1. Presentation 3: Objectives  To introduce you with the Principles of Investment Strategy for asset allocation and Modern Portfolio Theory  Topics to be covered  Capital Allocation Line, Sharpe Ratio, Optimal Portfolio, Capital Market Line, CAPM, APT, EMH 1

2. Risk Return Efficient Background

3. 6-3 rfrf  rf E(r p ) pp y = % in p(1-y) = % in r f Capital Allocation Line

4. 6-4  Rearrange and substitute y=  C /  P :  Sharpe Ratio Capital Allocation Line

5. Risk Tolerance and Asset Allocation

6.  Investor’s risk aversion level =3.  Fund manager A  E(R): 9%  SD: 15%.  Fund manager B  E(R): 18%  SD: 25%.  T-bill : 6%  What is the optimal position these two fund manager should take for this investor (if this investor becomes one of their clients)? Risk Tolerance and Asset Allocation

7.  Example  In risky portfolio – we have stocks and bond  Now we include a risk free asset giving a return of 3% Optimal Risky Portfolio with a Risk Free Asset

8. ER(%)

9. Optimal Risky Portfolio with a Risk Free Asset

10. Efficient Diversification with three risky assets A B C  3 assets portfolio

11. A B C Efficient Diversification with three risky assets

12. Efficient Diversification with many risky assets

13. Capital Market Line  Short Selling

14. Capital Market Line  Separation Theorem  James Tobin (1958) paper said if you hold risky securities and are able to borrow - buying stocks on margin - or lend - buying risk-free assets - and you do so at the same rate, then the efficient frontier is a single portfolio of risky securities plus borrowing and lending…

15. Capital Market Line  Tobin's Separation Theorem separate the problem into :  first finding that optimal combination of risky securities  deciding whether to lend or borrow, depending on your attitude toward risk.  if there's only one portfolio plus borrowing and lending, it's got to be the market.

16. Rf M CML Borrowing Lending Expected Return Standard Deviation Capital Market Line mm

17. RfRf A M. B.. CML Expected Return Standard Deviation Capital Market Line

19.  Tobin's Separation Theorem separate the problem into :  first finding that optimal combination of risky securities  deciding whether to lend or borrow, depending on your attitude toward risk.  if there's only one portfolio plus borrowing and lending, it's got to be the market.

20. CAPM  William F. Sharpe  Sharpe, W. (1964) A Theory of the Market Equilibrium under conditions of Risk, Journal of Finance, 19, 425-442 Sharpe, W. (1964) A Theory of the Market Equilibrium under conditions of Risk  Noble Prize in Economics 1990 google image 20

21. 21 CAPM  Treynor, J. (1961) Toward a Theory of Market Value of Risky Assets, unpublished manuscript.  J. Lintner (1965) The valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, Review of Economics and Statistics 47, 13-37  J. Mossin (1966) Equilibrium in a Capital Asset Market” Econometrica, 34, 768-783

22. 22 CAPM Assumptions  Investors rely on two factors in making their decisions: expected _ _ _ _ _ _ and variance.  Investors are rational and risk a_ _ _ _ _ and subscribe to Markowitz (1958) methods of portfolio diversification.  Investors all invest for the same period of time.  There is a risk _ _ _ _ investment, and investors can borrow and lend any amount at the risk-free rate.  Capital markets are completely competitive

23. 23  In the development of portfolio theory Markowitz (1958) defined the variance of the rate of return as the appropriate measure of risk.  However this can be sub-divided into two general types of risk: systematic and unsystematic risk.  William Sharpe (1963) defined systematic risk as the portion of an assets variability that can be attributed to a common factor.  Systematic (or market risk) is the minimum level of risk CAPM Terminologies: Systematic and Unsystematic risk

24. 24  Sharpe (1963) defined the portion of an assets variability that can be diversified away as unsystematic (or unique) risk. CAPM Terminologies: Systematic and Unsystematic risk

25.  Total Risk: Systematic + Unsystematic 25 CAPM Terminologies: Systematic and Unsystematic risk

26.  Select from the following as cause for systematic and Unsystematic Risks :  Inflation  Announcement of a small oil strike by a company  Government Tax Policy  Recession  Decision of management of the company to expand/ contract 26 CAPM Terminologies: Systematic and Unsystematic risk

27.  AKA (Systematic or Unsystematic?)  Diversifiable risk  Asset specific risks  Market risks  Unique risk  Controllable  Idiosyncratic risk  Uncontrollable  Portfolio risk 27 CAPM Terminologies: Systematic and Unsystematic risk

28. Standard Deviation of Return Number of Stocks in the Portfolio Standard Deviation of the Market Portfolio (systematic risk) Systematic Risk Total Risk CAPM Terminologies: Systematic and Unsystematic risk Even a little diversification can substantially reduce variability. Unsystematic Risk can be reduced by diversification Market risk Unique risk

29. Expected Return on Individual security (using CAPM)  The  is the covariance between the return of a security and the market return divided by the variance of the market return.  It is a stock’s sensitivity to changes in the value of the market portfolio 29

30. Expected Return on Individual security (using CAPM):  If an investor wants to avoid risk altogether, he must invest in a portfolio consisting entirely of ………………………. such as …………………….. 30

