html5-img
1 / 59

Chapter 6

Chapter 6. Risk and Rates of Return. 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 (security market line, CAPM). Historical Risk and Return.

gregory
Download Presentation

Chapter 6

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 6 Risk and Rates of Return

  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, CAPM)

  3. Historical Risk and Return • Annual From 1926 to 1999 Avg. ReturnStd Dev. Small Stocks 17.6% 33.6% Large Co. Stocks 13.3% 20.1% L-T Corp Bonds 5.9% 8.7% L-T Govt. Bonds 5.5% 9.3% T-Bills 3.8% 3.2% Inflation 3.2% 4.6%

  4. Why are these rates different? • 90-day Treasury Bill 1.7% • 90-day Commercial Paper 1.8% • 2-year US Treasury Note 3.0% • 10-year US Treasury Note 5.0% • 10-year Corporate Bond 6.9%

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

  6. Conceptually: Interest Rates

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

  11. 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%

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

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. Recent US Treasury Yield Curve

  18. 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.

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

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

  21. 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?

  22. 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.

  23. Holding Period (Actual) Returns • The realized return over a period of time (HPR). • HPR=(Ending Price - Beginning Price + Distributions Received)/Beginning Price • Example: What is your HPR if you buy a stock for $20, receive $1 in dividends, and then sell it for $25. • HPR = ($25-$20+$1)/$20 = 0.3 = 30%

  24. Calculation of Expected Returns • Expected Rate of Return (Expected Value) given a probability distribution of possible returns(ki): E(k) or k _ n E(k)=k = ki P(ki) i=1 • Realized or Average Return on Historical Data: - n k = 1/n k i i=1

  25. Expected Return and Standard Deviation Example • MAD E(r) = .25(80%) + .60(30%) + .15(-30%) = 33.5% • CON E(r) = .25(5%) + .60(10%) + .15(15%) = 9.5%

  26. Definition of Risk • Risk is an uncertain outcome or chance of an adverse outcome. • Concerned with the riskiness of cash flows from financial assets. • Namely, the chance that actual cash flows will be different from forecasted cash flows. • Standard Deviation can measure this type of risk.

  27. 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.

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

  29. Expected Return and Standard Deviation Example • MAD E(r) = .25(80%) + .60(30%) + .15(-30%) = 33.5% • CON E(r) = .25(5%) + .60(10%) + .15(15%) = 9.5%

  30. s = (ki - k)2 P(ki) n i=1 S MAD, Inc. ( 80% - 33.5%)2 (.25) = 540.56 (30% - 33.5%)2 (.6) = 7.35 (-30% - 33.5%)2 (.15) = 604.84 Variance = 1152.75% Stand. dev. = 1152.75 = 34.0%

  31. Expected Return and Standard Deviation Example • MAD E(r) = .25(80%) + .60(30%) + .15(-30%) = 33.5% • CON E(r) = .25(5%) + .60(10%) + .15(15%) = 9.5%

  32. s = (ki - k)2 P(ki) n i=1 S Contrary Co. (5% - 9.5%)2 (.25) = 5.06 (10% - 9.5%)2 (.6) = 0.15 (15% - 9.5%)2 (.15) = 4.54 Variance = 9.75% Stand. dev. = 9.75 = 3.1%

  33. Which stock would you prefer? How would you decide?

  34. Which stock would you prefer? How would you decide?

  35. Return Risk It depends on your tolerance for risk! Remember, there’s a tradeoff between risk and return.

  36. Coefficient of Variation • A relative measure of risk. Whereas, s is an absolute measure of risk. • Relates risk to expected return. • CV = s/E(k) • MAD’s CV = 34%/33.5% = 1.01 • CON’s CV = 3.1%/9.5% = 0.33 • CONtrary is the less risky of the two investments. Would choose CON if risk averse.

  37. Portfolios • Expected Portfolio Return is weighted average of the expected returns of the individual stocks = Σwjkj. • However, portfolio risk (standard deviation) is NOT the weighted average of the standard deviations of the individual stocks. • Combining several securities in a portfolio can actually reduce overall risk. • How does this work?

  38. kA rate of return kB time Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated).

  39. What has happened to the variability of returns for the portfolio? kA kp rate of return kB time

  40. Diversification • Investing in more than one security to reduce risk. • If two stocks are perfectly positively correlated, diversification has no effect on risk. • If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified.

  41. If you owned a share of every stock traded on the NYSE and NASDAQ, would you be diversified? YES! • Would you have eliminated all of your risk? NO! Common stock portfolios still have risk.

  42. Some risk can be diversified away and some cannot. • Market risk (systematic risk) is nondiversifiable. This type of risk cannot be diversified away. • Company-unique risk (unsystematic risk) is diversifiable. This type of risk can be reduced through diversification.

  43. Market Risk • Unexpected changes in interest rates. • Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle.

  44. Company-unique Risk • A company’s labor force goes on strike. • A company’s top management dies in a plane crash. • A huge oil tank bursts and floods a company’s production area.

  45. portfolio risk Market risk number of stocks As you add stocks to your portfolio, company-unique risk is reduced.

  46. portfolio risk company- unique risk Market risk number of stocks As you add stocks to your portfolio, company-unique risk is reduced.

  47. Do some firms have more market risk than others? Yes. For example: Interest rate changes affect all firms, but which would be more affected: a) Retail food chain b) Commercial bank

  48. Note: • The market compensates investors for accepting risk - but only for market risk. Company-unique risk can and should be diversified away. • So - we need to be able to measure market risk.

  49. This is why we have Beta. Beta: a measure of market risk. • Specifically, beta is a measure of how an individual stock’s returns vary with market returns. • It’s a measure of the“sensitivity”of an individual stock’s returns to changes in the market.

  50. The Concept of Beta • Beta(b) measures how the return of an individual asset (or even a portfolio) varies with the market portfolio. • b= 1.0 : same risk as the market • b< 1.0 : less risky than the market • b> 1.0 : more risky than the market • Beta is the slope of the regression line (y = a + bx) between a stock’s return(y) and the market return(x) over time, b from simple linear regression. • bi = Covariancei,m/Mkt. Var. =rimsism/sm2

More Related