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# Rohit File For Accounting And Finance

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• ### Transcript

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