CHAPTER 5 Risk and Rates of Return n

CHAPTER 5 Risk and Rates of Return n Stand-alone risk Portfolio risk Risk & return: CAPM / SML 5 -1

Investment returns The rate of return on an investment can be calculated as follows: Return = (Amount received – Amount invested) ____________ Amount invested For example, if $1, 000 is invested and $1, 100 is returned after one year, the rate of return for this investment is: ($1, 100 - $1, 000) / $1, 000 = 10%. 5 -2

What is investment risk? n Two types of investment risk n n Stand-alone risk Portfolio risk Stand-alone risk: The risk an investor would face if he or she held only one asset. Portfolio risk: The riskiness of assets held in portfolios. 5 -3

Expected Rate of return n Company IBM The rate of return expected to be realized from an investment. Expected Rate of Return -22% -2 20 35 50 Probability 10% 20 40 20 10 5 -4

Return: Calculating the expected return for each alternative 5 -5

Summary of expected returns for all alternatives IBM Market USR T-bill Shell Exp return 17. 4% 15. 0% 13. 8% 8. 0% 1. 7% IBM has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk? 5 -6

Risk: Calculating the standard deviation for each alternative 5 -7

Standard deviation calculation 5 -8

Comments on standard deviation as a measure of risk n n n Standard deviation (σi) measures total, or stand-alone, risk. The larger σi is, the lower the probability that actual returns will be closer to expected returns. Difficult to compare standard deviations, because return has not been accounted for. 5 -9

Comparing risk and return Security Expected return Risk, σ 8. 0% 0. 0% IBM 17. 4% 20. 04% Shell 1. 7% 13. 4% USR 13. 8% Market 15. 0% 15. 3% T-bills 5 -10

Coefficient of Variation (CV) A standardized measure of dispersion about the expected value, that shows the risk per unit of return. n Very useful in comparing the risk of assets that have different expected returns. n 5 -11

Risk rankings, by coefficient of variation T-bill IBM Shell USR Market n n CV 0. 000 1. 152 7. 882 1. 000 1. 020 Shell has the highest degree of risk per unit of return. IBM, despite having the highest standard deviation of returns, has a relatively average CV. 5 -12

Investor attitude towards risk n n Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities. 5 -13

Portfolio construction: Risk and return Assume a two-stock portfolio is created with $50, 000 invested in both IBM and Shell. n Expected return of a portfolio is a weighted average of each of the component assets of the portfolio. 5 -14

Calculating portfolio expected return 5 -15

Calculating portfolio standard deviation Forecasted return Year IBM Shell 2004 2005 2006 2007 2008 8% 10 12 14 16 16% 14 12 10 8 Portfolio Return Calculation (. 50*8%) + (. 50*16%) (. 50*10%) + (. 50*14%) (. 50*12%) + (. 50*12%) (. 50*14%) + (. 50*10%) (. 50*16%) + (. 50*8%) Expected Portfolio Return 12% 12% 12% 5 -16

Calculating portfolio standard deviation (cont. ) n Expected value of portfolio return, 2004 -2008 12% + 12% KP = 5 = 12% 5 -17

Calculating portfolio standard deviation (cont. ) 5 -18

Alternative Formula for Calculating portfolio standard deviation 5 -19

Returns distribution for two perfectly negatively correlated stocks (ρ = -1. 0) Stock W Stock M Portfolio WM 25 25 25 15 15 15 0 0 0 -10 -10 5 -20

Returns distribution for two perfectly positively correlated stocks (ρ = 1. 0) Stock M’ Stock M Portfolio MM’ 25 25 25 15 15 15 0 0 0 -10 -10 5 -21

Illustrating diversification effects of a stock portfolio sp (%) 35 Company-Specific Risk Stand-Alone Risk, sp 20 Market Risk 0 10 20 30 40 2, 000+ # Stocks in Portfolio 5 -22

Breaking down sources of risk Stand-alone risk = Market risk + Firm-specific risk n n Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta. (e. g. War, Inflation, High Interest Rates) Firm-specific risk – portion of a security’s stand -alone risk that can be eliminated through proper diversification. 5 -23

Capital Asset Pricing Model (CAPM) n n Model based upon concept that a stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification. CAPM : Ke= Rf + β(Rm – Rf) Rf = Risk free rate of return Rm = Market Return β = Beta Coefficient Ke = Required Return 5 -24

Beta n n Measures a stock’s market risk, and shows a stock’s volatility relative to the market. Indicates how risky a stock is if the stock is held in a well-diversified portfolio. 5 -25

Comments on beta n n n If beta = 1. 0, the security is just as risky as the average stock. If beta > 1. 0, the security is riskier than average. If beta < 1. 0, the security is less risky than average. Most stocks have betas in the range of 0. 5 to 1. 5. The beta coefficient for the market = 1 Betas May be positive or negative. But, positive is the norm. 5 -26

The Security Market Line (SML): Calculating required rates of return SML: ki = k. RF + (k. M – k. RF) βi n n n Assume k. RF = 8%, k. M = 15% and βi =1. 3 The market (or equity) risk premium is RPM = k. M – k. RF = 15% – 8% = 7%. ki = 8. 0% + (15. 0% - 8. 0%)(1. 30) = 8. 0% + (7. 0%)(1. 30) = 8. 0% + 9. 1% = 17. 10% 5 -27

An example: Equally-weighted two-stock portfolio n n Create a portfolio with 50% invested in HT and 50% invested in Collections. The beta of a portfolio is the weighted average of each of the stock’s betas. βP = w 1 β 1 + w 2 βP = 0. 5 (1. 30) + 0. 5 (-0. 87) βP = 0. 215 5 -28