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Risk and return (chapter 8)

Risk and return (chapter 8). 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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Risk and return (chapter 8)

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  1. Risk and return (chapter 8)

  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. Firm X Firm Y Rate of Return (%) 15 -70 0 100 Expected Rate of Return Firm X (red) has a lower distribution of returns than firm Y (purple) though both have the same average return. We say that firm X’s returns are less variable/volatile (smallerstandard deviation ) and thus X is a less risky investment than Y

  4. Selected Realized Returns, 1926-2009

  5. T-bills will return the promised 5.5%, regardless of the economy. No, T-bills do not provide a completely risk-free return, as they are still exposed to inflation. Although, very little unexpected inflation is likely to occur over such a short period of time. T-bills are also risky in terms of reinvestment risk. T-bills are risk-free in the default sense of the word. Why is the T-bill return independent of the economy? Do T-bills promise a completely risk-free return?

  6. Return: Calculating the expected return for each alternative OutcomeProb. of outcomeReturn in 1(recession) .1 -15% 2 (normal growth) .6 15% 3 (boom) .3 25% r^ =expected rate of return = (.1)(-15) + (.6)(15) +(.3)(25)=15%

  7. Risk: Calculating the standard deviation for each alternative Standard deviation (σ) measures total, or stand-alone, risk. Greater the σ, greater the risk. Why?

  8. 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 less risky asset, which serves as compensation for investors to hold riskier securities • Very often risk premium refers to the difference between the return on a risky asset and risk-free rate (ex. a treasury bond) • 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.

  9. A standardized measure of dispersion about the expected value, that shows the risk per unit of return. You want to invest in a security with the highest expected return per unit of risk, and thus the lowest CV Coefficient of Variation (CV) Average Standard ReturnDeviationCV Small-company stocks 17.3% 33.2% 1.92 Large-company stocks 12.7 20.2 1.59 L-T corporate bonds 6.1 8.6 1.41

  10. σA = σB , but A is riskier because of a larger probability of losses. In other words, the same amount of risk (as measured by σ) for smaller returns. Prob. A B Rate of Return (%) 0 Illustrating the CV as a Measure of Relative Risk

  11. Portfolio returns The rate of return on a portfolio is a weighted average of the rates of return of each asset comprising the portfolio, with the portfolio proportions as weights. rp = W1r1 +W2r2 W1 = Proportion of funds in Security 1 W2 = Proportion of funds in Security 2 r1 = Expected return on Security 1 r2 = Expected return on Security2

  12. Assume that you invested $3000 in Citistock and $2,000 in Yahoo stock. The expected return of Citi stock is 15% and the expected return of Yahoo is 20%. What is the portfolio expected return? Answer: W1=3,000/(3,000+2,000)=0.6 W2=2,000/ (3,000+2,000)=0.4 Expected portfolio return = 0.6*15%+0.4*20%= 17%

  13. The benefits of diversification • Come from the correlation between asset returns • Correlation, : a measure of the strength of the linear relationship between two variables • -1.0 < r < +1.0 • If r = +1.0, securities 1 and 2 are perfectly positively correlated • If r = -1.0, 1 and 2 are perfectly negatively correlated • If r = 0, 1 and 2 are not correlated • The smaller the correlation, the greater the risk reduction potential greater the benefit of diversification • If r = +1.0, no risk reduction is possible • Most stocks are positively correlated with the market (ρ 0.65) • Combining stocks and bonds in a portfolio generally lowers risk.

  14. Partial Correlation, ρ = +0.35

  15. sp (%) Company-Specific 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

  16. σp decreases as stocks are 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%. Creating a Portfolio: Beginning with One Stock and Adding Randomly Selected Stocks to Portfolio

  17. Illustrating Diversification Effects of a Stock Portfolio

  18. Breaking down sources of risk Stand-alone risk = Market risk + Firm-specific risk • Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta. • Firm-specific risk – portion of a security’s stand-alone risk that can be eliminated through proper diversification. • If an investor chooses to hold a one-stock portfolio (exposed to more risk than a diversified investor), would the investor be compensated for the risk they bear? • NO! • Stand-alone risk is not important to a well-diversified investor. • Rational, risk-averse investors are concerned with σp, which is based upon market risk.

  19. Capital Asset Pricing Model (CAPM) • Model based upon concept that a stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification. • Primary conclusion: The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio • Beta: measures a stock’s market risk Indicates how risky a stock is if the stock is held in a well-diversified portfolio Beta is calculated using regression analysis

  20. The Security Market Line (SML):Calculating required rates of return SML: ri= rRF+ βi(rM– rRF) • SML is the empirical part of CAPM • Assume rRF= 8% , rM= 15% and company’s BETA (βi ) is 1.2 • The market (or equity) risk premium is RPM = rM– rRF= • 15% – 8% = 7%. • ri= 8% + 1.2x(15% - 8%) = 16.4%

  21. Additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. Its size depends on the perceived risk of the stock market and investors’ degree of risk aversion. Varies from year to year, but most estimates suggest that it ranges between 4% and 8% per year. What is the market risk premium?

  22. Expected vs. Required Returns

  23. 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

  24. Create a portfolio with 50% invested in High Tech and 50% invested in Collections. The beta of a portfolio is the weighted average of each of the stock’s betas. bP = wHTbHT + wCollbColl bP = 0.5(1.32) + 0.5(-0.87) bP = 0.225 An Example:Equally-Weighted Two-Stock Portfolio

  25. The required return of a portfolio is the weighted average of each of the stock’s required returns. rP = wHTrHT + wCollrColl rP = 0.5(12.10%) + 0.5(1.15%) rP = 6.625% 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 = 6.625% Calculating Portfolio Required Returns

  26. What if investors raise inflation expectations by 3%, what would happen to the SML? Factors That Change the SML ri (%) SML2 ΔI = 3% 13.5 10.5 8.5 5.5 SML1 Risk, bi 0 0.5 1.0 1.5

  27. What if investors’ risk aversion increased, causing the market risk premium to increase by 3%, what would happen to the SML? Factors That Change the SML ri (%) SML2 ΔRPM = 3% 13.5 10.5 5.5 SML1 Risk, bi 0 0.5 1.0 1.5

  28. Comments on beta • If beta = 1.0, the security is just as risky as the average stock (the market) • If beta > 1.0, the security is riskier than average (the market) • If beta < 1.0, the security is less risky than average (the market) • CAPM/SML concepts are based upon expectations, but betas are calculated using historical data. A company’s historical data may not reflect investors’ expectations about future riskiness.

  29. 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. Can the beta of a security be negative?

  30. Well-diversified investors are primarily concerned with how a stock is expected to move relative to the market in the future. Without a crystal ball to predict the future, analysts are forced to rely on historical data. 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. Calculating Betas

  31. Learning objectives • Know how to calculate a rate of return; historical rates of return 1926-2001 • Discuss the investment risk; know that our risk measure will be the standard deviation of returns (no calculations are necessary) • Know how to calculate expected return, standard deviation and coefficient of variation given probabilities of each outcome • Know what is risk aversion and risk premium • Know how to calculate the portfolio return • Discuss the diversification effects of a portfolio; the role of correlation and its two signs and the benefits of diversification • Know the two sources of risk; market and firm specific • Briefly discuss what is CAPM and beta • Know how to calculate required return using SML • Recommended problems: ST-1, Questions 8-4,8-7,8-8, problems 8-1to 8-8

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