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Risk and Return

Risk and Return. Alasdair Mackay. 1. Learning Objectives. Define risk, risk aversion, and risk-return tradeoff. How to measure risk. Identify different types of risk. Explain methods of risk reduction. Describe how firms compensate for risk.

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Risk and Return

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  1. Risk and Return Alasdair Mackay 1

  2. Learning Objectives • Define risk, risk aversion, and risk-return tradeoff. • How to measure risk. • Identify different types of risk. • Explain methods of risk reduction. • Describe how firms compensate for risk. • Discuss the Capital Asset Pricing Model (CAPM) – how risk impacts rate of return 2

  3. Risk and Rates of Return • Risk is the potential for unexpected events to occur or a desired outcome not 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. 3

  4. Risk and Rates of Return • Risk averse investors will require higher expected rates of return as compensation for taking on higher levels of risk than someone who is risk tolerant (more willing to take on risk.) • The Chinese symbol for risk is made up of two characters. The first is for danger and the second is the character for opportunity. 4

  5. Measuring Risk • We can never avoid risk entirely, • Measuring risk is difficult; it depends on the degree of uncertainty in a situation • The greater the probability of an uncertain outcome, the greater the degree of risk 5

  6. Expected Return & Standard Deviation • Most decisions have a number of different possible outcomes or returns • Expected return is the mean, the average of a set of values, of the probability distribution of possible returns. • Future returns are not known with certainty. The standard deviation is a measure of this uncertainty. 6

  7. Standard Deviation • A numerical indicator of how widely dispersed the possible values are around a mean. • The more widely dispersed, the larger the standard deviation, and the greater the risk of unexpected values • The closer dispersed, the lower the standard deviation, and the lesser the risk of unexpected values. 7

  8. Expected Return • Expected return is the mean, or average, of the probability distribution of possible future returns. • To calculate expected return, compute the weighted average of possible returns where = Expected return Vi = Possible value of return during period i Pi = Probability (%) of V occurring during period i Vi x Pi) 8

  9. State of Economy Probability Return Economic Downturn .10 –5% Zero Growth .20 5% Moderate Growth .40 10% High Growth .30 20% 1.00 Expected Return Calculation Example: You are evaluating a common stock. You estimate the following returns given different states of the economy = – 0.5% = 1.0% = 4.0% = 6.0% k = 10.5% Expected rate of return on the stock is 10.5% 9

  10. =variance 2 = .005725 = 0.5725% • = SQRT of 0.005725 • = .07566 = 7.566% SQRT(P(V - )2) State of Economy Probability Return Economic Downturn .10 5% Zero Growth .20 5% Moderate Growth .40 10% High Growth .30 20% Measurement of Investment Risk • Standard Deviation (measures the dispersion of returns. It is the square root (SQRT) of the variance. Example: Compute the standard deviation on the common stock; the mean () was previously computed as 10.5% (- - 10.5%)2 = .24025% ( - 10.5%)2 = .0605% ( - 10.5%)2 = .001% ( - 10.5%)2 = .27075% = .5725% 10

  11. Measurement of Investment Risk • The standard deviation of 7.566% means that the stock return would be in the 10.5% range (the mean), plus or minus 7.566%! • That ‘s a very wide range! High Risk! • 10.5 + 7.566 = 18.066 • 10.5 – 7.566 = 2.934 • And this holds true for one standard deviation, or only 2/3 of the time • The other 1/3 of the time it could be above or below the standard deviation! 11

  12. Risk and Rates of Return 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 Diversification: If investors hold stock in many companies, the firm spefic risk will be cancelled out. Even if investors hold many stocks, cannot eliminate the market related risk. 13

  13. Diversifiable vs Non-diversifiable • Diversifiable risk, affects only one company, - give examples • Non-diversifiable risk, affects all companies, - give examples – credit/liquidity crisis. 14

  14. Variability of Returns # of stocks in Portfolio Risk and Rates of Return • Risk and Diversification • Total risk includes both company specific and market related risk • As you diversify, and cancel out company specific risk, total risk approximates market related risk Total Risk 15

  15. Variability of Returns # of stocks in Portfolio Risk and Rates of Return • Risk and Diversification • If an investor holds enough stocks in portfolio (about 20) company specific (diversifiable) risk is virtually eliminated Firm Specific Risk 16

  16. Variability of Returns # of stocks in Portfolio Risk and Rates of Return • Risk and Diversification • If an investor holds enough stocks in portfolio (about 20) company specific (diversifiable) risk is virtually eliminated • However, Market related risk remains Market Related Risk 17

