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The Relationship Between Risk and Return

The Relationship Between Risk and Return. Goal of Financial Management:.

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The Relationship Between Risk and Return

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  1. The Relationship Between Risk and Return

  2. Goal of Financial Management: Maximize the value of the firm as determined by: the present value of its expected cash flows, discounted back at a rate that reflects both the riskiness of the firms projects and the financing mix used to fund the projects.

  3. Goals of Risk Analysis • A good risk and return model • Should apply to all assets • Explain the types of risk that are rewarded • Develop standardized risk measures • Translate risk into a rate of return demanded by the investor • Should do well explaining past returns and forecasting future returns.

  4. Issues Relating to Risk • Riskiness of the expected future cash flows • Stand Alone vs. Portfolio Risk • Diversifiable Risk vs. Non-Diversifiable (Market) Risk • Higher Market Risk Implies Higher Return • The same principles apply to physical assets

  5. Stand Alone Risk The risk faced from owning the asset by itself. (there are no other assets which help to spread risk) The return from owning the asset varies based on outcomes in the market Need to look at the expected return and standard deviation

  6. Probability Distributions • Probability Distribution provides the combinations of outcomes and the probability that the outcome will occur • Example: Weather Forecast • Outcome Probability • Rain .6 = 60% • No Rain .4 = 40%

  7. Probability • The probability tells the likelihood that it will rain. The probability is based upon the current conditions. • Given 100 days with the current conditions (the history), it will rain on 60 of the following days. • We want to use the same logic when discussing the possible return from owning the stock - what is the history?

  8. An Example • Intel has decided to introduce its new computer chip. There are three possible outcomes and three possible returns • Outcome Return Prob • 1) High Demand 90% 40% • 2) Average Demand 30% 20% • 3) Low Demand -80% 40%

  9. Example Continued • Assume MidAmerican Energy is also facing three outcomes • Outcome Return Prob • 1) High Demand 15% 25% • 2) Average Demand 10% 50% • 3) Low Demand 5% 25% • How would you compare the two stocks?

  10. Expected Rate of Return • To compare the two stocks you would need to find the expected rate of return

  11. Intel Demand RetProbRet x Prob • High 90% 40% (.9)(.4) = .36 • Average 30% 20% (.3)(.2) = .06 • Low -80% 40% (-.8)(.4) = -.32 • expected return 10%

  12. Mid American Energy • Demand Ret Prob Ret x Prob • High 15% 25% (.15)(.25) = .0375 • Average 10% 50% (.1)(.5) = .0500 Low 5% 25% (.25)(.05) = .0125 • expected return 10% • The expected return for each stock is 10% • Which would you prefer to own?

  13. Measuring Stand Alone Risk To compare the stand alone risk you need to look at the standard deviation: To calculate Standard Deviation: 1) Find Expected return 2) Subtract expected return from each outcomes return 3) Square the number in 2) 4) Multiply the squares by the probabilities and sum them together 5) Take the square root of the number in 4

  14. Intel • Demand (Ret-ExpectRet)2 x Prob • High (90% - 10%)2 x(.40) = .2560 • Average (30% - 10%)2 x (.20) = .0080 • Low (-80% - 10%)2 x (.40) = .3240 • .5880 • take the square root (.5880)1/2 • standard deviation = .7668 =76.68%

  15. Mid American Energy • Demand (Ret-ExpectRet)2 x Prob • High (15%-10%)2 x (.25) = .000625 • Average (10%- 10%)2 x (.50) = 0.00 • Low (5% - 10%)2 x (.25) = .000625 • .00125 • take the square root (.00125)1/2 • standard deviation = .035355 = 3.54%

  16. Interpreting Standard Deviation • What does the standard deviation tell us? • Assuming that the returns are normally distributed: • The actual return will be within one standard deviation 68.26% of the time. • This means that we can expect the return to fall in a range between the expected return plus and minus the standard deviation 68% of the time

  17. Prob Ranges for Normal Dist. 68.26% 95.46% 99.74%

  18. Our Example Intel had an expected return of 10% and standard deviation of 76.64%. Therefore we expect the return to be between 10-76.64 = - 66.64% and 10+76.64 = 86.64% 68% of the time Mid American Energy had an expected return of 10% and standard deviation of 3.536 implying an interval form 6.464% to 13.536% Which would you rather own?

