Markowitz - sharpes and CAPM

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Portfolio construction using markowitz and sharpes model

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Markowitz - sharpes and CAPM

  1. 1. SYNOPSIS Efficient Market Theory Portfolio Analysis – Markowitz theory Sharpe’s optimum portfolio construction Capital Asset Pricing Model (CAPM)
  2. 2. Efficient Market Theory Efficient Market theory states that the share price fluctuations arerandom and do not follow any regular pattern.Features of Efficient Market All instruments are correctly priced as all available information isperfectly understood and absorbed by all the investors. No excess profits are possible. In a perfectly efficient market, analysts immediately compete away anychance of earning abnormal profits. The forces of demand and supply move freely and in an independentand random manner.
  3. 3. The three forms of market efficiencyWeak form: Market pricing information includes only past pricesSemi-strong form: includes public informationStrong form: includes public and private information
  4. 4. Portfolio Analysis Portfolio is a combination of securities such asstocks, bonds, etc. The process of blending together these securitiesso as to obtain optimum return with minimumrisk is called portfolio construction. A rational investor always attempts to minimize riskand maximize return on his investment. Investing in more than one security is a strategy toattain this goal.
  5. 5. Markowitz Theory Markowitz is considered the father of modern portfoliotheory, mainly because he is the first person who gave amathematical model for portfolio optimization and diversification. Modern portfolio theory (MPT) is a theory of finance that attemptsto maximize portfolio expected return for a given amount ofrisk, or minimize the risk for a given level of expected return. Markowitz theory advise investors to invest in multiple securitiesrather than pulling all eggs in one basket.
  6. 6. Markowitz model – PortfolioThe portfolio return can be calculated with the help of thefollowing formula:= return on the portfolio= proportion of total portfolio investment in security 1= expected return on security 1
  7. 7. Markowitz model – Portfolio riskThe portfolio risk can be calculated with the help of the following formula:σ p = √ X12 σ12 + X22 σ22 + 2 X1 X2 ( r12 σ1 σ2)σ p = Portfolio standard deviationX1 = Percentage of total portfolio value in stock X1X2 = Percentage of total portfolio value in stock X2σ1 = Standard deviation of stock X1σ2 = Standard deviation of stock X2r12 = correlation co-efficient of X1 and X2r12 = Covariance of X 12σ1 σ2
  8. 8. Sharpe’s optimum portfolio construction William Sharpe, tried to simplify the process of data inputs and reaching asolution, by developing a simplified variant of the Markowitz model. In the Sharpe’s model the desirability of any securities inclusion in theportfolio is directly related to its excess return-to-beta ratio. Then theyare ranked from highest to lowest order. The number of securities selected depends on a unique Cut- off rate suchthat all securities with higher ratios will be included. Percentage of investment in each of the selected security is then decidedon the basis of respective weights assigned to each security.
  9. 9. Constructs of Sharpe’s single index modelβ =Correlation CoefficientBetween Market and Stock×Standard Deviation of StockReturnsStandard Deviation of MarketReturns
  10. 10. Cut- off Point = variance of the market index = variance of a stock’s movement that is notassociated with the movement of market index i.e.stock’s unsystematic risk.
  11. 11. Cont…Where, C* = The cut- off point
  12. 12. List of Securities for analysisACC CIPLA HINDUNILVR LUPIN SESAGOAAMBUJACEM COALINDIA HDFC M&M SIEMENSASIANPAINT DLF ITC MARUTI SBINAXISBANK DRREDDY ICICIBANK NTPC SUNPHARMABAJAJ-AUTO GAIL IDFC ONGC TCSBANKBARODA GRASIM INFY POWERGRID TATAMOTORSBHEL HCLTECH JPASSOCIAT PNB TATAPOWERBPCL HDFCBANK JINDALSTEL RANBAXY TATASTEELBHARTIARTL HEROMOTOCO KOTAKBANK RELIANCE ULTRACEMCOCAIRN HINDALCO LT RELINFRA WIPRO
  13. 13. Calculation of Excess Return to Beta RatioSecurity β NEW RANKHCLTECH 27.56 0.00 41.01 5877.55 1BANKBARODA 24.90 0.02 42.03 1056.93 2MARUTI 19.04 0.03 39.51 410.78 3TCS 26.45 0.05 31.33 383.13 4HDFCBANK 21.10 0.04 32.73 349.92 5GRASIM 10.45 0.01 40.83 286.60 6ITC 24.83 0.08 23.87 225.71 7KOTAKBANK 19.10 0.06 55.49 210.20 8PNB 14.50 0.04 41.67 196.22 9HDFC 13.22 0.03 33.10 180.73 10CIPLA 19.38 0.08 25.69 153.02 11SESAGOA 18.17 0.10 52.31 107.64 12ASIANPAINT 30.17 0.22 28.76 104.43 13HINDALCO 11.01 0.10 53.33 36.29 14SBIN 11.67 0.12 45.15 33.83 15
  14. 14. Securities to be Included in the PortfolioSecurityHCLTECH 0.04BANKBARODA 0.17MARUTI 0.35TCS 1.17HDFCBANK 1.60GRASIM 1.61ITC 3.58KOTAKBANK 3.76PNB 3.88HDFC 4.01CIPLA 5.16SESAGOA 5.47ASIANPAINT 9.99
  15. 15. Proportion of Funds to be invested in Each SecuritySecurityHCLTECH 7.93 % 0.011907668BANKBARODA 6.49 % 0.009752967MARUTI 4.80 % 0.007208399TCS 12.51 % 0.018789105HDFCBANK 8.20 % 0.012327808GRASIM 1.13 % 0.00170528ITC 19.32 % 0.029033426KOTAKBANK 2.39 % 0.003584336PNB 2.55 % 0.003824456HDFC 3.28 % 0.004929159CIPLA 11.18 % 0.016800711SESAGOA 2.35 % 0.00353038ASIANPAINT 16.46 % 0.024734334
  16. 16. HCLTECH8%BANKBARODA7%MARUTI5%TCS13%HDFCBANK8%GRASIM1%ITC20%KOTAKBANK2%PNB3%HDFC3%CIPLA11%SESAGOA2%ASIANPAINT17%Optimal Portfolio using SIM
  17. 17. Capital Asset Pricing Model (CAPM)CAPM is used to determine a theoretically appropriate required rate ofreturn of an asset, if that asset is to be added to an already well-diversified portfolio, given that assets non-diversifiable risk.
  18. 18. Let us say that stock A has a beta (Bi = .5%), the risk free rate of return (Rf = 4%)and the expected rate of return for the market (Rm = 10%).Calculate the expected rate of return for the asset?
  19. 19. Assumptions of CAPMAll investors: Aim to maximize economic utilities and are rational and risk-averse. Are broadly diversified across a range of investments. Are price takers, i.e., they cannot influence prices. Can lend and borrow unlimited amounts under the risk free rate of interest. Trade without transaction or taxation costs. Deal with securities that are all highly divisible into small parcels. Assume all information is available at the same time to all investors. Further, the model assumes that standard deviation of past returns is a perfectproxy for the future risk associated with a given security

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