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Foundations of Finance Arthur J. Keown John D. Martin J. William Petty David F. Scott, Jr.

Foundations of Finance Arthur J. Keown John D. Martin J. William Petty David F. Scott, Jr. Chapter 6 The Meaning and Measurement of Risk and Return. Learning Objectives. Define and measure the expected rate of return of an individual investor.

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Foundations of Finance Arthur J. Keown John D. Martin J. William Petty David F. Scott, Jr.

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  1. Foundations of FinanceArthur J. Keown John D. MartinJ. William Petty David F. Scott, Jr. Chapter 6 The Meaning and Measurement of Risk and Return

  2. Learning Objectives • Define and measure the expected rate of return of an individual investor. • Define and measure the riskiness of an individual investment. • Compare the historical relationship between risk and return in the capital markets. Foundations of Finance

  3. Learning Objectives • Explain how diversifying investments affects the riskiness and expected rate of return of a portfolio or combination of assets. • Explain the relationship between an investor’s required rate of return on an investment and the riskiness of the investment. Foundations of Finance

  4. Principles Used in this Chapter • Principle 1: The Risk-Return Trade-off – We Won’t Take on Additional Risk Unless We Expect to Be Compensated with Additional Return. • Principle 3: Cash-Not Profits-Is King. Foundations of Finance

  5. Expected Cash Flow • Weighted Average of the possible cash flows outcomes such that the weights are the probabilities of the occurrence of the various states of the economy. Foundations of Finance

  6. Measuring the Expected Return Foundations of Finance

  7. Expected Rate of Return • Weighted average of all the possible returns, weighted by the probability that each return will occur. Foundations of Finance

  8. Studying and Understanding Risk • What is risk? • How do we know the amount of risk associated with a given investment; that is how do we measure risk? • If we choose to diversify our investments by owning more that one asset, as most of us do, will such diversification reduce the riskiness of our combined portfolio of investments? Foundations of Finance

  9. Risk • Potential variability in future cash flows • The wider the range of possible events that can occur, the greater the risk Foundations of Finance

  10. Standard Deviation of Return • Square root of the weighted average squared deviation of each possible return from the expected return • Quantitative measure of an asset’s riskiness • Measures the volatility or riskiness of portfolio returns Foundations of Finance

  11. Annual Rates of Return, 1926-2000 Foundations of Finance

  12. Total Risk or Variability • Company-Unique Risk (Unsystematic) • Market Risk (Systematic) Foundations of Finance

  13. Diversification • If we diversify investments across different securities, the variability in the returns declines Foundations of Finance

  14. Company-Unique Risk • Unsystematic risk • Diversifiable -- Can be diversified away Foundations of Finance

  15. Market Risk • Systematic • Non-diversifiable • Cannot be eliminated through random diversification Foundations of Finance

  16. Market Risk Events that affect market risk Changes in the general economy, major political events, sociological changes Examples: *Interest rates *General economic conditions *Changes in tax legislation that affect all companies *War Foundations of Finance

  17. Measuring Market Risk • Characteristic line • The slope of the characteristic line measures the average relationship between a stock’s returns and those of the S&P 500 Index Returns. • Indicates the average movement in a stock’s price to a movement in the S&P 500 Price Index. Foundations of Finance

  18. Measuring Market Returns Monthly Holding-Period Returns of Barnes & Noble and the S&P 500 Index, December 2002 to November 2004 Foundations of Finance

  19. Beta • Average relationship between a stock’s returns and the market’s returns • Slope of the characteristic line—or the line that measures the average relationship between a stock’s returns and the market • Measure of a firm’s market risk or systematic risk that remains for a company even after diversified our portfolio. Foundations of Finance

  20. Beta • A stock with a Beta of 0 has no systematic risk • A stock with a Beta of 1 has systematic risk equal to the “typical” stock in the marketplace • A stock with a Beta exceeding 1 has systematic risk greater than the “typical” stock • Most stocks have betas between .60 and 1.60 Foundations of Finance

  21. Portfolio Beta • Weighted average of the individual securities’ betas, with the weights being equal to the proportion of the portfolio invested in each security • Portfolio beta indicates the percentage change on average of the portfolio for every 1 percent change in the general market Foundations of Finance

  22. Portfolio Beta Holding-Period Returns: High- and Low-Beta Portfolios and the S&P 500 Index Foundations of Finance

  23. Risk and Diversification • The market rewards diversification • We can lower risk without sacrificing expected returns • We can increase expected returns without having to assume more risk Foundations of Finance

  24. Asset Allocation • Diversification among different kinds of asset types: T Bills Long-Term Government Bonds Common Stocks Foundations of Finance

  25. Required Rate of Return • Minimum rate of return necessary to attract an investor to purchase or hold a security • Considers the opportunity cost of funds • The next best investment Foundations of Finance

  26. Real Average Annual Rate of Return • Nominal rate of return less the inflation rate Foundations of Finance

  27. Required Rate of Return k=kfr + krp Where: k = required rate of return kfr = Risk-Free Rate krp = Risk Premium Foundations of Finance

  28. Risk-Free Rate • Required rate of return or discount rate for risk-less investments • Typically measured by U.S. Treasury Bill Rate Foundations of Finance

  29. Risk Premium • Additional return we must expect to receive for assuming risk • As risk increases, we will demand additional expected returns Foundations of Finance

  30. Measuring the Required Rate of Return • Systematic risk is the only relevant risk-the rest can be diversified away • The required rate of return, k, equals the risk free rate, krf, plus a risk premium, krp Foundations of Finance

  31. Measuring the Required Rate of Return Risk Premium = Required Return – Risk-Free rate krp = k - kfr Where: k = required rate of return kfr = Risk-Free Rate krp = Risk Premium Foundations of Finance

  32. Capital Asset Pricing Model • Equation that equates the expected rate of return on a stock to the risk-free rate plus a risk premium for the systematic risk. • CAPM provides for an intuitive approach for thinking about the return that an investor should require on an investment, given the asset’s systematic or market risk. Foundations of Finance

  33. CAPM If required return is 15% and the risk-free rate is 5%, then the risk premium is 10%. If the required rate of return for the market portfolio km is 12%, and the krf is 5%, the risk premium krp for the market would be 7%. Foundations of Finance

  34. CAPM This 7% risk premium would apply to any security having systematic (nondiversifiable) risk equivalent to the general market, or beta of 1. In the same market, a security with Beta of 2 would provide a risk premium of 14%. Foundations of Finance

  35. CAPM • CAPM suggests that Beta is a factor in required returns kj = krf + B(market rate – risk-free rate) Foundations of Finance

  36. CAPM Example: Market risk = 12% Risk-free rate = 5% 5% + B(12% - 5%) If B = 0 Required rate = 5% If B = 1 Required rate = 12% If B = 2 Required rate = 19% Foundations of Finance

  37. The Security Market Line • Graphic representation of the CAPM, where the line shows the appropriate required rate of return for a given stock’s systematic risk. Foundations of Finance

  38. The Security Market Line Foundations of Finance

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