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- 1. Risk and Return
- 2. Holding Period Return <ul><li>Three month ago, Peter Lynch purchased 100 </li></ul><ul><li>shares of Iomega Corp. at $50 per share. Last </li></ul><ul><li>month, he received dividends of $0.25 per </li></ul><ul><li>share from Iomega. These shares are worth </li></ul><ul><li>$56 each today. </li></ul><ul><li>Compute Peter’s holding period return from his investment in Iomega common shares. </li></ul>
- 3. Probability Concept <ul><li>Random variable </li></ul><ul><ul><li>Something whose value in the future is subject to uncertainty. </li></ul></ul><ul><li>Probability </li></ul><ul><ul><li>The relative likelihood of each possible outcome (or value) of a random variable </li></ul></ul><ul><ul><li>Probabilities of individual outcomes cannot be negative nor greater than 1.0 </li></ul></ul><ul><ul><li>Sum of the probabilities of all possible outcomes must equal 1.0 </li></ul></ul><ul><li>Moments </li></ul><ul><ul><li>Mean, Variance (or Standard deviation), covariance </li></ul></ul>
- 4. Computing the Basic Statistics A security analyst has prepared the following probability distribution of the possible returns on the common stock shares of two companies: Compu-Graphics Inc. (CGI) and Data Switch Corp. (DSC).
- 5. The Mean For CGI, the mean (or expected) return is: Similarly, the mean return for DSC is 24.00%
- 6. The Variance and Standard Deviation The variance of CGI’s returns is: The Standard Deviation of CGI’s return is:
- 7. The Covariance The covariance of the returns on CGI and DSC is:
- 8. The Correlation Coefficient The correlation coefficient between CGI and DSC is:
- 9. Summary of Results for CGI and DSC
- 10. <ul><li>A portfolio is a combination of two or more securities. </li></ul><ul><li>Combining securities into a portfolio reduces risk. </li></ul><ul><li>An efficient portfolio is one that has the highest expected return for a given level of risk. </li></ul><ul><li>We will look at two-asset portfolios in fair detail. </li></ul>Portfolio Securities
- 11. Portfolio Expected Return and Risk Expected Return Risk The Expected Returns of the Securities The Portfolio Weights The Risk of the Securities The Portfolio Weights The Correlation Coefficients
- 12. Portfolio Weights and Expected Return
- 13. Portfolio Expected Return and Risk
- 14. Diversification of Risk <ul><li>Note that while the expected return of the portfolio is between those of CGI and DSC, its risk is less than either of the two individual securities. </li></ul><ul><li>Combining CGI and DSC results in a substantial reduction of risk - diversification! </li></ul><ul><li>This benefit of diversification stems primarily from the fact that CGI and DSC’s returns are not perfectly correlated . </li></ul>
- 15. <ul><li>All else being the same, lower the correlation coefficient, lower is the risk of the portfolio. </li></ul><ul><ul><li>Recall that the expected return of the portfolio is not affected by the correlation coefficient. </li></ul></ul><ul><li>Thus, lower the correlation coefficient, greater is the diversification of risk. </li></ul>Correlation Coefficient and Portfolio Risk
- 16. Consider stocks of two companies, X and Y. The table below gives their expected returns and standard deviations . Plot the risk and expected return of portfolios of these two stocks for the following (assumed) correlation coefficients: -1.0 0.5 0.0 +0.5 +1.0 Correlation Coefficient and Portfolio Risk
- 17. Correlation Coefficient and Portfolio Risk Y Correlation Coefficient -1.0 -0.5 0.0 +0.5 +1.0 X
- 18. Portfolios with Many Assets <ul><li>The above framework can be expanded to the case of portfolios with a large number of stocks. </li></ul><ul><li>In forming each portfolio, we can vary </li></ul><ul><ul><li>the number of stocks that make up the portfolio, </li></ul></ul><ul><ul><li>the identity of the stocks in the portfolio, and </li></ul></ul><ul><ul><li>the weights assigned to each stock. </li></ul></ul><ul><li>Look at the plot of the expected returns versus the risk of these portfolios </li></ul>
- 19. All Combinations of Risky Assets
- 20. Efficient Frontier <ul><li>A portfolio is an efficient portfolio if </li></ul><ul><ul><li>no other portfolio with the same expected return has lower risk, or </li></ul></ul><ul><ul><li>no other portfolio with the same risk has a higher expected return. </li></ul></ul><ul><li>Investors prefer efficient portfolios over inefficient ones. </li></ul><ul><li>The collection of efficient portfolio is called an efficient frontier . </li></ul>
- 21. (risk) Efficient Frontier (expected return) F E
- 22. Choosing the Best Risky Asset <ul><li>Investors prefer efficient portfolios over inefficient ones. </li></ul><ul><li>Which one of the efficient portfolios is best? </li></ul><ul><li>We can answer this by introducing a riskless asset . </li></ul><ul><ul><li>There is no uncertainty about the future value of this asset (i.e. the standard deviation of returns is zero). Let the return on this asset be r f . </li></ul></ul><ul><ul><li>For practical purposes, 90-day U.S. Treasury Bills are (almost) risk free. </li></ul></ul>
- 23. Combinations of a Risk Free and a Risky Asset (risk) (expected return) F E N r f
- 24. Best Risky Asset (expected return) (risk) F E M r f
