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# Rohit File For Accounting And Finance

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• ### Rohit File For Accounting And Finance

1. 1. CHAPTER 5 Risk and Rates of Return <ul><li>Stand-alone risk </li></ul><ul><li>Portfolio risk </li></ul><ul><li>Risk & return: CAPM / SML </li></ul>
2. 2. Risk and Rates of Return <ul><li>How do you determine the rate of return that an investment in a new, fixed asset should provide? </li></ul><ul><li>It will depend on the project’s risk. But how do you define “risk”? And how do you measure risk? </li></ul><ul><li>And once you’ve measured the risk, how do you determine the rate of return that is appropriate for that risk? </li></ul>
3. 3. Calculating Rates of Return for Stocks <ul><li>A stock’s rate of return for a past or future year is calculated by: </li></ul><ul><li>r = D/P 0 + (P 1 – P 0 )/P 0 </li></ul><ul><li>The expected rate of return (“expected return”) to be realized from an investment is the mean value of the probability distribution of possible returns. </li></ul>
4. 4. What is investment risk? <ul><li>Two types of investment risk </li></ul><ul><ul><li>Stand-alone risk </li></ul></ul><ul><ul><li>Portfolio risk </li></ul></ul><ul><li>Investment risk is related to the probability of earning a low or negative actual return. </li></ul><ul><li>The greater the chance of lower than expected or negative returns, the riskier the investment. </li></ul>
5. 5. Probability Distributions <ul><li>Probability Distribution – A list of all the possible outcomes of a future event together with the probability (chance of occurrence) for each outcome. </li></ul><ul><li>You can calculate the mean (expected value), the standard deviation, and the variance of a probability distribution. </li></ul>
6. 6. Calculating Expected Returns for Stocks <ul><li>The “expected value of returns” or “expected return” for a stock is the weighted average of the possible outcomes (possible returns) where the weights are the probabilities associated with the outcomes. </li></ul><ul><li>If there are n possible outcomes for a given stock: </li></ul>
7. 7. Measuring the Risk of Stocks: The Variance of Returns <ul><li>The standard deviation, denoted by “sigma”( σ), is a measure of the variability, tightness , or spread of a set of outcomes expressed in a probability distribution. </li></ul><ul><li>Variance ( σ 2 ) is the standard deviation squared. </li></ul><ul><li>Variance is the expected value of the squared deviations. </li></ul><ul><li>Deviation i = </li></ul>
8. 8. Selected Realized Returns, 1926 – 2001 <ul><li> Average Standard </li></ul><ul><li> Return Deviation </li></ul><ul><li>Small-company stocks 17.3% 33.2% </li></ul><ul><li>Large-company stocks 12.7 20.2 </li></ul><ul><li>L-T corporate bonds 6.1 8.6 </li></ul><ul><li>L-T government bonds 5.7 9.4 </li></ul><ul><li>U.S. Treasury bills 3.9 3.2 </li></ul><ul><li>Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2002 Yearbook (Chicago: Ibbotson Associates, 2002), 28. </li></ul>
9. 9. Coefficient of Variation (CV) <ul><li>A standardized measure of dispersion about the expected value, that shows the risk per unit of return. </li></ul>
10. 10. How Investors View Risk and Return <ul><li>Investors like return . They seek to maximize return. </li></ul><ul><li>But investors dislike risk . They seek to avoid or minimize risk. Why? </li></ul><ul><ul><li>Because human beings possess the psychological trait of “ risk aversion ” which is a dislike for taking risks. </li></ul></ul>
11. 11. Implications of Risk Aversion <ul><li>The “risk-return tradeoff” - Risk averse investors require higher rates of return to induce them to invest in higher risk securities. </li></ul><ul><li>The higher a security’s risk, the higher the return investors demand. Thus, the less they are willing to pay for the investment, i.e. as risk increase, P 0 decreases . </li></ul><ul><li>Risk averse investors will diversify their investments in order to reduce risk. </li></ul>
