Define risk, risk aversion, and riskreturn

Size: px

Start display at page:

Download "Define risk, risk aversion, and riskreturn"

Daniela Summers
5 years ago
Views:

1 Risk and 1

2 Learning Objectives Define risk, risk aversion, and riskreturn tradeoff. Measure risk. Identify different types of risk. Explain methods of risk reduction. Describe how firms compensate for risk. Discuss the CAPM. 2

3 Expected Expected return is the mean of the probability distribution of possible returns. Future returns are not known with certainty. The standard deviation is a measure of this uncertainty. 3

weighted average of possible returns μ = Σ(V i x P i ) where μ V i P i = Expected return

4 Expected Expected return is the mean of the probability distribution of possible returns. Future returns are not known with certainty To calculate expected return, compute the weighted average of possible returns μ = Σ(V i x P i ) where μ V i P i = Expected return = Possible value of return during period i = Probability of V occurring during period i 4

different states of the economy State of

10 5% Zero Growth.20 5% Moderate Growth.

5 Expected Calculation Example: You are evaluating Zumwalt Corporation s common stock. You estimate the following returns given different states of the economy State of Economy Probability Economic Downturn.10 5% Zero Growth.20 5% Moderate Growth.40 10% High Growth.30 20% Expected rate of return on the stock is 10.5% = 0.5% = 1.0% = 4.0% = 6.0% k = 10.5% 5

will choose the less risky alternative because they are risk averse i.e. they don t like risk.

6 Risk is the potential for unexpected events to occur. If two financial alternatives are similar except for their degree of risk, most people will choose the less risky alternative because they are risk averse i.e. they don t like risk. Risk averse investors will require higher expected rates of return as compensation for taking on higher levels of risk. 6

Measurement of Investment Risk Example: You

Corporation s common stock and a one year

owning Zumwalt 30% stock, no risk in owning

7 Measurement of Investment Risk Example: You evaluate two investments: Zumwalt Corporation s common stock and a one year Gov't Bond paying a guaranteed 6%. Probability of T-Bill Probability of Zumwalt Corp 100% 40% There is risk in owning Zumwalt 30% stock, no risk in owning the T-bills 20% 10% 6% 5% 5% 10% 20% Link to Society for Risk Analysis 7

Measurement of Investment Risk Standard Deviation (σ) measures the

σ = SQRT( Σ P(V - μ) 2 ) Example: Compute the standard deviation on

the mean (μ) was previously computed as 10.5% σ 2 =.005725 = 0.

005725 Economic Downturn.10 (-σ 5% =.07566-10.5%) = 2 7.566% =.

8 Measurement of Investment Risk Standard Deviation (σ) measures the dispersion of returns. It is the square root of the variance. σ = SQRT( Σ P(V - μ) 2 ) Example: Compute the standard deviation on Zumwalt Σ= σ 2 = common variance stock. the mean (μ) was previously computed as 10.5% σ 2 = = % State of Economy Probability σ = SQRT of Economic Downturn.10 (-σ 5% = %) = % =.24025% Zero Growth.20 ( 5% %) 2 =.0605% Moderate Growth.40 ( 10% %) 2 =.001% High Growth.30 ( 20% %) 2 =.27075% 8

9 Risk of a company's stock can be separated into two parts: Firm Specific Risk - Risk due to factors within the firm Market related Risk - Risk due to overall market conditions Stock price will most likely fall if a major government contract is discontinued unexpectedly. Stock price is likely to rise if overall stock market is doing well. Diversification: If investors hold stock in many companies, the firm specific risk will be cancelled out. Even if investors hold many stocks, cannot eliminate the market related risk 9

(diversifiable) risk is virtually eliminated

10 Risk and Diversification If an investor holds enough stocks in portfolio (about 20) company specific (diversifiable) risk is virtually eliminated Variability of s Market Related Risk # of stocks in Portfolio 10

11 Risk and Diversification If an investor holds enough stocks in portfolio (about 20) company specific (diversifiable) risk is virtually eliminated Variability of s Firm Specific Risk # of stocks in Portfolio 11

12 Risk and Diversification If an investor holds enough stocks in portfolio (about 20) company specific (diversifiable) risk is virtually eliminated Variability of s Total Risk # of stocks in Portfolio 12

A proxy for the market is usually used: An index of stocks such as the S&P 500 Market risk

13 Market risk is the risk of the overall market, so to measure we need to compare individual stock returns to the overall market returns. A proxy for the market is usually used: An index of stocks such as the S&P 500 Market risk measures how individual stock returns are affected by this market Regress individual stock returns on the returns of the market index 13

14 Regress individual stock returns on Market index PepsiCo 15% 10% 5% -15% -10% -5% 5% 10% 15% -5% S&P -10% -15% 14

15 Regress individual stock returns on Market index PepsiCo 15% 10% 5% -15% -10% -5% 5% 10% 15% S&P Jan 1999 PepsiCo-0.37% S&P -1.99% -5% -10% -15% 15

16 Regress individual stock returns on Market index PepsiCo 15% 10% 5% -15% -10% -5% 5% 10% 15% S&P Plot Remaining Points -5% -10% -15% 16

17 Regress individual stock returns on Market index returns PepsiCo 15% Best Fit Regression Line 10% 5% -15% -10% -5% 5% 10% 15% -5% S&P -10% -15% 17

18 Regress individual stock returns on Market index returns PepsiCo 15% 10% 5% -15% -10% -5% 5% 10% 15% S&P Slope = rise run 5.5% = = 1.1 5% -5% -10% -15% 18

19 Market Risk is measured by Beta Beta is the slope of the regression (characteristic) line 19

20 Market Risk is measured by Beta Beta is the slope of the regression (characteristic) line PepsiCo 15% 10% 5% S&P -15% -10% -5% 5% 10% 15% -5% -10% Slope = 1.1 = Beta (β) -15% 20

21 Interpreting Beta Beta = 1 Market Beta = 1 Company with a beta of 1 has average risk Beta < 1 Low Risk Company on stock will be less affected by the market than average Beta > 1 High Market Risk Company Stock return will be more affected by the market than average 21

22 The Capital Asset Pricing Model Investors adjust their required rates of return to compensate for risk. The CAPM measures required rate of return for investments, given the degree of market risk measured by beta. Security Market Line k j = k RF + β j ( k M k RF ) where: K j = required rate of return on the j th security K RF = risk free rate of return K M = required rate of return on the market = Beta for the j th security B j 22

23 CAPM Example Suppose that the required return on the market is 12% and the risk free rate is 5%. Security Market Line k j = k RF + β j ( k M k RF ) 23

24 CAPM Example Suppose that the required return on the market is 12% and the risk free rate is 5%. k j = 5% + β j (12% 5% ) 15% 10% 5% Risk Free Rate Beta

25 CAPM Example Suppose that the required return on the market is 12% and the risk free rate is 5%. k j = 5% + β j (12% 5% ) 15% 10% Risk & on market 5% Risk Free Rate Beta

26 CAPM Example Suppose that the required return on the market is 12% and the risk free rate is 5%. 15% SML 10% Market 5%.50 Connect Points for Security Market Line Beta

27 CAPM Example Suppose that the required return on the market is 12% and the risk free rate is 5%. If beta = 1.2 k j = 13.4 k j = 5% + β j (12% 5% ) 15% 13.4% 10% Market SML 5% Beta

Chapter 13 Return, Risk, and Security Market Line

1 Chapter 13 Return, Risk, and Security Market Line Konan Chan Financial Management, Spring 2018 Topics Covered Expected Return and Variance Portfolio Risk and Return Risk & Diversification Systematic