- 25. The Capital Market Line <ul><li>Assume investors can lend and borrow at the risk free rate of interest. </li></ul><ul><ul><li>borrowing entails a negative investment in the riskless asset. </li></ul></ul><ul><li>Since every investor hold a part of the “best” risky asset M, M is the market portfolio. </li></ul><ul><li>The Market portfolio consists of all risky assets. </li></ul><ul><ul><li>Each asset weight is proportional to its market value. </li></ul></ul>
- 26. The Capital Market Line Sharpe Ratio
- 27. The Capital Market Line r f (expected return) (risk) F E M
- 28. <ul><li>Explain the importance of asset pricing models. </li></ul><ul><li>Demonstrate choice of an investment position on the Capital Market Line (CML). </li></ul><ul><li>Understand the Capital Asset Pricing Model (CAPM), Security Market Line (SML) and its uses. </li></ul>Next Coverage <ul><li>Understand the determination of the expected rate of return Capital Asset Pricing Model </li></ul><ul><li>Decomposition of Risk: Systematic Vs. Unsystematic. </li></ul>
- 29. Asset Pricing Models <ul><li>These models provide a relationship between an asset’s required rate of return and its risk . </li></ul><ul><li>The required return can be used for: </li></ul><ul><ul><li>computing the NPV of your investment. </li></ul></ul>
- 30. Individual’s Choice on the CML (risk) (risk)
- 31. The Capital Asset Pricing Model (CAPM) <ul><li>It allows us to determine the required rate of return (=expected return) for an individual security. </li></ul><ul><ul><li>Individual securities may not lie on the CML. </li></ul></ul><ul><ul><li>Only efficient portfolios lie on the CML </li></ul></ul><ul><li>The Security Market Line ( SML ) can be applied to any securities or portfolios including inefficient ones. </li></ul>
- 32. The Security Market Line (SML) <ul><li>where </li></ul>
- 33. What does the SML tell us <ul><li>The required rate of return on a security depends on: </li></ul><ul><ul><li>the risk free rate </li></ul></ul><ul><ul><li>the “beta” of the security, and </li></ul></ul><ul><ul><li>the market price of risk. </li></ul></ul><ul><li>The required return is a linear function of the beta coefficient. </li></ul><ul><ul><li>All else being the same, higher the beta coefficient, higher is the required return on the security. </li></ul></ul>
- 34. Graphical Representation of the SML
- 35. Computing Required Rates of Return <ul><li>Common stock shares of Gator Sprinkler Systems (GSS) have a correlation coefficient of 0.80 with the market portfolio, and a standard deviation of 28%. The expected return on the market portfolio is 14%, and its standard deviation is 20%. The risk free rate is 5%. </li></ul><ul><li>What is the required rate of return on GSS? </li></ul>
- 36. Required Return on GSS First compute the beta of GSS: Next, apply the SML:
- 37. Required Rate of Return on GSS <ul><li>What would be the required rate of return on GSS if it had a correlation of 0.50 with the market? (All else is the same) </li></ul><ul><ul><li>Beta = 0.70 and GSS = 11.30% </li></ul></ul><ul><li>What would be the required rate of return on GSS if it had a standard deviation of 36%, and a correlation of 0.80? (All else is the same) </li></ul><ul><ul><li>Beta = 1.44 and GSS = 17.96% </li></ul></ul>
- 38. Estimating the Beta Coefficient <ul><li>If we know the security’s correlation with the </li></ul><ul><li>market, its standard deviation, and the standard </li></ul><ul><li>deviation of the market, we can use the </li></ul><ul><li>definition of beta: </li></ul><ul><li>Generally, these quantities are not known. </li></ul><ul><li>We therefore rely on their historical values to provide us with an estimate of beta. </li></ul>
- 39. Interpreting the Beta Coefficient The beta of the market portfolio is always equal to 1.0. The beta of the risk free asset is always equal to 0.0
- 40. Interpreting the Beta Coefficient <ul><li>Beta indicates how sensitive a security’s returns are to changes in the market portfolio’s return . </li></ul><ul><ul><li>It is a measure of the asset’s risk. </li></ul></ul><ul><li>Suppose the market portfolio’s risk premium is +10% during a given period. </li></ul><ul><ul><li>if = 1.50, the security’s risk premium will be +15%. </li></ul></ul><ul><ul><li>if = 1.00, the security’s risk premium will be +10% </li></ul></ul><ul><ul><li>if = 0.50, the security’s risk premium will be +5% </li></ul></ul><ul><ul><li>if = - 0.50, the security’s risk premium will be - 5% </li></ul></ul>
- 41. Beta Coefficients for Selected Firms
- 42. Beta of a Portfolio <ul><li>The beta of a portfolio is the weighted average of the beta values of the individual securities in the portfolio. </li></ul><ul><li>where w i is the proportion of value invested in security i, and i is the beta of the security i. </li></ul>
- 43. Applying the CAPM <ul><li>The CML prescribes that investors should invest in the riskless asset and the market portfolio. </li></ul><ul><li>The true market portfolio, which consists of all risky assets, cannot be constructed. </li></ul><ul><li>How much diversification is necessary to get substantially “all” of the benefits of diversification? </li></ul><ul><ul><li>About 25 to 30 stocks! </li></ul></ul>

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