31. Expected Return on Individual security (using CAPM):  If an investor wants to avoid risk altogether, he must invest in a portfolio consisting entirely of risk free securities such as Government Debt  If the investor holds only an undiversified portfolio of shares he will suffer unsystematic risk as well as systematic risk.  If an investor holds a ‘balanced portfolio’ of all the stocks and shares on the stock market, he will suffer risk which is the same as the average systematic risk in the market.  Individual shares will have risk characteristics which are different to this market average.  Their risk will be determined by the industry sector and gearing. Some shares will be more risky and some less. 31

32.  The market portfolio (remember, this is the portfolio of all the shares in the market weighted by capitalization) is taken to be the benchmark and is given a β factor of 1.  All other shares or portfolios will have a β factor greater or smaller than 1 depending on their systematic risk which is measured by considering their required returns. If a share or portfolio has a β factor of 0.5 it will move in line with the market movements but only half as much. If the share or portfolio has a β factor of 2, it will again move in line with the market but twice as much. 32 Expected Return on Individual security (using CAPM)

33.  If a stock has the same risk as the whole market portfolio then, B = ……..  If asset is less risky than the whole market portfolio then Beta = ………  If asset is more risky than the whole market portfolio then Beta = …….. 33

34. Expected Return on Individual security (using CAPM)  Shares classified by their betas are described by some writers as aggressive, defensive or Neutral  b = 1, > 1, < 1 34

35.  Shows the relationship between the return of a equity and the β of the equity  Higher b means higher risk premium 35 Rf  Rm SML Expected Return CAPM: The Security Market Line (SML)

36.  Suppose Rf is 6 %, Rm is 10% and if  = 1 then  Return on equity (also, Cost of equity) =  = 6% + 1 x (10% - 6%)  = 10%  Now suppose the  is 0.5 then  = 6% + 0.5 x (10% - 6%)  = 8%  Again if  = 2  = 14% 36 CAPM: The Security Market Line (SML)

37.  SML then will be 37 6%  10% SML Expected Return  8% 14%

38. EMH  19 th Sept :$ 93.89  14 th Oct :$ 84.95  28 th Oct:$ 99.68 38 21/10/201490.9 22/10/201491.63 23/10/201494.45 24/10/201495.76 27/10/201497.79 28/10/201499.68

39. EMH  “Don’t bother if the bill were real someone would have picked it up already”  Markets are generally very efficient but rewards to the especially - diligent, Intelligent, Creative may in fact be waiting

40. Random Walks  "The Theory of Speculation”  Random Walk – 114 Years  Karl Pearson (1905), walk of drunk, Nature.  Burton Malkiel, A Random Walk Down Wall Street, 1973. Louis Bachelier

41. Market is Irrational  Kendall and Hill (1953) Kendall and Hill (1953)  Stock Price -No logical rules  Erratic Market Psychology AKA “Animal Spirits”  Prices seems to evolve randomly -Market is Irrational

42. £103.00 £100.00 £106.09 £100.43 £97.50 £100.43 £95.06  Coin Toss Game Head Tail Random Walks

43. 43 Informational Efficiency - Efficient Markets Hypothesis (EMH)  Fama (1970) - identified three classifications of efficiency:-  Weak form - prices reflect all _ _ _ _information.  Semi-strong form - prices reflect all past and _ _ _ _ _ _ _ publicly available information.  Strong form - prices reflect all public AND _ _ _ _ _ _ _ information - may include privileged (_ _ _ _ _ _ ) information.  Empirical evidence suggests all major stock markets are at least _ _ _ _ form efficient.

44. 44 Efficient Markets Hypothesis (EMH) Implications of 3 forms  An implication of weak form efficiency is that investors cannot out-predict the market when they predict returns using models based on _ _ _ _ _ _ _ _ _ _ prices.  An implication of semi-strong form efficiency is that when a public announcement is made which is relevant for a security, the price of that security should immediately _ _ _ _ to its equilibrium level.  An implication of strong-form efficiency is that investors can _ _ _ earn extra returns, even when they use their own private information to forecast future returns and prices.

45. 45 EMH - example  Company X has 1 m shares and a market value of £3million.  On 1/12/2013 it considers a project which will cost £2million and yield cash flows of £0.5million per year forever.  The discount rate is 20%.  On 4/12/2013 the board disclose details of the project to the market but do not mention additional redundancy costs of £0.4million.  On 10/12/2013 all relevant information is released to the market.

46. 46  Opening Share Price : = …………per share  Semi-Strong form efficiency:  1/12/2013 : _ _ change as no info is made public.  4/12/2013 : NPV of project = ………………  Share Price = …………….  10/12/13 : All information is made public.  Share Price = ……………… EMH - example

47. 47  Strong Form efficiency:  Provided all financial implications were known on 1/12/2013 the share price would immediately go to ………….  Final price is the same but speed of adjustment is quicker. EMH - example

48. Event Studies  Read the news  5 th January 2009  Read the news : Fortunately, after further testing, my doctors think they have found the cause—a hormone imbalance that has been “robbing” me of the proteins my body needs to be healthy. Sophisticated blood tests have confirmed this diagnosis. 48