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Portfolio Theory and The Capital Asset Pricing Model

Portfolio Theory and The Capital Asset Pricing Model. Lecture 6 Dr Francesca Gagliardi. 2BUS0197 – Financial Management. Learning outcomes. By the end of the session students should appreciate: The rationale behind the diversification decisions of investors and companies

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Portfolio Theory and The Capital Asset Pricing Model

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  1. Portfolio Theory and The Capital Asset Pricing Model Lecture 6 Dr Francesca Gagliardi 2BUS0197 – Financial Management

  2. Learning outcomes By the end of the session students should appreciate: • The rationale behind the diversification decisions of investors and companies • The mechanics of optimal portfolio construction • The limitations of portfolio analysis • The rationale underlying CAPM • How to calculate the required rate of return of a security using the CAPM • The practical applicability and reliability of CAPM

  3. Risk and its measurement Companies face risk from variability in project cash flows Investors face risk from variability in capital gains and dividends Rational aim is to minimise risk for a given level of return To control risk, this must be understood and measured Risk is measured by the standard deviation of the returns on a share, based on either historical returns or expected future returns

  4. Rationale for diversification • Investment activities involve risk due to uncertainty on future returns • Diversification is a strategic device for dealing with risk: it allows to control and manage risk • Diversification works because the prices of different securities do not move exactly together. Hence, an opportunity to reduce risk • Question: Which type of risk can be reduced?

  5. Risk components • Systematic risk(market risk): the returns from an investment are affected by systematic factors (e.g. business cycle, government policy, interest rates fluctuations) • Unsystematic risk(unique risk): risk specific to a particular investment activity (e.g. the risk of a project performing badly) • An investor can only reduce unsystematic risk. This can be done by spreading investments over a number of different assets

  6. Reducing unsystematic risk through diversification

  7. Portfolio theory • Originally proposed by Harry Markowitz (1952), was later developed by James Tobin (1958) and William Sharpe (1964) – All Nobel laureates for Economics • Not all investments perform well at the same time, some never do, some may perform extremely well • Since one cannot predict which investments fall into each category in any one period, it is rational to spread his/her funds over a wide set of investments

  8. Achieving a perfect portfolioeffect • A moves in parallel with the economy as a whole • B moves in an exactly opposite way. Returns from Bare contra-cyclical • Equal and offsetting fluctuations in returns from A and B, result in a perfectly level profile for a diversified enterprise comprising both activities • The dampening effect on the variability of returns is called a portfolio effect

  9. Creating a risk-free portfolio • The previous portfolio completely removes the variability in returns (measured by standard deviation). Hence, risk = 0 • Why does risk disappear? • Correctly weighted portfolio • Perfect negative correlation between the two investments

  10. Creating a risk-free portfolio • The extent to which portfolio combinations can achieve a reduction in risk depends on the degree of correlation (ρ) between returns • If ρ = -1 all risk will be diversified away • If ρ = 0 no correlation between returns • If ρ = 1 no risk can be diversified away • In reality cases of perfect negative correlation between the returns from investments are rare

  11. Towards an optimal portfolio • An investor can undertake two possible investment, A and B, in sectors of the economy that do not move exactly together (ρ = 0.2) • Investment A • Expected return (ER) of 20% p.a • Standard deviation of 58.5% • Investment B • Expected return of 10% p.a • Standard deviation of 31.5%

  12. Towards an optimal portfolio • Suppose a portfolio invested 35% in A and 65% in B • The expected return on this portfolio is: • ERP = ERA +ERB =(0.35 x 20%) + (0.65 x 10%) = = 7% + 6.5% = 13.5% • ρ = 0.2 gives a portfolio risk of 30.3%

  13. The efficient portfolios’ frontier Return (%) B 20 Q P 65% B 35% A 13.5 C 10 A 30.3 31.5 58.5% Risk (%)

  14. Portfolios with more than two components Return (%) A and C combined A A, B, C combined A and B combined B E B and C combined A and C combined C Risk (%) 14

  15. Central result of portfolio theory • The optimal portfolio depends on the decision maker’s attitude towards risk • If the extent of risk aversion is known, it is possible to specify the best portfolio

  16. The model implies constant returns to scale Difficult to have perfect knowledge of investors’ utility functions Identification of market portfolio requires knowledge of investments’ risk, return and correlation coefficient Transaction costs faced by investors not accounted for The composition of the market portfolio changes over time Unrealistic to assume that investors can borrow at the risk-free rate Limitations of approach

  17. The Capital asset pricing model (CAPM) • Development of portfolio theory (Sharpe, 1964): attempt to construct a market equilibrium theory of asset prices under conditions of risk • Positive CAPM uses the systematic risk of individual securities to determine their fair price • Normative portfolio theory considers the total risk and return of portfolios and advises investors on which portfolios to invest in

  18. CAPM assumptions Investors are rational and utility maximisers All information is freely available to investors All investors have similar expectations Investors can borrow and lend at the risk-free rate Investors hold diversified portfolios, thereby eliminating all unsystematic risk Capital markets are perfectly competitive Investment occurs over a single, standardised holding period

  19. Using CAPM to value shares Rj = Rf + βj (Rm - Rf) • CAPM is based on a linear relationship between risk and return • This linear representation is defined by a security market line (SML) • The SML compares the systematic risk of a security with the risk and return of the market and the risk-free rate of return in order to calculate a required return for the security and hence a fair price • The equation of the SML is: • Rj = Predicted rate of return of security j • βj = Beta value of the ordinary shares of a company • Rm = Return of the market • Rf = Risk-free rate of return • Equity risk premium (Rm – Rf)

