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Lecture 5: Portfolio Theory & Capital Asset Pricing Model

Lecture 5: Portfolio Theory & Capital Asset Pricing Model. At the end of this session you should be able to: Distinguish between different types of risk; Calculate risk, return and covariance Explain relationship between risk and return; Discuss portfolio theory Calculate and explain beta

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Lecture 5: Portfolio Theory & Capital Asset Pricing Model

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  1. Lecture 5: Portfolio Theory & Capital Asset Pricing Model At the end of this session you should be able to: • Distinguish between different types of risk; • Calculate risk, return and covariance • Explain relationship between risk and return; • Discuss portfolio theory • Calculate and explain beta • Discuss the Capital Asset Pricing Model; • Use CAPM to calculate project’s hurdle rate • Discuss the uses and limitations of the capital asset pricing model

  2. Risk Risk • possibility that actual future returns will be different from expected return. • Risk implies that there is a chance for some unfavourable event to occur.

  3. Measurement of Risk • Risk is the possibility that actual outcome will deviates from expected outcome. • Risk is measured by standard deviation

  4. Measurement of Risk

  5. Lecture example 5.1 Security A Rate of Return Probability • 8.5% 35% • 11.0% 10% • 13.5% 30% • 16.0% 25% 100%

  6. Solution 5.1

  7. Standard deviation

  8. Modern Portfolio Theory Risk Diversification: Process of spreading an investment across assets. It is based on common English saying “Don’t put all your eggs in one basket”.

  9. Risk Diversification Markowitz Risk Diversification • Markowitz (1952) provides the tools for identifying portfolio which give the highest return for a particular level of risk. • According to Markowitz, if an investor holds a portfolio of two assets he or she can reduce portfolio risk below the average risk attached to the individual assets. • This can be achieved by investing in assets that have low positive correlation, or better still, a negative correlation.

  10. Example 5.2

  11. Solution 5.2

  12. Solution 5.2

  13. Solution 5.2

  14. Exercise 5.1 Now state the formula with the correct letters

  15. Solution 5.2 b

  16. Solution 5.2 b

  17. Solution 5.2 b

  18. Exercise 5.2 Compare and contrast the covariance of 24 and the correlation coefficient of 0.21 and comment on the figures.

  19. Fig 5.1 Multi –Asset Portfolio

  20. Fig 5.2 Multi-assets portfolio Graphical representation

  21. Capital Asset Pricing Model CAPM (Sharpe, 1964) a method used in analysing the relationship between portfolio risk and return (linear relationship)

  22. Figure 5.3 Security Market Line (SML)

  23. Capital Asset Pricing Model • Systematic risk: • refers to that portion of risk of individual security’s returns caused by factors affecting the market as a whole such as interest rate changes, and inflation

  24. Capital Asset Pricing Model • Unsystematic risk • risk unique to the firm. This caused by such factors such as: • strikes (e.g. London Underground)

  25. Fig 5.4 Systematic and Unsystematic Risk

  26. Measurement of Systematic Risk • Beta: • measure of systematic risk. • It is a measure of the volatility of a security’s return relative to the returns of a broad-based Market portfolio.

  27. Measurement of Systematic Risk Categories of Beta: beta >1 beta <1 beta =1

  28. Portfolio Beta: Example 5.3 Suppose we had the following investments: Security Amount invested Expected Return(%) Beta Stock A $1,000 8 0.80 Stock B $2,000 12 0 .95 Stock C $3,000 15 1.10 Stock D $4,000 18 1.40 • What is the expected return on this portfolio? • What is the beta of this portfolio? • Does this portfolio have more or less systematic risk than the average asset?

  29. Solution 5.3 • Calculate the portfolio weight: Total amount invested is $10,000 • A = 10%, B = 20%, C = 30%, D = 40% • Expected return = .10 x 8% + .20 x 12% + .30 x 15 + .40 x 18% = 14.9 • Portfolio beta = .10 x .80 + .20 x .95 + .30 x 1.10 + .40 x 1.40 = 1.16 • Beta is larger than 1, this portfolio has greater systematic risk than an average asset.

  30. Estimating systematic risk of company (Beta) • Approach 1: Company shares traded in stock exchange • In such situations, the beta coefficients for other companies, with same systematic risk as the project, can be used • Approach 2 • When market-generated beta coefficients are unavailable the systematic risk measure must be constructed artificially

  31. Estimating systematic risk of company (Beta) • Approach 2 • Estimates begin with a beta coefficient for the company or division thinking of undertaking the project and adjust that beta for differences between the project and the company or division • If the betas for the company or division unknown, one can find a market-traded company’s beta to which economic attributes of the project can legitimately be compared

  32. How to calculate beta Read on pages 46-47 of the hand book

  33. CAPM

  34. Example 5.4

  35. Solution to example 5.4 Cov(Jm) = std of j x std of M x correlation of j and M = 0.1 x 0.05 x 0.7 = 0.0035 Therefore j = 0.0035 = 1.40 (0.05)2

  36. Example 5.5 Suppose that the risk free return on the market portfolio is 12% and the beta value of a share in the ABC company is 1.30. Calculate the return on ABC share using CAPM.

  37. Solution to 5.5 Using the equation above: E(rj) = rf + βj(rm – rf) = 5 + 1.30(2 -5) =14.1%

  38. Applications of CAPM • Portfolio selection • Mispriced shares • Mearsuring portfolio performance • Calculating the required rate of return on a firm’s investment

  39. Technical problems with CAPM • Measuring beta • Ex ante theory with ex post testing • Investors expectations drive share price • The market portfolio is unobtainable • Proxies can be poor substitutes for the market portfolio • One period model • Unrealistic assumptions

  40. Empirical findings on CAPM Key question: is the return on the market the only single determinant of individual security returns? • According to CAPM the answer is yes. • Fama and French (1992): no evidence supporting the relationship between security returns and beta. Conclusion- security risk was multi-dimensional. • Beenstock and Chan (1986), Poon and Taylor (1991) found no significant positive relationship between security returns and beta.

  41. Factor Models Fama and French (1992), attempt to overcome the problem of CAPM. These models include two components: • Factors identified as having significant influence on security returns • a measure of the sensitivity of the return on particular securities’ returns to changes in these factors.

  42. Types of risk in multifactor models • Factor risk: is caused by variations in the stock returns that is explained by variations in the identified factor(s). This is equivalent to market risk. • Non factor risk: is risk caused by variations in factors not included in the model. This is equivalent to specific risk.

  43. Multifactor models

  44. Further reading *Cassell, M. (1999), Risk and Return, Management Accounting Fama, G. and French, K. (1992) ‘The cross-section of expected stock return’, Journal of Finance, 47, June, pp. 427-65 Fama, E.F. and French, K.R. (1996) ‘Multifactor explanations of asset pricing anomalies’, Journal of Finance, 50(1), March, pp. 131-55.

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