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Chapter 4 - Risk and Rates of Return

Chapter 4 - Risk and Rates of Return. Ó 2005, Pearson Prentice Hall. Chapter 6: Objectives. Inflation and rates of return How to measure risk (variance, standard deviation, beta) How to reduce risk (diversification) How to price risk

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Chapter 4 - Risk and Rates of Return

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  1. Chapter 4 - Risk and Rates of Return Ó 2005, Pearson Prentice Hall

  2. Chapter 6: Objectives • Inflation and rates of return • How to measure risk (variance, standard deviation, beta) • How to reduce risk (diversification) • How to pricerisk (security market line, Capital Asset Pricing Model)

  3. Interest Rates Inflation, Rates of Return, and the Fisher Effect

  4. Interest Rates Conceptually:

  5. Conceptually: Nominal risk-free Interest Rate krf Interest Rates

  6. Conceptually: Nominal risk-free Interest Rate krf = Interest Rates

  7. Conceptually: Real risk-free Interest Rate k* Nominal risk-free Interest Rate krf = Interest Rates

  8. Conceptually: Real risk-free Interest Rate k* Nominal risk-free Interest Rate krf = + Interest Rates

  9. Conceptually: Real risk-free Interest Rate k* Nominal risk-free Interest Rate krf Inflation- risk premium IRP = + Interest Rates

  10. Conceptually: Mathematically: Real risk-free Interest Rate k* Nominal risk-free Interest Rate krf Inflation- risk premium IRP = + Interest Rates

  11. Conceptually: Mathematically: Real risk-free Interest Rate k* Nominal risk-free Interest Rate krf (1 + krf) = (1 + k*) (1 + IRP) Inflation- risk premium IRP = + Interest Rates

  12. Conceptually: Mathematically: Real risk-free Interest Rate k* Nominal risk-free Interest Rate krf (1 + krf) = (1 + k*) (1 + IRP) Inflation- risk premium IRP = + This is known as the “Fisher Effect” Interest Rates

  13. Interest Rates • Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate premium? (1 + krf) = (1 + k*) (1 + IRP) (1.08) = (1.03) (1 + IRP) (1 + IRP) = (1.0485), so IRP = 4.85%

  14. Term Structure of Interest Rates • The pattern of rates of return for debt securities that differ only in the length of time to maturity.

  15. yield to maturity time to maturity (years) Term Structure of Interest Rates • The pattern of rates of return for debt securities that differ only in the length of time to maturity.

  16. yield to maturity time to maturity (years) Term Structure of Interest Rates • The pattern of rates of return for debt securities that differ only in the length of time to maturity.

  17. yield to maturity time to maturity (years) Term Structure of Interest Rates • The yield curve may be downward sloping or “inverted” if rates are expected to fall.

  18. yield to maturity time to maturity (years) Term Structure of Interest Rates • The yield curve may be downward sloping or “inverted” if rates are expected to fall.

  19. For a Treasury security, what is the required rate of return?

  20. Required rate of return = For a Treasury security, what is the required rate of return?

  21. Required rate of return Risk-free rate of return = For a Treasury security, what is the required rate of return? Since Treasuries are essentially free of default risk, the rate of return on a Treasury security is considered the “risk-free” rate of return.

  22. For a corporate stock or bond, what is the required rate of return?

  23. Required rate of return = For a corporate stock or bond, what is the required rate of return?

  24. Required rate of return Risk-free rate of return = For a corporate stock or bond, what is the required rate of return?

  25. Required rate of return Risk-free rate of return Risk premium = + For a corporate stock or bond, what is the required rate of return? How large of a risk premium should we require to buy a corporate security?

  26. Returns • Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc. • Required Return - the return that an investor requires on an asset given itsriskand market interest rates.

  27. Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% For each firm, the expected return on the stock is just a weighted average:

  28. Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% For each firm, the expected return on the stock is just a weighted average: k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn

  29. Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn k (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%

  30. Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn k (OI) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%

  31. Based only on your expected return calculations, which stock would you prefer?

  32. Have you considered RISK?

  33. What is Risk? • The possibility that an actual return will differ from our expected return. • Uncertainty in the distribution of possible outcomes.

  34. What is Risk? • Uncertainty in the distribution of possible outcomes.

  35. Company A return What is Risk? • Uncertainty in the distribution of possible outcomes.

  36. Company A Company B return return What is Risk? • Uncertainty in the distribution of possible outcomes.

  37. How do We Measure Risk? • To get a general idea of a stock’s price variability, we could look at the stock’s price range over the past year. 52 weeks Yld Vol Net Hi Lo Sym Div % PE 100s Hi Lo Close Chg 134 80 IBM .52 .5 21 143402 98 95 9549 -3 115 40 MSFT … 29 558918 55 52 5194 -475

  38. How do We Measure Risk? • A more scientific approach is to examine the stock’s standard deviation of returns. • Standard deviation is a measure of the dispersion of possible outcomes. • The greater the standard deviation, the greater the uncertainty, and, therefore, the greater the risk.

  39. s n i=1 S Standard Deviation = (ki - k)2 P(ki)

  40. n i=1 s S = (ki - k)2 P(ki) Orlando Utility, Inc.

  41. n i=1 s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2

  42. n i=1 s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0

  43. n i=1 s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0 (14% - 10%)2 (.3) = 4.8

  44. n i=1 s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0 (14% - 10%)2 (.3) = 4.8 Variance = 12

  45. n i=1 s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0 (14% - 10%)2 (.3) = 4.8 Variance = 12 Stand. dev. = 12 =

  46. n i=1 s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0 (14% - 10%)2 (.3) = 4.8 Variance = 12 Stand. dev. = 12 = 3.46%

  47. n i=1 s S = (ki - k)2 P(ki) Orlando Technology, Inc.

  48. n i=1 s S = (ki - k)2 P(ki) Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2

  49. n i=1 s S = (ki - k)2 P(ki) Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2 (14% - 14%)2 (.5) = 0

  50. n i=1 s S = (ki - k)2 P(ki) Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2 (14% - 14%)2 (.5) = 0 (30% - 14%)2 (.3) = 76.8

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