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Risk and Return

Risk and Return. Objectives:. Define Expected Return Define Risk Systematic versus Unsystematic Examine the relationship between Asset Risk and Return Understand the effect of diversification on the Risk and Return of a portfolio

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Risk and Return

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  1. Risk and Return Richard MacMinn

  2. Objectives: • Define Expected Return • Define Risk • Systematic versus Unsystematic • Examine the relationship between Asset Risk and Return • Understand the effect of diversification on the Risk and Return of a portfolio • Determine an investor’s required rate of return on a security as a function of its risk Richard MacMinn

  3. Expected Returns • The expected benefits or returns that an investment generates come in the form of cash flows. • Cash flows, not accounting profits, are the relevant variable used to measure returns. • Conventionally, we measure the expected cash flow as follows:where Xi is the cash flow in the ith state of the economy and Pi is the probability of the ith state of the economy Richard MacMinn

  4. Expected Returns • Similarly, the Expected Rate of Return is given by: • where Ri is the rate of return in the ith state of the economy and pi is the probability of ith state of the economy. Richard MacMinn

  5. Risk • Risk can be defined as the possible variation in cash flow about an expected cash flow. • Statistically, risk may be measured by the standard deviation of the random cash flow. • The standard deviation of an asset a is denoted by a and is calculated as follows:where n is the number of states of the economy, Rai is the return in the ith state and pi is the probability of the ith state of the economy Richard MacMinn

  6. Risk Richard MacMinn

  7. Summary Statistics Example Richard MacMinn

  8. Risk • The attractiveness of a security cannot be determined by standard deviation alone. • The risk and return of a security has to be compared with the alternatives available for investment. • If two securities have the same risk, the one with the higher return is preferable. • Alternatively, if two securities have the same return, then the one with lower risk is preferable. Richard MacMinn

  9. Risk & Diversification • Total Risk or variability of returns can be divided into: • The variability of returns unique to the security • Commonly referred to as Firm Specific Risk or Unique Risk or Diversifiable Risk or Unsystematic Risk • The risk related to market movements • Also referred to as Market Risk or Non-diversifiable Risk or Systematic Risk • By diversifying, the investor can eliminate the “unique” security risk. The systematic risk, however, cannot be diversified. Richard MacMinn

  10. Effects of Diversification Standard Deviation Total Risk = Unique Risk + Systematic Risk Unique Risk Systematic Risk Number of Stocks in Portfolio Richard MacMinn

  11. Benefits of Diversification Richard MacMinn

  12. How do investors diversify? • The Portfolio Problem • Markowitz (Portfolio Selection) • Tobin (Portfolio Separation) • Sharpe (CAPM) Richard MacMinn

  13. What risk is priced? • Risk averse investors demand higher returns, or equivalently, a risk premium for undertaking risk. • Investors cannot expect the market to compensate them for risk that they can eliminate through diversification. • Because stocks can be combined in portfolios to eliminate specific risk, only diversifiable or systematic risk matters, i.e. commands a risk premium. • Only systematic risk contributes to the riskiness of a portfolio and cannot be eliminated through diversification. Richard MacMinn

  14. Measuring Systematic Risk • Systematic Risk affects all securities. • To measure systematic risk, we measure the tendency of a stock to move relative to the market. • The plot of firm excess returns versus market excess returns is called the characteristic line, i.e., ERa - Rf =  (ERm - Rf) • The measure of a stock’s systematic risk or market risk is commonly called beta • Beta is also the slope of the characteristic line. Richard MacMinn

  15. Stock/Portfolio Returns (%) Characteristic line Market Returns (%) Characteristic Line Richard MacMinn

  16. Measuring Beta • The beta of stock A is calculated as follows: where Ra is the return on stock A and Rm is the return on the market portfolio and where • The beta of a portfolio is the weighted average of the individual securities’ betas • The beta of the market is 1. Richard MacMinn

  17. Required Rate of Return • The required rate of return equals the risk free rate plus a return to compensate for the additional risk. • The required rate of return can be expressed as R = Rf + RP,where R is the investor’s required rate of return, Rf is the risk-free rate, and RP is the risk premium Richard MacMinn

  18. The Required Rate of Return • Capital Asset Pricing Model (CAPM) • According to the CAPMERa = Rf + a [ERm - Rf]where ERa is the expected rate of return on stock “a” and ERm is the expected rate of return on the market portfolio. Richard MacMinn

  19. ERa (%) ERm - Rf Rf a The Security Market Line Richard MacMinn

  20. Criticisms of CAPM • Can Beta capture all dimensions of risk? Is beta the appropriate measure of risk? • Some empirical research has shown that the CAPM does not hold. Various anomalies such as the size effect and the friday the 13th effect have been known and investigated for some time. • How do we determine the market portfolio? Richard MacMinn

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