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CHAPTER 8 Risk and Rates of Return

CHAPTER 8 Risk and Rates of Return. Stand-alone risk Portfolio risk Risk & return: CAPM / SML. Investment returns. The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return = ________________________ Amount invested

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CHAPTER 8 Risk and Rates of Return

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  1. CHAPTER 8Risk and Rates of Return Stand-alone risk Portfolio risk Risk & return: CAPM / SML

  2. Investment returns The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return =________________________ Amount invested For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.

  3. What is investment risk? • Investment risk is related to the probability of earning a low or negative actual return. • The greater the chance of lower than expected or negative returns, the riskier the investment.

  4. Selected Realized Returns, 1990 – 2007 Average Standard ReturnDeviation Small-company stocks 17.5% 33.1% Large-company stocks 12.4 20.3 L-T corporate bonds 6.2 8.6 Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2008 Yearbook (Bursa Malaysia, 2008)

  5. Investment alternatives & Rate of Returns( %)

  6. Investment alternatives & Rate of Returns( %) • T-bills will return the promised 5.5%, regardless of the economy- risk-free return • Do T-bills promise a completely risk-free return? • T-bills do not provide a completely risk-free return, as they are still exposed to inflation.. • T-bills are also risky in terms of reinvestment rate risk. • However, T-bills are risk-free in the default sense of the word.

  7. “Reinvestment Risk” • CF • CF • CF • CF • CF 5.5% 5.5% 5.5% 5.5% 5.5% • “reinvest cash inflow at going market rates” • Thus, if market rates , may experience income reduction

  8. “inflation risk” If inflation rate = 8% - funds deposited loses the purchasing power - “inflation risk”

  9. How do the returns of HT and Coll. behave in relation to the market? • HT – Moves with the economy, and has a positive correlation. This is typical. • Coll. – Is countercyclical with the economy, and has a negative correlation. This is unusual.

  10. Calculating the expected return

  11. Summary of expected returns Expected return HT 12.4% Market 10.5% USR 9.8% T-bill 5.5% Coll. 1.0% HT has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?

  12. Expected returns & Standard deviation 12.4 HT’s expected return

  13. Calculating standard deviation

  14. (-27-1.24)2(0.1) + (-7-12.4)2(0.2) (15-12.4)2(0.4) + (30-12.4)2(0.2) (45-12.4)2(0.1) 1/2 6HT = 6HT 20% =

  15. Expected returns & Standard deviation -7.6% 12.4% 32.4%

  16. Standard deviation for each investment

  17. Prob. T - bill USR HT 0 5.5 9.8 12.4 Rate of Return (%) Comparing standard deviations

  18. Comments on standard deviation as a measure of risk • Standard deviation (σi) measures total, or stand-alone, risk. • The larger σi is, the lower the probability that actual returns will be closer to expected returns. • Larger σi is associated with a wider probability distribution of returns.

  19. Comparing risk and return ^

  20. Investor attitude towards risk • Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. • Risk premium – the difference between the return on a risky asset and a riskless asset, which serves as compensation for investors to hold riskier securities.

  21. Portfolio construction:Risk and return • Assume a two-stock portfolio is created with $50,000 invested in both HT and Collections. • A portfolio’s expected return is a weighted average of the returns of the portfolio’s component assets.

  22. Calculating portfolio expected return = expected return = 12.4% = 1.0%

  23. An alternative method for determining portfolio expected return *A: 0.5(-27%) + 0.5(27) = 0% *B: 0.5(-7%) + 0.5(13%) = 3%

  24. Calculating portfolio standard deviation

  25. Comments on portfolio risk measures • σp = 3.4% is much lower than the σi of either stock (σHT = 20.0%; σColl. = 13.2%). • Therefore, the portfolio provides the average return of component stocks, but lower than the average risk. • Why? Negative correlation between stocks. • Combining stocks in a portfolio generally lowers risk.

  26. Stock W Stock M Portfolio WM 25 15 0 0 0 -10 -10 Returns distribution for two perfectly negatively correlated stocks (ρ = -1.0) 25 25 15 15 -10

  27. Stock M’ Portfolio MM’ Stock M 25 25 25 15 15 15 0 0 0 -10 -10 -10 Returns distribution for two perfectly positively correlated stocks (ρ = 1.0)

  28. sp (%) Diversifiable Risk 35 Stand-Alone Risk, sp 20 0 Market Risk 10 20 30 40 2,000+ # Stocks in Portfolio Illustrating diversification effects of a stock portfolio

  29. Creating a portfolio:Beginning with one stock and adding randomly selected stocks to portfolio • σp decreases as stocks added, because they would not be perfectly correlated with the existing portfolio. • Expected return of the portfolio would remain relatively constant. • Eventually the diversification benefits of adding more stocks dissipates (after about 10 stocks), and for large stock portfolios, σp tends to converge to  20%.