  17. Risk and Rates of Return • Market risk is the risk that affects the overall market. • To measure how an individual company’s stock reacts to overall market fluctuations, we need to compare individual stock returns to the overall market returns. 18

  18. Risk and Rates of Return • A proxy for the market return is usually used: An index of stocks such as the S&P 500, or Dow Jones Industrial Average • A regression analysis of the individual stock returns to the returns of the market index measures the degree that stocks are impacted by the market • Let’s compare PepsiCo to the S & P 500 19

  19. PepsiCo Return 15% 10% 5% S&P Return -15% -10% -5% 5% 10% 15% -5% -10% -15% Risk and Rates of Return • Regress individual stock (PepsiCo) returns on Market (S & P 500) index 20

  20. PepsiCo Return 15% 10% 5% S&P Return -15% -10% -5% 5% 10% 15% -5% -10% -15% Risk and Rates of Return • Regress individual stock returns on Market index Jan 1999 PepsiCo -0.37% S&P -1.99% 21

  21. PepsiCo Return 15% 10% 5% S&P Return -15% -10% -5% 5% 10% 15% -5% -10% -15% Risk and Rates of Return • Regress individual stock returns on Market index for 22 months Plot Remaining Points 22

  22. PepsiCo Return 15% 10% 5% S&P Return -15% -10% -5% 5% 10% 15% -5% -10% -15% Risk and Rates of Return Regress individual stock returns on Market index returns – draw a best fit line Best Fit Regression Line 23

  23. PepsiCo Return 15% 10% 5% S&P Return -15% -10% -5% 5% 10% 15% rise run 5.5% 5% -5% Slope = = 1.1 = -10% -15% Risk and Rates of Return Regress individual stock returns on Market index returns – calculate the slope of the line 24

  24. Risk and Rates of Return • Market Risk is measured by Beta • Beta is the slope of the regression (characteristic) line, i.e., 1.1 for PepsiCo • Beta measures the relationship between the company returns and the market returns; measures non-diversifiable risk • PepsiCo has 1.1 times more volatility than the average stock in the S & P 500, which has a slope of 1.0.(by definition) 25

  25. Risk and Rates of Return • Interpreting Beta • Beta = 1 Market Beta = 1 Company with a beta of 1 has average risk • Beta < 1 Low Risk Company. Return on stock will be less affected by the market than average. It is extremely rare for stocks to have a negative beta(gold?) • Beta > 1 High Market Risk Company Stock return will be more affected by the market than average 26

  26. kj = kRF + j ( kM – kRF ) 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 as measured by beta. Security Market Line where: Kj= required rate of return on the jth security KRF= risk free rate of return (T-Bill) KM= required rate of return on the market Bj= Beta for the jth security 27

  27. kj = kRF + j ( kM – kRF ) CAPM Example • Suppose that the required return on the market is 12% and the risk free rate is 5%. Security Market Line 28

  28. 15% 10% 5% Beta .50 1.0 1.5 CAPM Example • Suppose that the required return on the market is 12% and the risk free rate is 5%. kj = 5% + j (12% – 5%) Risk Free Rate 29

  29. 15% 10% 5% Beta .50 1.0 1.5 CAPM Example • Suppose that the required return on the market is 12% and the risk free rate is 5%. kj = 5% + j (12% – 5%) Risk & Return on market Risk Free Rate 30

  30. SML 15% 13.4% 10% 5% Beta .50 1.5 1.0 1.2 CAPM Example Suppose that the required return on the market is 12% and the risk free rate is 5%. If Beta is 1.2, then Kj = 13.4 If beta = 1.2 kj = 13.4 kj = 5% + j (12% – 5%) Market 31

  31. Conclusion • What have we learnt: • Risk is two dimensional a product of impact and probability. • We call the most likely outcome the Mean. • We attempt to measure the probability by the Standard Deviation. • Risk of returns on stock is quantified by its Beta • Beta recognizes systemic risk but not un-systemic risk • The CAPM defines the Required Rate of Return on a stock. 32

  32. Small Standard Deviation Large Standard Deviation Same Means Different Standard Deviations Different Means Same Standard Deviations Different Means Different Standard Deviations The mean and standard deviation are useful ways to describe a set of returns. If the returns are grouped closely together, they will have a smaller standard deviation than if they are spread farther apart.

  33. If your data fits a normal distribution, approximately 68% of your returns will fall within one standard deviation of the mean. Approximately 95% of your returns will fall within two standard deviations of the mean. Over 99% of your returns will fall within three standard deviations of the mean.

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