12. 12. Diversification <ul><li>Definition - An investment strategy designed to reduce risk by spreading the funds invested across many securities. </li></ul><ul><li>It is holding a broad portfolio of securities so as “not to have all your eggs in one basket.” </li></ul><ul><li>Since people hold diversified portfolios of securities, they are not very concerned about the risk and return of a single security . They are more concerned about the risk and return of their entire portfolio . </li></ul>
13. 13. The Two Components of a Security’s Variance (Risk) <ul><li>1. Unique Risk - Also called “ diversifiable risk ” and “ unsystematic risk.” The part of a security’s risk associated with random outcomes generated by events specific to the firm. This risk can be eliminated by proper diversification. </li></ul><ul><li>2. Market Risk – Also called “ systematic risk .” The part of a security’s risk that cannot be eliminated by diversification because it is associated with economic or market factors that systematically affect most firms. </li></ul><ul><ul><li>Market risk reflects economy-wide sources of risk that affect most firms and, hence, the overall stock market . </li></ul></ul>
14. 14. The Expected Return on a Portfolio of Stocks <ul><li>Assume N stocks are held in the portfolio. </li></ul><ul><li>Stock i is held in the proportion, w i </li></ul>
15. 15. The Variance of Returns for a Portfolio of Stocks <ul><li>σ ij = the covariance between stocks i and j </li></ul><ul><li>ρ ij = the correlation coefficient for stocks i and j </li></ul>
16. 16. Correlation Coefficient <ul><li>The “Correlation Coefficient” is a measure of the extent that two variables move or vary together. </li></ul><ul><li>It ranges between –1.0 and +1.0 </li></ul><ul><ul><li>Positive correlation: a high value on one variable is likely to be associated with a high value on the other. </li></ul></ul><ul><ul><li>Negative correlation: a high value on one variable is likely to be associated with a low value on the other. </li></ul></ul><ul><ul><li>No correlation: values of each are independent of the other </li></ul></ul>
17. 17. Correlation Coefficient-Cont’d <ul><li>It is denoted by the Greek letter, “rho”: ρ </li></ul><ul><ul><li>If ρ = +1.0, perfect positive correlation </li></ul></ul><ul><ul><li>If ρ = -1.0, perfect negative correlation </li></ul></ul><ul><ul><li>If ρ = 0, uncorrelated or independent </li></ul></ul><ul><li>ρ ij = the correlation coefficient for returns of stock i and stock j </li></ul>
18. 18. The Variance of Returns for a Portfolio of Stocks <ul><li>σ ij = the covariance between stocks i and j </li></ul><ul><li>ρ ij = the correlation coefficient for stocks i and j </li></ul>
19. 19. How Diversification Reduces Risk <ul><li>Combining stocks into a portfolio reduces the variability of possible returns as long as the returns on the individual stocks are not perfectly correlated, i.e. as long as their correlation coefficients are less than +1.0. </li></ul><ul><li>Assume: </li></ul><ul><ul><li>Invest 50% in Stock A and 50% in Stock B </li></ul></ul><ul><ul><li>Stock A: r = 13%; σ = 20%, σ 2 = 400 </li></ul></ul><ul><ul><li>Stock B: r = 13%; σ = 20%, σ 2 = 400 </li></ul></ul>
20. 20. How Diversification Reduces Risk - Cont’d
21. 21. Portfolio Risk Falls As You Add Securities
22. 22. You Can’t Eliminate “Market Risk”
23. 23. This Pattern Occurs Because of the Two Components of a Stock’s Variance (Risk): <ul><li>1. Unique Risk </li></ul><ul><li>2. Market Risk </li></ul><ul><li>The unique risk is “diversified away” when individual stocks are combined in a portfolio. </li></ul><ul><li>Only market risk remains. </li></ul><ul><li>The amount of the market risk is determined by the market risk of the individual stocks in the portfolio. </li></ul>
24. 24. How Should We Measure Portfolio Risk Now? <ul><li>Diversification eliminates unique risk and leaves market risk . </li></ul><ul><li>Therefore, the relevant measure of risk for a portfolio is the portfolio’s “beta”: a measure of the sensitivity of the portfolio’s returns to changes in the return on the “market portfolio” which is closely approximated by a portfolio consisting of the S&P 500 stocks. </li></ul>
25. 25. How Do Investors View the Risk of a Single Security Held in a Portfolio?
