Portfolio Selection Project 1 1 Part One 1. Read Brown and Warner (Journal of Financial Economics, 1985) and summarize main analysis and equations 2. Reproduce key equations using equation editor Part...

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Answered Same DayJun 12, 2021

Answer To: Portfolio Selection Project 1 1 Part One 1. Read Brown and Warner (Journal of Financial Economics,...

Kushal answered on Jun 17 2021
150 Votes
Question 1
            d    Normal Distribution    Cumulative distribution        Mean    0
            -5.00    0.0000    0.0000        Standard Deviation    1
            -4.8    0.0000    0.0000
            -4.6    0.0000    0.0000
            -4.4    0.0000    0.0000
            -4.2    0.0001    0.0000
            -4    0.0001    0.0000
            -3.8    0.0003    0.0001
            -3.6    0.0006    0.0002
            -3.4    0.0012    0.0003
            -3.2    0.0024    0.0007
            -3    0.0044    0.0013
            -2.8    0.0079    0.0026
            -2.6    0.0136    0.0047
            -2.4    0.0224    0.0082
            -2.2    0.0355    0.0139
            -2    0.0540    0.0228
            -1.8    0.0790    0.0359
            -1.6    0.1109    0.0548
            -1.4    0.1497    0.0808
            -1.2    0.1942    0.1151
            -1    0.2420    0.1587
            -0.8    0.2897    0.2119
            -0.6    0.3332    0.2743
            -0.4    0.3683    0.3446
            -0.2    0.3910    0.4207
            0    0.3989    0.5000
            0.2    0.3910    0.5793
            0.4    0.3683    0.6554
            0.6    0.3332    0.7257
            0.8    0.2897    0.7881
    
