SOLUTION TO PORTFOLIO MANAGEMENT ASSIGNMENT - CA FINAL SFM

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BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGHPRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854Portfolio managementQ1 Year 05 06 07 08 09 10 X 12 18 -6 20 22 24 (X- ) -3 3 -21 5 7 9 (X-)2 9 9 441 25 49 81__________PRAVINN MAHAJAN CA CLASESS614 = σ =Ʃ =90 6= 15% =614 6(;)2 =10.11% 2 =Q2 No. 1 2 3 4 5 6 7614 6= 102.33Prob. 0.05 0.10 0.24 0.26 0.18 0.12 0.05 (X-) -8.56 -5.56 -2.56 -0.56 3.44 5.44 9.44 P(X-)2 3.66 3.09 1.57 0.082 2.13 3.55 4.46 18.542

Transcript of SOLUTION TO PORTFOLIO MANAGEMENT ASSIGNMENT - CA FINAL SFM

BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH

PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854

Portfolio managementQ1 Year 05 06 07 08 09 10 X 12 18 -6 20 22 24 (X- ) -3 3 -21 5 7 9 (X-)2 9 9 441 25 49 81__________

PRAVINN MAHAJAN CA CLASESS

614 = =

=

90 6

= 15% =614 6

(;)2

=

10.11%

2 =Q2 No. 1 2 3 4 5 6 7

614 6

= 102.33Prob. 0.05 0.10 0.24 0.26 0.18 0.12 0.05 (X-) -8.56 -5.56 -2.56 -0.56 3.44 5.44 9.44 P(X-)2 3.66 3.09 1.57 0.082 2.13 3.55 4.46 18.542

Return (X) 12 15 18 20 24 26 30

Expected return =

= 12 x 0.05 + 15 x 0.10 + 18 x 0.24 + 20 x 0.26 + 24 x 0.18 + 26 x 0.12 + 30 x 0.05 = 20.56 = ( )2 = 18.542 = 4.31%

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fb-id PRAVINN MAHAJAN CA CLASSES

BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q3 Year 1 2 3 4 5 6 7 Return(X) -24 -10 0 12 18 22 30

PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854 Prob. 0.05 0.15 0.15 0.20 0.20 0.15 0.10 PX -1.2 -1.5 0 2.4 3.6 3.3 3.0 9.6 (X-) -33.6 -19.6 -9.6 2.4 8.4 22.4 20.4 P(X-)2 56.448 57.624 13.824 1.152 14.112 23.064 41.616 207.84

Expected return =

9.6

= ( )2 =

207.84 = 14.417 %

Q4 Year PRAVINN MAHAJAN CA CLASESS 1 2 3 4 5 Return = -33.33 50 33.33 25 20

10 0

=X

Prob. 0.10 0.20 0.40 0.20 0.10

PX -3.33 10.00 13.33 5 2

(X-) -60.33 23 6.33 -2 -7 27

P(X-)2 363.97 105.8 16.027 0.8 4.9 491.497

Expected Return = 27 = ( )2 = 491.497 = 22.169 %

Q5 Year 04-05 05-06 06-07 07-08 08-09 09-10 Return =1 :(10 ) 0

=X

(X-) -10.845 8.105 7.755 17.461 11.625 0.818

(X-)2 117.614 65.691 60.140 304.886 135.140 0.669 684.14

1.8:(38;38) = 4.73 38 2.0:(45;38) = 23.68 38 2.5:(53;45) = 23.33 45 2.0:(50;53) = -1.886 53 2.6:(61;50) = 27.2 50 3.0:(68;61) = 16.393 61

93.447 Expected Return = 93.447 6 = 15.575% =(;)2 684.14 6

=

= 10.67%

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fb-id PRAVINN MAHAJAN CA CLASSES

BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q6 Year 96 97 98 PRAVINN MAHAJAN CA CLASESS 99 00 Return =1 :(10 )

PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854

0 1.53:(20.75;31.25) 31.25 1.53:(30.88;20.75) 20.75 2:(67;30.88) 30.88 2:(100;67) 67