  20. The security market line Return (%) Rj = Rf + βj (Rm - Rf) Rm Rj Rf 0 βj Systematic risk (β) βm= 1

  21. Meaning of beta • The beta (β) of a security is an index of responsiveness of changes in returns of the security relative to a change in returns on the market • By definition the beta of the market is always 1 and acts as a benchmark against which the systematic risk of securities can be measured • The beta of a security measures the sensitivity of the returns on the security on changes in systematic factors • Βj < 1 = defensive security (e.g. food retail, utilities, necessity goods); Βj > 1 = aggressive security (e.g. consumer durables, leisure and luxury goods) • Example: • βj= 0.75 • Market return increases by 10% • Return on βj increases by 7.5%

  22. Calculation of beta • Beta can be found from: βj = (σj σm ρjm)/σm2 where: σj = standard deviation of returns on asset j σm = standard deviation of market returns ρjm = correlation coefficient between j and m σm2 = variance of returns on the market

  23. Calculation of beta Beta can be found by regression analysis of security returns against market returns The slope of the line of best fit will give the value of beta The coefficient of determination (R2) will indicate to which extent the total variability of a security’s returns is explained by systematic risk, as measured by beta, as opposed to other factors Beta can be found from a line of best fit of a plot of security returns against market returns Company beta values are found in the Beta Books published quarterly by the London Business School Risk Management Service and from other financial resources such as DataStream

  24. Security return % x x x x x x x x x x x x A x x B x 0 Market return % Slope of the Characteristic Line (A/B) gives the security’s beta Calculation of beta

  25. Finding the portfolio beta Obtained by weighting the individual security betas by their relative market value Weight = ns * (ps/mp) where: ns = number of shares ps = price of shares mp = portfolio market value

  26. The portfolio beta Security Beta Weight Weighted beta Barclays 1.17 20% 0.234 BP 0.75 35% 0.263 Kingfisher 1.00 15% 0.150 Severn Trent 1.15 20% 0.230 Tesco 0.49 10% 0.049 Portfolio Beta 0.926 Question: Is this an aggressive or defensive portfolio? 26

  27. Determining the risk-free rate of return • The risk-free rate of return (Rf ) represents the rate of return earned by investing in the risk-free asset • No assets aretotally risk-free, but bonds issued by governments of stable countries are seen as almost risk-free • Hence, the risk-free rate is proxied by the current rate of return (or yield) on short-dated government bonds

  28. Determining the market return • The market rate of return (Rm) isapproximated by using stock exchange index, such as FTSE 100 Rm = [(P1 - P0)/P0] +Div where P1 = stock exchange index at the end of the period P0 = stock exchange index at the beginning of the period Div = average dividend yield of the stock exchange index over the period • Calculated on a moving average basis from monthly or annual data • Equity risk premium can be determined on either a 'geometric' or an 'arithmetic’ basis • Arithmetic risk premium over-estimates, so geometric risk premium is recommended

  29. Example: Using CAPM Equity beta of British Airways: 1.65 Risk-free rate (yield on Treasury bills): 4.5% Market risk premium (Rm - Rf): 5.0% Rj = 4.5 + (1.65 × 5.0) = 12.8% This represents shareholders' required rate of return and hence the cost of equity of British Airways

  30. Implications of CAPM Investors will require compensation only for systematic risk, since unsystematic risk can be eradicated by portfolio diversification Securities with high levels of systematic risk should, on average, yield high rates of return There should be a linear relationship between systematic risk and return Correctly priced securities should plot on the security market line (SML)

  31. Empirical evidence • Evidence in years following development of CAPM was supportive: • Sharpe and Cooper (1972) found portfolio betas (10 or more shares) were stable while individual betas were not • Jacob (1971) and Black, Jenson & Scholes (1972) found a linear relationship between systematic risk and return, but the fitted SML was shallower that the theoretical SML • Evidence in recent years is not supportive: • Black (1993) found strong relationship for the NYSE over 1931-65 and poor relationship over 1966-91 • Fama & French (1992) said ‘results do not support that average stock returns are positively related to market betas’ for US shares over 1963-90 • It seems factors other than systematic risk help to determine a security’s required return Multi factors models subsequently proposed

  32. Is CAPM useful? A theory should be judged on its performance rather than on its assumptions Portfolio betas are relatively stable Strong evidence on validity of security market line has now given way to doubts Is there a better alternative to the CAPM? Perhaps multivariate models such as APM (Arbitrage Pricing Model)? Managers and investors doubting the validity of the EMH are unlikely to accept a CAPM-derived discount rate

  33. Summary Today we have looked at: • Diversification in investment decisions • Markowitz’s optimal portfolio construction • Graphical analysis of portfolio selection • Applicability of the model • CAPM rationale • Application of CAPM to value shares • Implications and applicability of CAPM

  34. Readings Textbook • Watson, D., Head, A. (2009). Corporate Finance. Principles & Practice, 5th Ed., FT Prentice Hall – Chapter 8. Research papers • Markowitz, H. (1952), Portfolio Selection. The Journal of Finance, 7(1), pp. 77-91. • Sharpe, W. F. (1964), Capital Asset Prices - A Theory of Market Equilibrium Under Conditions of Risk. The Journal of Finance, 19(3), pp. 425–42. • Tobin (1958), Liquidity Preference as Behavior Towards Risk. Review of Economic Studies, 25(1), pp. 65–86.

  35. Your tutorial activities for next week During the seminar you will be expected to work on: Q1 p.254; Q4 p.255; Q5 p.255 (5th ed) Q1 p.237; Q4 p.238; Q5 p.239 (4th ed) To prepare for the seminar you should answer the following practice questions: Q1,2,6 p.251; Q2 p.252 (5th ed) Q1,2,6 p.235; Q2 p.236 (4th ed) 35

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