        1    0.2420    0.8413
            1.2    0.1942    0.8849
            1.4    0.1497    0.9192
            1.6    0.1109    0.9452
            1.8    0.0790    0.9641
            2    0.0540    0.9772
            2.2    0.0355    0.9861
            2.4    0.0224    0.9918
            2.6    0.0136    0.9953
            2.8    0.0079    0.9974
            3    0.0044    0.9987
            3.2    0.0024    0.9993
            3.4    0.0012    0.9997
            3.6    0.0006    0.9998
            3.8    0.0003    0.9999
            4    0.0001    1.0000
            4.2    0.0001    1.0000
            4.4    0.0000    1.0000
            4.6    0.0000    1.0000
            4.8    0.0000    1.0000
            5    0.0000    1.0000
d values and probability
Normal Distribution    -5    -4.8    -4.5999999999999996    -4.3999999999999995    -4.1999999999999993    -3.9999999999999991    -3.7999999999999989    -3.5999999999999988    -3.3999999999999986    -3.1999999999999984    -2.9999999999999982    -2.799999999999998    -2.5999999999999979    -2.3999999999999977    -2.1999999999999975    -1.9999999999999976    -1.7999999999999976    -1.5999999999999976    -1.3999999999999977    -1.1999999999999977    -0.99999999999999778    -0.79999999999999782    -0.59999999999999787    -0.39999999999999786    -0.19999999999999785    0    0.2    0.4    0.60000000000000009    0.8    1    1.2    1.4    1.5999999999999999    1.7999999999999998    1.9999999999999998    2.1999999999999997    2.4    2.6    2.8000000000000003    3.0000000000000004    3.2000000000000006    3.4000000000000008    3.600000000000001    3.8000000000000012    4.0000000000000009    4.2000000000000011    4.4000000000000012    4.6000000000000014    4.8000000000000016    5.0000000000000018    1.4867195147342977E-6    3.9612990910320745E-6    1.0140852065486758E-5    2.4942471290053617E-5    5.8943067756540051E-5    1.3383022576488583E-4    2.919469257914613E-4    6.1190193011377515E-4    1.2322191684730251E-3    2.3840882014648547E-3    4.4318484119380301E-3    7.9154515829800067E-3    1.3582969233685689E-2    2.2394530294843017E-2    3.5474592846231626E-2    5.3990966513188306E-2    7.8950158300894496E-2    0.11092083467945597    0.14972746563574532    0.19418605498321345    0.24197072451914386    0.28969155276148323    0.33322460289180006    0.36827014030332356    0.39104269397545599    0.39894228040143265    0.39104269397545582    0.36827014030332328    0.33322460289179962    0.28969155276148267    0.24197072451914334    0.19418605498321292    0.14972746563574485    0.11092083467945557    7.8950158300894177E-2    5.3990966513188077E-2    3.5474592846231452E-2    2.2394530294842896E-2    1.3582969233685611E-2    7.9154515829799564E-3    4.4318484119379989E-3    2.3840882014648378E-3    1.2322191684730152E-3    6.1190193011377016E-4    2.9194692579145892E-4    1.3383022576488488E-4    5.8943067756539638E-5    2.494247129005344E-5    1.0140852065486669E-5    3.9612990910320397E-6    1.4867195147342843E-6    Cumulative Normal Distribution    -5    -4.8    -4.5999999999999996    -4.3999999999999995    -4.1999999999999993    -3.9999999999999991    -3.7999999999999989    -3.5999999999999988    -3.3999999999999986    -3.1999999999999984    -2.9999999999999982    -2.799999999999998    -2.5999999999999979    -2.3999999999999977    -2.1999999999999975    -1.9999999999999976    -1.7999999999999976    -1.5999999999999976    -1.3999999999999977    -1.1999999999999977    -0.99999999999999778    -0.79999999999999782    -0.59999999999999787    -0.39999999999999786    -0.19999999999999785    0    0.2    0.4    0.60000000000000009    0.8    1    1.2    1.4    1.5999999999999999    1.7999999999999998    1.9999999999999998    2.1999999999999997    2.4    2.6    2.8000000000000003    3.0000000000000004    3.2000000000000006    3.4000000000000008    3.600000000000001    3.8000000000000012    4.0000000000000009    4.2000000000000011    4.4000000000000012    4.6000000000000014    4.8000000000000016    5.0000000000000018    2.8665157187701349E-7    7.9332823554878473E-7    2.1124547034956365E-6    5.4125439523655672E-6    1.3345749027338094E-5    3.1671241831343622E-5    7.2348043927972228E-5    1.5910859015622059E-4    3.3692926567741033E-4    6.8713793791552735E-4    1.3498980316299924E-3    2.5551303304280903E-3    4.661188023718732E-3    8.1975359245961554E-3    1.3903447513498701E-2    2.275013194817932E-2    3.593031911292599E-2    5.4799291699558217E-2    8.07566592337714E-2    0.11506967022170878    0.15865525393145763    0.2118553985833973    0.27425311775007433    0.34457825838967659    0.42074029056089779    0.5    0.57925970943910299    0.65542174161032418    0.72574688224992645    0.78814460141660325    0.84134474606854293    0.88493032977829178    0.91924334076622882    0.94520070830044212    0.96406968088707412    0.97724986805182068    0.98609655248650152    0.99180246407540396    0.99533881197628127    0.99744486966957169    0.99865010196837001    0.99931286206208436    0.99966307073432203    0.99984089140984422    0.99992765195607136    0.99996832875816222    0.99998665425097588    0.99999458745605208    0.9999978875453247    0.9999992066715675    0.99999971334842808    d
Normal Distribution Probability
Cumulative distribution Probability
Question 2-A
        Inputs                    A.
        S0    20
        X    21                Two Step                C++                    Four Step                                                Six Step
        Risk Free Rate    10%                                28.8                                                        C++++
        U    1.2                        C+        7.8                                                        41.472                U    1.2                                            C++++++
        D    0.8333333333                        24                                                        C+++        20.472                D    0.8333333333                                            59.71968
        P    0.81                C0        3        C+-                                                34.56                        P    0.81                                    C+++++        38.71968
        1-P    0.19                20                20                                        C++        13.56        C+++-                1-P    0.19                                    49.7664
                            0        C-        0                                        28.8                28.8                                                C++++        28.7664        C+++++-
                                    16.67                                        C+        7.8        C++-        7.8                                                41.472                41.472
                                    0        C--                                24                24                                                C+++        20.472        C++++-        20.472
                                            13.89                        C0        3        C+-        3        C++--                                        34.56                34.56
                                            0                        20                20                20                                C++        13.56        C+++-        13.56        C+++--+
                                                                    0        C-        0        C+--        0                                28.8                28.8                28.8
                            Time Period    2                                            16.6666666667                16.6666666667                                C+        7.8        C++-        7.8        C+++--        7.8
                            Option price     5.03                                            0        C--        0        C+---                        24                24                24
                                                                                    13.8888888889                13.8888888889                C0        3        C+-        3        C++--        3        C+++---
                                formula : e ^ ( - r * t ) * ( p^2 * c++ + 2 * p * (1-p)* c +- + (1-p)^2 * c--)                                                    0        C---        0                20                20                20                20
                                                                                            11.5740740741                        0        C-        0        C+--        0        C++---        0
                                                                                            0        C----                        16.6666666667                16.6666666667                16.6666666667
                                                                                                    9.6450617284                        0        C--        0        C+---        0        C++----
                                                                                                    0                                13.8888888889                13.8888888889                13.8888888889
        As a the number of time period increases, the options prices keep increasing because the probability of the stock price above the strike price increases                                                                                                                            0        C---        0        C+----        0
        Because of this reason the options seller will need higher premium                                                                                                                                    11.5740740741                11.5740740741
                                                                    Time Period    4                                                                    0        C----        0        C+-----
                                                                    Option price     10.05                                                                            9.6450617284                9.6450617284
                                                                                                                                                    0        C-----        0
                                                                        formula : e ^ ( - r * t ) * ( p^4 * c++++ + 2 * p^3 * (1-p)* c +++- )                                                                                    8.0375514403
                                                                                                                    Time Period    6                                    0        C------
                                                                                                                    Option price     13.21                                            6.6979595336
                                                                                                                                                                    0
                                                                                                                        formula : e ^ ( - r * t ) * ( p^6 * c++++++ + 2 * p^5 *...
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