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Kevin Amor goes through an introduction to portfolio theory and CAPM from Unit 4.

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- 1. Unit 4 Portfolio Theory and Capital Asset Pricing Model
- 2. Diversification Diversification is the financial equivalent of the cliche “Don’t put all your eggs in one basket” Diversification results in reduced risk in the portfolio. This is because of the averaging effect Price Time
- 3. Diversification Diversification is the financial equivalent of the cliche “Don’t put all your eggs in one basket” Diversification results in reduced risk in the portfolio. This is because of the averaging effect Price Time We think of “risk” as being linked to the volatility of returns – so averaging tends to smooth volatility
- 4. Diversification Remember that the risk that is diversified away is the “specific” risk: the risk pertaining to the industries and businesses in that portfolio. “Market” risk: the risk of investing in equities rather than , say, bonds, cannot be diversified away.
- 5. Diversification Remember that the risk that is diversified away is the “specific” risk: the risk pertaining to the industries and businesses in that portfolio. “Market” risk: the risk of investing in equities rather than , say, bonds, cannot be diversified away. Hence: Average risk No shares in portfolio Market risk
- 6. Portfolio Theory This theory assumes that investors are “risk averse” Note: “risk averse” does NOT means that investors will not take risks (“risk avoidance”)
- 7. Portfolio Theory This theory assumes that investors are “risk averse” Note: “risk averse” does NOT means that investors will not take risks Instead it means that investors will take on risk if the returns on offer are sufficient So the attractions of an investment are a combination of the expected returns and the risk, as measured by standard deviation
- 8. Portfolio Theory – Expected returns and standard deviation Consider the following distribution of returns Frequency ReturnR
- 9. Portfolio Theory – Expected returns and standard deviation Consider the following distribution of returns Frequency ReturnR
- 10. Portfolio Theory – 2 share portfolio Let us assume that we have a portfolio comprising two shares The expected return of this portfolio is given by: E(Rp) = WxE(Rx) + WyE(Ry) (the weighted average of the two returns)
- 11. Portfolio Theory – 2 share portfolio Let us assume that we have a portfolio comprising two shares The expected return of this portfolio is given by: E(Rp) = WxE(Rx) + WyE(Ry) (the weighted average of the two returns) Proportion of the portfolio that is X or Y (for example, 0.6 & 0.4) Expected returns on X & Y (eg 10% and 12%) What is the expected returns here?
- 12. Portfolio Theory – 2 share portfolio Let us assume that we have a portfolio comprising two shares The expected return of this portfolio is given by: E(Rp) = WxE(Rx) + WyE(Ry) (the weighted average of the two returns) Proportion of the portfolio that is X or Y (for example, 0.6 & 0.4) Expected returns on X & Y (eg 10% and 12% Using these figures the expected return would be 0.6 x 10% + 0.4 x 12% = 10.8%
- 13. Portfolio Theory – 2 share portfolio Let us assume that we have a portfolio comprising two shares The expected return of this portfolio is given by: E(Rp) = WxE(Rx) + WyE(Ry) (the weighted average of the two returns) The risk of the portfolio is given by: Sp = √(Wx 2Sx 2 + Wy 2Sy 2 + 2WxWySxSyCorrxy
- 14. Portfolio Theory – 2 share portfolio Let us assume that we have a portfolio comprising two shares The expected return of this portfolio is given by: E(Rp) = WxE(Rx) + WyE(Ry) (the weighted average of the two returns) The risk of the portfolio is given by: Sp = √(Wx 2Sx 2 + Wy 2Sy 2 + 2WxWySxSyCorrxy The standard deviations (ie risk) of the investment , say 30% and 40% The correlation coefficient of X & Y – say 0.3 What is the risk (SD) of the portfolio? (recall that the weightings are 0.6 and 0.4)
- 15. Portfolio Theory – 2 share portfolio Let us assume that we have a portfolio comprising two shares The expected return of this portfolio is given by: E(Rp) = WxE(Rx) + WyE(Ry) (the weighted average of the two returns) The risk of the portfolio is given by: Sp = √(Wx 2Sx 2 + Wy 2Sy 2 + 2WxWySxSyCorrxy =√(0.6 x 0.6 x 30 x 30 + 0.4 x 0.4 x 40 x 40 + 2 x 0.6 x 0.4 x 30 x 40 x 0.3) = 27.4%
- 16. Portfolio Theory – 2 share portfolio Combining these formulae one can start to plot a graph of return against risk for varying weights of portfolio Return Risk This graph represents all the possible combinations of holding shares in X & Y (eg 10% X 90%Y, or 20% X, 80% Y etc)
- 17. Portfolio Theory – 2 share portfolio Combining these formulae one can start to plot a graph of return against risk for varying weights of portfolio Return Risk You would not pick this weighting. Why not?
