk averse about the stock market?  Check out the following graphs with our base SML = 5% + (14%-5%)b 28

29. 29

30. 30

31.  There are two functions in Excel that will find the X coefficient (beta).  The functions are LINEST and SLOPE.  The format is =LINEST(y range,x range)  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. 31