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    Investment Analysis and

    Portfolio Management

    Prof. Rana Abdul Qudous

    Portfolio Construction

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    Portfolio Construction

    Value Averaging

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    month

    share

    price total value

    share to

    own share to buy/sell investment

    Jan-09 4.64 100 21.55 21.55 -99.99

    Feb-09 4.38 200 45.66 24.11 -105.60

    Mar-09 4.56 300 65.79 20.13 -91.78Apr-09 4.25 400 94.12 28.33 -120.39

    May-09 3.81 500 131.23 37.12 -141.41

    Jun-09 3.19 600 188.09 56.85 -181.36

    Jul-09 2.99 700 234.11 46.03 -137.62

    Aug-09 3.6 800 222.22 -11.89 42.81Sep-09 4.7 900 191.49 -30.73 144.44

    Oct-09 4.41 1000 226.76 35.27 -155.53

    Nov-09 4.34 1100 253.46 26.70 -115.87

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    Jan-10 5.26 1300 247.15 -8.72 45.84

    Feb-10 4.54 1400 308.37 61.22 -277.95

    Mar-10 5.38 1500 278.81 -29.56 159.03

    Apr-10 7.47 1600 214.19 -64.62 482.71

    May-10 7.39 1700 230.04 15.85 -117.14Jun-10 6.31 1800 285.26 55.22 -348.44

    Jul-10 7.07 1900 268.74 -16.52 116.80

    Aug-10 6.48 2000 308.64 39.90 -258.56

    Sep-10 7.07 2100 297.03 -11.61 82.10

    Oct-10 6.96 2200 316.09 19.06 -132.67

    Nov-10 5.05 2300 455.45 139.35 -703.74

    Dec-10 5.8 2400 413.79 -41.65 241.58

    Jan -11 5.06 413.79 2093.78 -1684.03

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    Jan-10 5.26 100 19.01 315.98 1662Feb-10 4.54 100 22.03 338.01 1535

    Mar-10 5.38 100 18.59 356.60 1919

    Apr-10 7.47 100 13.39 369.99 2764

    May-10 7.39 100 13.53 383.52 2834

    Jun-10 6.31 100 15.85 399.37 2520Jul-10 7.07 100 14.14 413.51 2924

    Aug-10 6.48 100 15.43 428.94 2780

    Sep-10 7.07 100 14.14 443.09 3133

    Oct-10 6.96 100 14.37 457.45 3184

    Nov-10 5.05 100 19.80 477.26 2410Dec-10 5.8 100 17.24 494.50 2868

    11-Jan 5.06 494.5 2502

    2400

    Average 5.18 4.85

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    Markowitz Portfolio Selection

    Markowitz provided a comprehensive framework for analysis of portfolio

    Portfolio of securities is an integrated whole, each securities complementing the

    other

    Consider both the characteristics of individual security and the relationshipbetween these securities.

    Investors like return and dislike risk

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    Find the set of portfolio that

    Provides the minimum risk for every possible level of return.

    The Efficient Set

    Investor select from the efficient set that meets his/her requirements

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    Maximize the expected return

    Minimize the variance

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    Minimize portfolio Risk

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    Subject to:

    A Stated Expected Return

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    Covariancemeasures the extent to which two securities tend to move, or not move,

    together.

    The variance of an individual security is the sum of the probability-weighted

    average of the squared differences between the securitys expected return and its

    possible returns.

    The standard deviation is the square root of the variance. Both variance and

    standard deviation measure of total risk, including both systematic and specific risk.

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    Correlation Co-efficient

    A correlation of +1.0 would indicate perfect positive correlation, and a value of 1.0

    would mean that the returns moved in a completely opposite direction. A value of zero

    would mean that the returns had no linear relationship, that is, they were uncorrelated

    statistically.

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    Month Closing Price X Closing Price Y

    Dec-00 40 20

    Jan-01 44 22

    Feb-01 50.6 24.64

    Mar-01 51.62 25.38

    Apr-01 54.7 23

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    Month Closing Price X Return X Closing Price Y Return Y

    Dec-00 40 20

    Jan-01 44 .10 22 .10

    Feb-01 50.60 .15 24.64 .12

    Mar-01 51.62 .02 25.38 .03

    Apr-01 54.7 .06 23 -.09

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    Return X Return Y

    .10 0.10

    .15 0.12

    .02 0.03

    .06 -0.09

    0.33 0.16

    A.M x = 0.33/4

    A.M x = 0.0825

    A.M y =. 016/4

    A.M y = 0.04

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    Return X Average

    Return

    Dx Return Y Average

    Return

    Dy dx.dy

    .10 0.0825 0.01750 0.10 .04 0.06 0.00105

    .15 0.0825 0.0675 0.12 .04 0.08 0.0054

    .02 0.0825 -0.0625 0.03 .04 -0.01 0.000625

    .06 0.0825 -0.0225 -0.09 .04 -0.13 0.002925

    0.33 0.16 0.01

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    Covariance = sum of dx*dy /n