  19. Trade off Between Risk and Return

  20. Risk Aversion • Generally, people are risk averse. (They avoid risk) • In our example the expected return is the same for both stocks, but Intel is much riskier (as measured by the standard deviation) • What if the expected returns were not the same?

  21. Which do you prefer? • Project A expected return of 50% with standard deviation of 30% • Project B expected return of 8% with standard deviation of 15%

  22. Coefficient of Variation • The amount of risk per unit of return which is equal to: • Calculating the Coefficient of Variation: Project A 30/50 = .6 Project B 15/8 = 1.875

  23. Semi Variance • If stocks are normally distributed they are symmetric about the mean. • This teats upside and downside risk equally. • An investor is often more concerned about the chance that a return falls below what is expected – or in other words the downside risk.

  24. Semi Variance Where: n = number of periods where actual return<average return

  25. Sources of Risk • Project Risk – Factors influencing the realized cash flows of the project – error in estimation • Competitive Risk – Cash flows impacted by the actions of a competitor • Industry-Specific Risk – Technology, Legal, and Commodity Risk • International risk – Political risk and exchange rate risk • Market Risk – Impacts all firms, marcoeconomic changes such as inflation and interest rates

  26. Risk Intuition • Diversification – It is possible to decrease the impact of some of the risks through diversification. • Example: Project risk can be offset by other projects undertaken by the firm. • Which of the risks on the previous slide can be diversified? Which Can’t? • As an investor, which risks should you be more concerned with (which can be diversified)?

  27. Risk and Diversification Project Risk Competitive Risk Industry Wide Risk International Risk Market Risk Firm Specific Affects One Firm Market Risk Affects All Firms Firm Can Reduce Risk By: Multiple Projects Acquiring Competitors Diversifying Across Sectors Diversifying Across Countries Cannot Affect Investors Can Mitigate Risk By: Diversifying Across Domestic Firms & Markets Diversifying Globally Diversifying Across Asset Classes

  28. Quick Stats Review • Covariance: • Combines the relationship between the stocks with the volatility. • (+) the stocks move together • (-) The stocks move opposite of each other

  29. Stats Review 2 • Correlation coefficient: The covariance is difficult to compare when looking at different series. Therefore the correlation coefficient is used. • The correlation coefficient will range from • -1 to +1

  30. Risk in a Portfolio Context • The expected return of a portfolio of assets is equal to the weighted average of the expected returns of the individual assets. • Example four stocks 25% of your $ in each • Intel 25% Disney 10% • BP 15% Citicorp 16% Portfolio Expect Ret (.25)(.25)+(.1)(.25)+(.15)(.25)+(.16)(.25)=.165

  31. Standard Deviation • The standard deviation of the portfolio will not equal the weighted average of the standard deviations of the stocks in the portfolio. • The standard deviation can be calculated from each years portfolio expected return just like for an individual asset.

  32. Example 1 Two stocks with correlation coefficient = -1 Year Stock A Stock B Portfolio 2004 26% -6% 10% 2005 6% 14% 10% 2006 -4% 24% 10% 2007 12% 8% 10% Avg Ret 10% 10% 10% Stand dev 10.86 10.86 0

  33. Example 2 Two stocks with correlation coefficient =+1 Year Stock A Stock B Portfolio 2004 16% 19% 17.5% 2005 8% 7% 7.5% 2006 12% 13% 12.5% 2007 4% 1% 2.5% Avg Ret 10% 10% 10% Stand dev 4.47 6.71 5.59

  34. Example 3 Two stocks with correlation coefficient =+.571 Year Stock A Stock B Portfolio 2004 18% 22% 20% 2005 -4% 12% 4% 2006 24% 18% 21% 2007 2% -12% -5% Avg Ret 10% 10% 10% Stand dev 11.4 13.19 10.9

  35. Real World • Most stocks have a correlation between +0.5 and +0.7 • Why is it usually positive? • What type of risk does this represent?