- 18. Portfolio Theory – 2 share portfolio Combining these formulae one can start to plot a graph of return against risk for varying weights of portfolio Return Risk Because the portfolio at “A” has the same risk but a higher return A
- 19. Portfolio Theory – many-share portfolio If we had significantly more shares than 2 then the graph would be a follows Return Risk
- 20. Portfolio Theory – many-share portfolio If we had significantly more shares than 2 then the graph would be a follows Return Risk All of the possible combinations of the shares would be in the shaded area
- 21. Portfolio Theory – many-share portfolio If we had significantly more shares than 2 then the graph would be a follows Return Risk Any portfolios lying on this edge are the most efficient – they earn the highest returns at the lowest risk – hence it is called the “efficient frontier”
- 22. Portfolio Theory – many-share portfolio If we had significantly more shares than 2 then the graph would be a follows Return Risk Any portfolios lying on this edge are the most efficient – they earn the highest returns at the lowest risk – hence it is called the efficient frontier You want the portfolio to be as far in the north west of this graph as possible
- 23. Portfolio Theory – Domination Would we prefer A or B and C or D? Return Risk A C B D
- 24. Portfolio Theory – Domination Would we prefer A or B and C or D? Return Risk A C B D A has a higher return than B for the same risk and C has the same return as D for a lower risk. So we prefer A and C
- 25. Portfolio Theory – the Market Portfolio Return Risk So the most efficient portfolio will be the one along the frontier that is most north-west. This is called the “market portfolio” M
- 26. Capital Asset Pricing Model (CAPM) Let us now combine our market portfolio with a risk free investment - what is meant by a risk free investment ?
- 27. Capital Asset Pricing Model (CAPM) Let us now combine our market portfolio with a risk free investment - what is meant by a risk free investment ? In CAPM we assume that we can invest or borrow at the risk free rate Rf M Here we are only investing in risk free
- 28. Capital Asset Pricing Model (CAPM) Let us now combine our market portfolio with a risk free investment - what is meant by a risk free investment ? In CAPM we assume that we can invest or borrow at the risk free rate Rf M Here we are only investing in risk free Here we are only investing in the market portfolio
- 29. Capital Asset Pricing Model (CAPM) Let us now combine our market portfolio with a risk free investment - what is meant by a risk free investment ? In CAPM we assume that we can invest or borrow at the risk free rate Rf M Here we are only investing in risk free Here we are investing in part risk free and part market Here we are only investing in the market portfolio
- 30. Capital Asset Pricing Model (CAPM) Let us now combine our market portfolio with a risk free investment - what is meant by a risk free investment ? In CAPM we assume that we can invest or borrow at the risk free rate Rf M Here we are only investing in risk free Here we have BORROWED at the risk free rate and invested in the market portfolio Here we are investing in part risk free and part market Here we are only investing in the market portfolio
- 31. CAPM As the risk-free – market portfolio relationship is a straight line it is straightforward to describe it mathematically. Once we have that relationship we then have a formula for the return on a share compared to the risk of that share
- 32. CAPM So we want an easy measure of risk. For this we use beta (β). This measures the relative volatility of the share against the market portfolio.
- 33. CAPM So we want an easy measure of risk. For this we use beta (β). This measures the relative volatility of the share against the market portfolio. Beta for the market is set as one. Shares whose beta are greater than one are called “aggressive”; less than one “defensives”
- 34. CAPM Let us build up the relationship. The y axis will be the expected return on a share and the x axis the risk associated with the share as measured by its beta Risk = β Return = Re
- 35. CAPM A straight line is given as y = mx + c Let us put in some points we know: the risk free and market . What is c? Rf M Risk = β Rm 10
- 36. CAPM A straight line is given as y = mx + c What is c? It is the y-intercept = Rf What is m? Rf M Risk = β Rm 10
- 37. CAPM A straight line is given as y = mx + c Y = the return on the share Re, X = risk, using beta What is c? It is the y-intercept = Rf What is m? It is the gradient Rf M Risk = β Rm 1 The gradient is given by: Rm-Rf 1 0
- 38. CAPM So the formula of the return on equity is: Re = (Rm-Rf)β + Rf Rf M Risk = β Rm 1 Re
- 39. CAPM A defensive will have a lower return than an aggressive Re = (Rm-Rf)β + Rf Rf M Risk = β Rm 1 Defensives β< 1 Aggresives β > 1
- 40. Next Time We shall look at project appraisals – discounted cash flow etc - from unit 5

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