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8/10/2019 Porfolio Construction.ppt.pptx

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Investment Analysis and

Portfolio Management

Prof. Rana Abdul Qudous

Portfolio Construction


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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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