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# Chapter 8 risk and return

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### Chapter 8 risk and return

2. 2. Portfolio Returns and Portfolio Risk• With appropriate diversification, we can lower the risk of the portfolio without lowering the portfolio’s expected rate of return.• Some risk can be eliminated by diversification, and those risks that can be eliminated are not necessarily rewarded in the financial marketplace.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-2
3. 3. Calculating the Expected Return of aPortfolio• To calculate a portfolio’s expected rate of return, we weight each individual investment’s expected rate of return using the fraction of the portfolio that is invested in each investment.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-3
4. 4. Calculating the Expected Return of aPortfolio (cont.)• Example 8.1 : If you invest 25%of your money in the stock of Citi bank (C) with an expected rate of return of -32% and 75% of your money in the stock of Apple (AAPL) with an expected rate of return of 120%, what will be the expected rate of return on this portfolio?Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-4
5. 5. Calculating the Expected Return of aPortfolio (cont.)• Expected rate of return = .25(-32%) + .75 (120%) = 82%Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-5
6. 6. Calculating the Expected Return of aPortfolio (cont.)• E(rportfolio) = the expected rate of return on a portfolio of n assets.• Wi = the portfolio weight for asset i.• E(ri ) = the expected rate of return earned by asset i.• W1 × E(r1) = the contribution of asset 1 to the portfolio expected return.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-6
7. 7. Evaluating Portfolio Risk• Unlike expected return, standard deviation is not generally equal to the a weighted average of the standard deviations of the returns of investments held in the portfolio. This is because of diversification effects.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-7
8. 8. Portfolio Diversification• The effect of reducing risks by including a large number of investments in a portfolio is called diversification.• As a consequence of diversification, the standard deviation of the returns of a portfolio is typically less than the average of the standard deviation of the returns of each of the individual investments.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-8
9. 9. Portfolio Diversification (cont.)• The diversification gains achieved by adding more investments will depend on the degree of correlation among the investments.• The degree of correlation is measured by using the correlation coefficient.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-9
10. 10. Portfolio Diversification (cont.)• The correlation coefficient can range from -1.0 (perfect negative correlation), meaning two variables move in perfectly opposite directions to +1.0 (perfect positive correlation), which means the two assets move exactly together.• A correlation coefficient of 0 means that there is no relationship between the returns earned by the two assets.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-10
11. 11. Portfolio Diversification (cont.)• As long as the investment returns are not perfectly positively correlated, there will be diversification benefits.• However, the diversification benefits will be greater when the correlations are low or positive.• The returns on most investment assets tend to be positively correlated.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-11
12. 12. Diversification Lessons1. A portfolio can be less risky than the average risk of its individual investments in the portfolio.2. The key to reducing risk through diversification is to combine investments whose returns do not move together.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-12
14. 14. Calculating the Standard Deviationof a Portfolio Returns (cont.)• Determine the expected return and standard deviation of the following portfolio consisting of two stocks that have a correlation coefficient of . 75. Portfolio Weight Expected Standard Return Deviation Apple .50 .14 .20 Coca-Cola .50 .14 .20Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-14
15. 15. Calculating the Standard Deviationof a Portfolio Returns (cont.)• Expected Return = .5 (.14) + .5 (.14) = .14 or 14%Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-15
16. 16. Calculating the Standard Deviationof a Portfolio Returns (cont.)• Insert equation 8-2• Standard deviation of portfolio = √ { (.52x.22)+(.52x.22)+(2x.5x.5x.75x.2x.2)} = √ .035 = .187 or 18.7% Correlation CoefficientCopyright © 2011 Pearson Prentice Hall. All rights reserved. 8-16
17. 17. Calculating the Standard Deviationof a Portfolio Returns (cont.)• Had we taken a simple weighted average of the standard deviations of the Apple and Coca-Cola stock returns, it would produce a portfolio standard deviation of .20.• Since the correlation coefficient is less than 1 (.75), it reduces the risk of portfolio to 0.187.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-17
20. 20. Calculating the Standard Deviationof a Portfolio Returns (cont.)• Figure 8-1 illustrates the impact of correlation coefficient on the risk of the portfolio. We observe that lower the correlation, greater is the benefit of diversification. Correlation between Diversification Benefits investment returns +1 No benefit 0.0 Substantial benefit -1 Maximum benefit. Indeed, the risk of portfolio can be reduced to zero.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-20
21. 21. Systematic Risk and MarketPortfolio• It would be an onerous task to calculate the correlations when we have thousands of possible investments.• Capital Asset Pricing Model or the CAPM provides a relatively simple measure of risk.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-21
22. 22. Systematic Risk and MarketPortfolio (cont.)• CAPM assumes that investors chose to hold the optimally diversified portfolio that includes all risky investments. This optimally diversified portfolio that includes all of the economy’s assets is referred to as the market portfolio.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-22
23. 23. Systematic Risk and MarketPortfolio (cont.)• According to the CAPM, the relevant risk of an investment relates to how the investment contributes to the risk of this market portfolio.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-23
24. 24. Systematic Risk and MarketPortfolio (cont.)• To understand how an investment contributes to the risk of the portfolio, we categorize the risks of the individual investments into two categories: – Systematic risk, and – Unsystematic riskCopyright © 2011 Pearson Prentice Hall. All rights reserved. 8-24
25. 25. Systematic Risk and MarketPortfolio (cont.)• The systematic risk component measures the contribution of the investment to the risk of the market. For example: War, hike in corporate tax rate.• The unsystematic risk is the element of risk that does not contribute to the risk of the market. This component is diversified away when the investment is combined with other investments. For example: Product recall, labor strike, change of management.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-25
26. 26. Systematic Risk and MarketPortfolio (cont.)• An investment’s systematic risk is far more important than its unsystematic risk.• If the risk of an investment comes mainly from unsystematic risk, the investment will tend to have a low correlation with the returns of most of the other stocks in the portfolio, and will make a minor contribution to the portfolio’s overall risk.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-26
28. 28. Diversification and UnsystematicRisk• Figure 8-2 illustrates that as the number of securities in a portfolio increases, the contribution of the unsystematic or diversifiable risk to the standard deviation of the portfolio declines.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-28
29. 29. Diversification and Systematic Risk• Figure 8-2 illustrates that systematic or non-diversifiable risk is not reduced even as we increase the number of stocks in the portfolio.• Systematic sources of risk (such as inflation, war, interest rates) are common to most investments resulting in a perfect positive correlation and no diversification benefit.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-29
30. 30. Diversification and Risk• Figure 8-2 illustrates that large portfolios will not be affected by unsystematic risk but will be influenced by systematic risk factors.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-30
31. 31. Systematic Risk and Beta• Systematic risk is measured by beta coefficient, which estimates the extent to which a particular investment’s returns vary with the returns on the market portfolio.• In practice, it is estimated as the slope of a straight line (see figure 8-3)Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-31
34. 34. Beta• Beta could be estimated using excel or financial calculator, or readily obtained from various sources on the internet (such as Yahoo Finance and Money Central.com)Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-34
36. 36. Beta (cont.)• Table 8-1 illustrates the wide variation in Betas for various companies. Utilities companies can be considered less risky because of their lower betas.• For example, a 1% drop in market could lead to a .74% drop in AEP but much larger 2.9% drop in AAPL.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-36
37. 37. Calculating Portfolio Beta• The portfolio beta measures the systematic risk of the portfolio and is calculated by taking a simple weighted average of the betas for the individual investments contained in the portfolio.Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-37