Portfolio markowitz model

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Portfolio markowitz model

  1. 1. A REPORT ONPortfolio-Markowitz ModelPRESENTED BY:- SATYABRATA PRADHAN KRUPAJAL BUSINESS SCHOOL REGD.NO.-11KB009 BATCH.NO:-2011-2013
  2. 2. Markowitz Model� 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.� Markowitz Risk Diversification� This can be achieved by investing in assets that have low positive correlation, or better still, a negative correlation. 2/12 Satyabrata pradhan
  3. 3. Security Market Line (SML) Expected Return SML M Rf β 3/12 Satyabrata pradhan
  4. 4. Multi –Asset Portfolio The Efficient Frontier Return % B A Risk (std. dev.) 4/12 Satyabrata pradhan
  5. 5. 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. 5/12 Satyabrata pradhan
  6. 6. Measurement of Risk� Risk is the possibility that actual outcome will deviates from expected outcome.� Risk is measured by standard deviation 6/12 Satyabrata pradhan
  7. 7. Type of riskSystematic 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 inflationUnsystematic risk � Risk unique to the firm. This caused by such factors such as: � Strikes 7/12 Satyabrata pradhan
  8. 8. Systematic and Unsystematic RiskRiskstd. dev. Unsystematic risk Total risk Systematic or market risk 20 30 No of securities in a portfolio 8/12 Satyabrata pradhan
  9. 9. ExampleSuppose the shares of two companies, C & D, have the following probabilitydistributions:Economy Probability Return C Return DBoom 0.2 24% 5%Growth 0.6 12% 30%Slump 0.2 0% -5%Requireda) Calculate the expected return and the exp ected risk for each security separately andb) Calculate the expected return and expected risk for a portfolio comprising 75 per cent C and 25 percent D. 9/12 Satyabrata pradhan
  10. 10. Solutiona)Economy Prob. Return ri x pi ri r i – ri (ri – ri)2piC Boom 0.2 +24 4.8 12 12 28.8 Growth 0.6 +12 7.2 12 0 0 Recession 0.2 0 0 12 -12 28.0 Expected Return 12 Variance 57.6 Standard Deviation 7.59% 7.59% 10/12 Satyabrata pradhan
  11. 11. Cont…D Boom 0.2 5 1 18 -13 33.8 Growth 0.6 30 18 18 12 86.4 Recession 0.2 -5 -1 18 +23 105.8 Expected Return 18 Variance 226 Standard Deviation 15.03% 11/12 Satyabrata pradhan
  12. 12. Cont…b)Expected return of the portfolio comprising C and D Security Expected Return C 12x 0.75= 9 D 18x0.25= 4.5 13.5% 12/12 Satyabrata pradhan
  13. 13. Thank you…..

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