    = =.01 /4

    = .0025

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    Return X Return Y dx dy dx2 dy2

    .10 0.10 0.01750 0.06 0.000306 0.0036

    .15 0.12 0.0675 0.08 0.004556 0.0064

    .02 0.03 -0.0625 -0.01 0.003906 0.0001

    .06 -0.09 -0.0225 -0.13 0.000506 0.0169

    0.33 0.16 0.009275 0.027

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    Variance X =. 0.009275 / 4

    = 0.00231875

    SDx = 0.00231875

    SDx = 0.048153

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    Variance Y =. 027 / 4

    = 0.00675

    SDy = 0.00675

    SDy = 0.082158

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    S.D x =

    0.048153

    0.082158S.Dy =

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    0.0025r =

    0.048153 * 0.082158

    r = 0.631919

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    Average Return

    Coca Cola = 17.61/12

    = 1.47

    Home Depot = -21.75/12

    =1.81

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    DATE

    COCA-COLA

    (Ri)

    HOME

    DEPOT (Rj) Deviation (i)

    Deviation

    (j)

    Deviation

    (i)*Deviation

    (j)Jan-01 -4.82 5.50 -3.01 4.03 -12.13

    Feb-01 -8.57 -11.83 -6.76 -13.29 89.81

    Mar-01 -14.50 1.51 -12.69 0.04 -0.49

    Apr-01 2.28 9.28 4.09 7.81 31.98

    May-01 2.62 4.65 4.43 3.18 14.11Jun-01 -4.68 -4.08 -2.87 -5.54 15.92

    Jul-01 -0.89 6.63 0.92 5.16 4.76

    Aug-01 9.13 -8.70 10.94 -10.16 -111.16

    Sep-01 -3.37 -16.50 -1.56 -17.96 27.97

    Oct-01 2.20 -0.36 4.01 -1.83 -7.35Nov-01 -1.55 22.16 0.27 20.69 5.52

    Dec-01 0.40 9.35 2.22 7.88 17.47

    AR(i)= -1.81 AR(j)= 1.47 76.42

    Covij= 76.42/12 = 6.37

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    COCA-COLA

    DATE Deviation Sq. Deviation

    Jan-01 -3.01 9.05

    Feb-01 -6.76 45.65

    Mar-01 -12.69 161.01

    Apr-01 4.09 16.75

    May-01 4.43 19.64

    Jun-01 -2.87 8.24

    Jul-01 0.92 0.85

    Aug-01 10.94 119.64

    Sep-01 -1.56 2.42

    Oct-01 4.01 16.09

    Nov-01 0.27 0.07Dec-01 2.22 4.92

    Sum = 404.34

    Variance = 404.34/12 = 33.69

    Standard Deviation = sqrt(33.69) =5.80

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    Expected Return and Standard Deviation of Two stocks is given below

    E(R1) = 0.201 = 0.10

    E(R2) = 0.20

    2 = 0.10

    Both the assets have equal weight i.e. (W1 = 0.50; W2 = 0.50).

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    Correlation co-efficient between Stock 1 and 2 is as follows:

    a. r1,2 = 1

    b. r1,2 = 0.50

    C. r1,2 = 0.00

    d. r1,2 = -0.50

    e. r1,2 = -1Calculate Portfolio Risk under all the five conditions

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    Both the assets have equal weight i.e. (W1 = 0.50; W2 = 0.50).

    .

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    You are considering two assets with the following characteristics:

    E(R1) = .15

    E(R2) = .20

    1 = .10 W1 = .52 = .20 W2 = .5

    Compute the mean and standard deviation of two portfolios if r1,2 = 0.40 and0.60,

    respectively.

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    Given:E(R1) 0 .10

    E(R2) 0 .15

    1 = .03

    2 = .05

    Calculate the expected returns and expected standard deviations of a two-stock

    portfolio in which Stock 1 has a weight of 60 percent under the following conditions:

    a. r1,2 = 1.00b. r1,2 = 0.75

    c. r1,2 = 0.25

    d. r1,2 = 0.00

    e. r1,2 =0.25

    f. r1,2 =0.75

    g. r1,2 =1.00

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    The standard deviation of Shamrock Corp. stock is 19 percent. The standarddeviation of Baron Co. stock is 14 percent. The covariance between these two

    stocks is 100. What is the correlation between Shamrock and Baron stock?

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