  36. Portfolio Effects • Each stock has two types of risk • Market Related (Non diversifiable) • Firm Specific (Diversifiable) • Increasing the number of stocks in your portfolio should increase the diversification, lowering the portfolio risk. • However there is a limit to the decrease in risk, since most stocks are positively correlated you can not eliminate all of the market risk

  37. Calculations of Standard Deviation • Variance and Standard Deviation can be calculated if you know the correlation coefficient and standard deviation of each asset. • For two assets:

  38. Marginal Investor • The investor “trading at the margin” who has the most influence on the price. • The type of marginal investor plays a key role in determining how a firm may respond to different circumstances • Usually it is assumed that the marginal investor is well diversified.

  39. Measuring Market Risk and The Market Portfolio • A market portfolio of all stocks available still has a positive standard deviation. The market portfolio would represent the return on the “average” stock.

  40. Capital Asset Pricing Model • CAPM relates an assets market risk to the expected return from owning the asset. • Major components: • Risk Free Rate - the return earned on an asset that is risk free (US Treasuries) • Beta - A measure of the firms market risk compared to the “average” firm • Market Return - the expected return on a portfolio of all similar assets

  41. Beta - Intuition Beta measures the sensitivity of the individual asset to movements in the market for similar assets. • Stock example: • Assume the S&P500 increases by 10% • If a stock also increase by 10% over the same period it would have a beta equal to 1. • If a stock increases by more than 10% its beta will be greater than 1.

  42. Beta - Intuition • A higher beta implies that the stock is more sensitive to an economy wide fluctuation than the market portfolio. • In other words the stock has a higher amount of Non-diversifiable risk. • Since the Market risk for the stock is higher it should also have a higher return...

  43. Risk and Return • The CAPM compares the return on the market portfolio to a risk free rate, the difference is the market risk premium. • The Market Risk Premium represents the extra return for accepting the market risk related to the riskier asset (the extra return on the “average” stock).

  44. CAPM ri=rRF+Bi(rM-rRF) Where: ri = The return on asset i rRF = The return on the Risk Free Asset rM = The return on the Market Portfolio Bi = the beta on asset i

  45. ri=rRF+Bi(rM-rRF) • Example: • Bank of America has a beta of 1.55 • Let If rRF = 7% and rM = 9.2% • The return on Bank of America stock is: • ri= rRF + Bi ( rM - rRF )r = .07 +1.55 (.092-.07) = .104

  46. Market Risk Premium • The Market Risk Premium is the extra return from investing in the “average” stock. In the CAPM this is equal to rM-rRF • The market risk premium represents the market risk. • If a stock had a beta of 1 it would earn • ri= rRF + Bi ( rM - rRF )r= .07 + 1.0 (.092-.07) = .092 • which is the market return

  47. Risk and Return • Given the inputs to the CAPM you can develop the relationship between the risk of an asset (as measured by beta) and its return. • An easy way to demonstrate this is to graph the possible risk and return combinations.

  48. Graphing the Security Market Line • ri= rRF + Bi ( rM - rRF ) • Let risk (Bi) be on the horizontal axis and return (ri) be on the vertical axis. • The slope of the line is then equal to the market risk premium (rm-rRF) • Then you can graph all the possible combinations of risk and return.

  49. ri= rRF + Bi ( rM - rRF ) • Lets put in some numbers for beta and ki • beta = 0 ri = .07+0(.092-.07)=.07= rRF • beta = 1 ri = .07+1(.092-.07)=.092= rM • beta =1.55 ri = .07 +1.55(.092-.07) = .104

  50. B=0,r=rRFB=1,r=0.092B=1.55,r=.104 Return Security Market Line .104 0.092 rRF 0 1.0 1.55 Beta

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