  30. Breaking down sources of risk • Diversifiable risk – portion of a security’s stand-alone risk that can be eliminated through proper diversification. • Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta.

  31. Beta • Measures a stock’s market risk, and shows a stock’s volatility relative to the market. • If beta = 1.0, the security is just as risky as the average stock. • If beta > 1.0, the security is riskier than average. • If beta < 1.0, the security is less risky than average. • Most stocks have betas in the range of 0.5 to 1.5.

  32. Calculating betas • Well-diversified investors are primarily concerned with how a stock is expected to move relative to the market in the future. • A typical approach to estimate beta is to run a regression of the security’s past returns against the past returns of the market. • The slope of the regression line is defined as the beta coefficient for the security.

  33. _ ri . 20 15 10 5 . Year rM ri 1 15% 18% 2 -5 -10 3 12 16 _ -5 0 5 10 15 20 rM Regression line: ri = -2.59 + 1.44 rM . -5 -10 ^ ^ Illustrating the calculation of beta

  34. Comparing expected returns and beta coefficients SecurityExpected Return Beta HT 12.4% 1.32 Market 10.5 1.00 USR 9.8 0.88 T-Bills 5.5 0.00 Coll. 1.0 -0.87 Riskier securities have higher returns, so the rank order is OK.

  35. Can the beta of a security be negative? • Yes, if the correlation between Stock i and the market is negative (i.e., ρi,m < 0). • If the correlation is negative, the regression line would slope downward, and the beta would be negative. • However, a negative beta is highly unlikely.

  36. _ ri HT: b = 1.30 40 20 T-bills: b = 0 _ kM -20 0 20 40 Coll: b = -0.87 -20 Beta coefficients for HT, Coll, and T-Bills

  37. Capital Asset Pricing Model (CAPM) • Model linking risk and required returns. CAPM suggests that there is a Security Market Line (SML) that states that a stock’s required return equals the risk-free return plus a risk premium. ri = rRF + (rM – rRF) bi

  38. The Security Market Line (SML):Calculating required rates of return SML: ri = rRF + (rM – rRF) bi ri = rRF + (RPM) bi • Assume the rRF = 5.5% and RPM = 5.0%.

  39. What is the market risk premium (RPM)? • Additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. • Varies from year to year, but most estimates suggest that it ranges between 4% and 8% per year.

  40. Calculating required rates of return • rHT = 5.5% + (5.0%)(1.32) = 5.5% + 6.6% = 12.10% • rM = 5.5% + (5.0%)(1.00) = 10.50% • rUSR = 5.5% + (5.0%)(0.88) = 9.90% • rT-bill = 5.5% + (5.0%)(0.00) = 5.50% • rColl = 5.5% + (5.0%)(-0.87) = 1.15%

  41. Illustrating the Security Market Line SML: ri = 5.5% + (5.0%) bi ri (%) SML . HT . . rM = 10.5 rRF = 5.5 . USR T-bills . Risk, bi -1 0 1 2 Coll.

  42. Expected vs. Required returns

  43. An example:Equally-weighted two-stock portfolio • Create a portfolio with 50% invested in HT and 50% invested in Collections. • The beta of a portfolio is the weighted average of each of the stock’s betas. bP = wHT bHT + wColl bColl bP = 0.5 (1.32) + 0.5 (-0.87) bP = 0.225

  44. Calculating portfolio required returns • The required return of a portfolio is the weighted average of each of the stock’s required returns. rP = wHT rHT + wColl rColl rP = 0.5 (12.10%) + 0.5 (1.2%) rP = 6.6% • Or, using the portfolio’s beta, CAPM can be used to solve for expected return. rP = rRF + (RPM) bP rP = 5.5%+ (5.0%) (0.225) rP = 6.6%

  45. Factors that change the SML • What if investors raise inflation expectations by 3%, what would happen to the SML? ri (%) SML2 D I = 3% SML1 13.5 10.5 8.5 5.5 Risk, bi 0 0.5 1.0 1.5

  46. Y = C + mx ri = rf + (Rm - Rf)b RPm SML line • - Inflation is captured by rf - Inflation - rf • - Risk factor is captured by (Rm – Rf) - Risk factor - (Rm – Rf)

  47. Factors that change the SML • What if investors’ risk aversion increased, causing the market risk premium to increase by 3%, what would happen to the SML? ri (%) SML2 D RPM = 3% SML1 13.5 10.5 5.5 Risk, bi 0 0.5 1.0 1.5

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