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MBA 643 Managerial Finance Lecture 8: Modern Portfolio Theory, Part II

MBA 643 Managerial Finance Lecture 8: Modern Portfolio Theory, Part II. Spring 2006 Jim Hsieh. What do we know about portfolio risk? -- Recap. Most stocks are positively correlated. Average correlation between two stocks is 0.65.

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MBA 643 Managerial Finance Lecture 8: Modern Portfolio Theory, Part II

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  1. MBA 643Managerial FinanceLecture 8: Modern Portfolio Theory, Part II Spring 2006 Jim Hsieh

  2. What do we know about portfolio risk? -- Recap • Most stocks are positively correlated. • Average correlation between two stocks is 0.65. • So long as the stocks in the portfolio are not perfectly correlated (i.e., <1), the standard deviation of the portfolio will be less than the weighted average of the standard deviation of the stocks in the portfolio. • When we add more securities in the portfolio, we can lower the risk of the portfolio even further. • This is because the added securities would not be perfectly correlated with existing securities in the portfolio. • Q: Can we eliminate the portfolio risk completely by adding more assets/securities into our portfolio?

  3. Stand-alone Risk in Individual Securities • Stand-alone risk consists of: • Diversifiable risk • Company or industry specific • Also called unsystematic, unique, or idiosyncratic risk • Non-diversifiable risk • Related to market as a whole • Also called systematic, portfolio, or market risk • It shows the degree to which a stock moves systematically with other stocks. • Total risk of security = unsystematic risk + portfolio risk • We can eliminate unsystematic risk by adding more securities into the portfolio.

  4. Diversification reduces risk • In this example, the table shows portfolio risk (std dev) by adding one more stock.

  5. Diversification

  6. Question • If Stephen holds a one-stock portfolio and Jennifer holds a multiple-stock portfolio. Thus Stephen is exposed to more risk than Jennifer. Do you think Stephen should be compensated for all the risk he bears?

  7. Answer • Even though Stephen holds only one stock, he will not be compensated for the additional risk he bears. • Stand-alone risk as a whole is not as important to a well-diversified investor, and most of it can be eliminated at virtually no cost through diversification. • Thus, bearing the diversifiable risk should not be rewarded. • Rational risk averse investors are concerned with P, which is based on market risk.

  8. The Systematic Risk Principal • The reward for bearing risk depends only on the systematic risk of an investment since unsystematic risk can be diversified away. • This implies that the expected return on any asset depends only on that asset’s systematic risk. • If investors are well diversified, they only care how a stock correlates with the rest of their portfolio (the “market portfolio”). The variance of that stock (i2) is, essentially, irrelevant. • Important Implication: If two assets have the same correlation with the market portfolio, they must have the same expected return.

  9. Measuring Systematic Risk • Beta (β) measures a stock’s market (or systematic) risk. It shows the relative volatility of a given stock compared to the average stock. An average stock (or the market portfolio) has a beta = 1.0. • Beta shows how risky a stock is if the stock is held in a well-diversified portfolio. • β=1 → stock has average risk. • β>1 → stock is riskier than average. • β<1 → stock is less risky than average. • β=0 → risk free assets (e.g., Treasury bills) • Q: Can β be negative?

  10. More on Beta • Definition of Beta: • Note that stock i’s beta has two components: • Covariance of returns between stock i and market portfolio. • Variance of return on market portfolio • NO variance of return on stock i

  11. Beta Coefficients for Selected Companies (From Table 10.7)

  12. Portfolio Betas • The beta of a portfolio (βP) is the weighted average of the betas from its constituent securities. • βP = β1 + β2 + … + βN for N securities • Example 1: You have $6,000 invested in IBM, $4,000 in GM. You estimate that IBM has a beta of 0.95 and GM has a beta of 1.15. What is the beta of your portfolio?

  13. Beta and Risk Premium • Consider a portfolio which consists of stock A with a beta of 1.2 and expected return of 18%, and a Treasury bill with a 7% return.

  14. The Relationship Between E(R) and Beta

  15. Reward to Risk Ratio • We can vary the amount invested in each type of asset and get an idea of the relation between portfolio expected return and beta: • It estimates the expected risk premium per unit of risk. • We can also calculate the reward to risk ratio for all individual securities.

  16. What happens if two securities have different reward-to-risk ratios? • Investors would only buy the securities (portfolios) with a higher reward-to-risk ratio. Here, it would be A. • Eventually, all securities will have the same reward-to-risk ratio. • Because the reward-to-risk ratio is the same for all securities, it must hold for the market portfolio too. • Result:

  17. The Capital Asset Pricing Model (CAPM) • Since we know: • Then: E(RA) = Rf + A[E(RM) – Rf] • The CAPM describes the relationship between the expected risk premium on a security, E(Ri)-Rf, and the risk, . • What determines a security’s expected return? • The risk-free rate • The market risk premium • The beta coefficient • The CAPM holds for individual assets as well as portfolios of those assets.

  18. An Example of CAPM • Suppose the risk-free rate is 4%, the market risk premium is 8.6%, and a stock has a beta of 1.3. Based on the CAPM, what is the expected return on this stock? What would the expected return be if the beta were to double?

  19. The Security Market Line (SML)CAPM: E(Ri) = Rf + i[E(RM) – Rf] • The security market line (SML) is a line that shows the relationship between risk () and the required rate of return on individual securities. Required Rate of Return Risk, i

  20. SML • All of the “fair-valued” securities should fall on the SML. Required Rate of Return SML Rf Risk, i

  21. Summary of Risk and Return • Investors like high E(R) and low standard deviation. Portfolios that offer the highest E(R) for a given standard deviation are called efficient. • If investors are well diversified, they only care how a stock correlates with the rest of their portfolio (the “market portfolio”). They only care about the covariance of that stock with other stocks in the portfolio. • A stock’s sensitivity to changes in the value of the market portfolio is its beta. • The CAPM is a simple, linear model that links risk premia on assets to risk premium on the market portfolio, using beta as a measure of risk.

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