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ar Programmi Problem 12-23 Marawita pot option Harry Markowit received the 1990 Nobel Prize for his path breaking work in parte option. One version of the Markowitz model is based on ming the variance of the portfolio subject to a contraint on return. The below table shows me annual return (s) for five year periods for the so mutual funds with the last row that we the SAP turn for each planeing scenario, sino resents a year in which the annual returns are good for all the mutual funds Somano 2 good year for most of the mutual funds. But scenario 3 a bad year for the small cap va fund, somente 4 is a bad year for the intermediateurmond funds and some wa bad year for four of the funds MUTUAL FUND PERFORMANCE IN HVE SELECTED YEARLY SCENARIOS me) 731 Slutalund Foreign Stock InmediataTerm Bond Largo-Cap Growth Large-CapValue Small Cap Growth Small Cap Value S&P 500 Return Manning Scenario Scenario 1 Scenario 2 Scenario 3 Scenario 1 Scenario 10.06 13.12 13.47 45.42 -2193 17.6 3.25 -1.33 7.36 32:41 18.71 33.28 41.46 ---23.26 32.36 2061 12.99 7.06 -5.37 3.44 19.40 3.85 58.68 -9.00 24.56 25.32 -6.70 5.43 17.31 25.00 20.00 8.00 30.000 -10.40 of the issually hely and cours with proty 1/5. then the man return or expected return of the portfolio - . The variance of the portfolio return is - SR. - Using the scenario return data given in Table above, the Markowitz mean variance model can be formidated. The objective hinction is the variance of the portfolio and should be minimized. Assume that the required return on the portfolio 10%. There is also a una constram that all of the money must be invited in mutual funds Most investors are happy when their retums are above average, but not so happy when they are below average. In the Markowite portfolio optimization model ven above, the objective function is to minimire variance, which is given by Mint SR - RY where R is the portfolio return under scenarios and is the expected or average retum of the portfolio with this objective function, we are choosing a portfolio that minimizes deviations both above and below the average, R. However, most investors are hapoy when but unhappy when Re

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