26. 26. Answer: “Beta” Measures a Stock’s Market Risk Covariance with the market Variance of the market
27. 27. How to Interpret a Beta <ul><li>If β i > 1, returns to stock i are amplified relative to the market. </li></ul><ul><li>If β i is between 0 and 1.0, returns to stock i tend to move in the same direction as the market but not as far. </li></ul><ul><li>If β i < 1(very rare), returns to stock i tend to move in the opposite direction as the market. </li></ul>
28. 28. How To Interpret a Beta-Cont’d <ul><li>A stock with β = 1 has average market risk. </li></ul><ul><ul><li>A well-diversified portfolio of such stocks tends to move by the same percentage as the overall market moves and has the same σ as the overall market. </li></ul></ul><ul><li>A stock with β = +.5 has below average market risk. </li></ul><ul><ul><li>A well-diversified portfolio of these stocks tends to move half as far as the overall market moves and has half the standard deviation </li></ul></ul>
29. 29. Betas Are Calculated Using Regression Analysis 1. Total risk = diversifiable risk + market risk 2. Market risk is measured by beta, the sensitivity to market changes beta Expected return Expected market return 10% 10% - + <ul><li>10% </li></ul>+10% stock Copyright 1996 by The McGraw-Hill Companies, Inc -10%
30. 30. General comments about risk <ul><li>Most stocks are positively correlated with the market ( ρ i,m  0.65). </li></ul><ul><li>σ  35% for an average stock. </li></ul><ul><li>Combining stocks in a portfolio generally lowers risk. </li></ul>
31. 31. A model that relates an asset’s risk to its rate of return <ul><li>The “Capital Asset Pricing Model” won the Nobel Prize in economics. </li></ul><ul><li>Referred to as the “CAP-M” </li></ul>
32. 32. General Comments About CAPM <ul><li>Concerned with “equilibrium conditions” </li></ul><ul><li>CAPM seeks to predict: </li></ul><ul><ul><li>In equilibrium, what will be the relationship between expected return and risk for portfolios ? </li></ul></ul><ul><ul><li>In equilibrium, what will be the relationship between expected return and risk for individual securities ? </li></ul></ul>
33. 33. Capital Asset Pricing Model k i = k RF + B i ( k M - k RF ) CAPM
34. 34. CAPM Graphically: The Security Market Line Return BETA k RF SML SML Equation: k i = k RF + B i ( k M - k RF )
35. 35. Plotting the Security Market Line Return BETA . Risk Free Rate = k RF Market Return = k M Market Portfolio 1.0
36. 36. The Security Market Line (SML): Calculating required rates of return <ul><li>SML: k i = k RF + (k M – k RF ) β i </li></ul><ul><li>Assume k RF = 8% and k M = 15%. </li></ul><ul><li>The market (or equity) risk premium is RP M = k M – k RF = 15% – 8% = 7%. </li></ul>
37. 37. An example: Equally-weighted two-stock portfolio <ul><li>Create a portfolio with 50% invested in HT and 50% invested in Collections. </li></ul><ul><li>The beta of a portfolio is the weighted average of each of the stock’s betas. </li></ul><ul><li>β P = w HT β HT + w Coll β Coll </li></ul><ul><li>β P = 0.5 (1.30) + 0.5 (-0.87) </li></ul><ul><li>β P = 0.215 </li></ul>
38. 38. Factors that change the SML <ul><li>What if investors raise inflation expectations by 3%, what would happen to the SML? </li></ul>SML 1 k i (%) SML 2 0 0.5 1.0 1.5 18 15 11 8  I = 3% Risk, β i
39. 39. Factors that change the SML <ul><li>What if investors’ risk aversion increased, causing the market risk premium to increase by 3%, what would happen to the SML? </li></ul>SML 1 k i (%) SML 2 0 0.5 1.0 1.5 18 15 11 8  RP M = 3% Risk, β i
40. 40. Verifying the CAPM empirically <ul><li>The CAPM has not been verified completely. </li></ul><ul><li>Statistical tests have problems that make verification almost impossible. </li></ul><ul><li>Some argue that there are additional risk factors, other than the market risk premium, that must be considered. </li></ul>
41. 41. More thoughts on the CAPM <ul><li>Investors seem to be concerned with both market risk and total risk. Therefore, the SML may not produce a correct estimate of k i . </li></ul><ul><li> k i = k RF + (k M – k RF ) β i + ??? </li></ul><ul><li>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. </li></ul>