=X

(X-) -80.732 4.158 71.408 0.198 4.968

(X-)2 6517.65 17.288 5099.102 0.0392 24.681 11658.76

= - 28.7 = 56.19

= 123.44

= 52.23 57 260.16

3:(154;100) = 100

Expected return =(;)2

=11,658.76 5

260.16 5

= 52.032

=

= 48.28%

Q7 Market Condition Good Normal Bad probability 0.25 0.50 0.25 Dividend 9 5 31 :(10) 0

Expected Dividend 9 x 0.25 = 2.25 5 x 0.5 = 2.5 3 x 0.25 = 0.75 5.5 =

Market price 115 107 97 12%

Expected Mkt. price 115 x 0.25 = 28.75 107 x 0.5 = 53.5 97 x 0.25 = 24.25 106.5

Return of security =**

5.5:(106.5;100 ) = 100

The current market price of the share is Rs 106 cum bonus 10% debenture of Rs 6 each, company had offered buyback of debentures at face value, so Rs 6 will be returned , thus net investment in share is Rs 100 Risk of security Probability(P) 0.25 0.50 0.25 P(X-)2 0.25(24 12)2 = 36 0.50(12-12)2 = 0 0.25(0 12)2 = 36 72

Capital gain 115 100 = 15 107 100 = 7 97 100 = -3

Dividend 9 5 3

Return(X) 15 + 9 = 24 7 + 5 = 12 0

P(X) 6 6 0 12

= ( )2 = 72 = 8.485% Company has offered buyback of debenture at face value. Rate of interest of debenture is 10% whereas expected market rate of return is 12%, so investor should accept the offer of buyback.

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fb-id PRAVINN MAHAJAN CA CLASSES

BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q8 Security X X 30 20 10 5 -10Return =

PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854 Security Y

PRAVINN MAHAJAN CA CLASESS

P 0.10 0.20 0.40 0.20 0.10

PX 3 4 4 1 -1

(X-) 19 9 -1 -6 -22

P(X-) 36.1 16.2 0.40 7.20 44.10104

2

Y -20 10 20 30 40Return =

P 0.05 0.25 0.30 0.30 0.10

PX -1 2.5 6.0 9.0 4

(Y-) -40.5 -10.5 0.5 9.5 19.5

P(Y-)2 82.0125 27.5625 0.75 27.075 38.025174.75

11 = 11%

20.5 = 20.5%

= (

)2

= 104 = 10.19%

= ( )2 = 174.75 = 13.21%

Coefficient of variation =

=

=

10.19 11

Coefficient of variation =

=

=

13.21 20.5

= 0.926

= 0.644

In case of security X for 1% of return there is risk of 0.926%, and in security Y for 1% return risk is 0.644%. since for 1% of return , risk is lower in case of Y, so Y is better. Q9 X -10 10 15 20 40Return =

Security X P 0.10 0.2 0.4 0.2 0.10 PX -1 2 6 4 4 (X-) -25 -5 0 5 25 P(X-)2 62.5 5.0 0 5.0 62.5135

Security Y X 2 7 12 15 16Return =

P 0.2 0.2 0.3 0.2 0.1

PX 0.4 1.4 3.6 3.0 1.6

(Y-) -8 -3 2 5 6

P(Y-)2 12.8 1.8 1.2 5.0 3.624.4

15 = 15%

10 = 10%

= (

)2

= 135 = 11.618%

= ( )2 = 24.4 = 4.93%11.618 15

Coefficient of variation =

= =

Coefficient of variation =

= =

4.93 10

= 0.774

= 0.493

In case of security X for 1% of return there is risk of 0.774%, and in security Y for 1% return risk is 0.493%. since for 1% of return , risk is lower in case of Y, so Y is better. Q10 1 2 3 4 5 Portfolio 29.5 -3.8 26.8 24.6 7.2 AAA bonds 13.4 12.8 10.5 8.9 9.2 Risk premium 16.1 -16.6 16.3 15.7 -2.0 29.5

Average risk premium = = 5.9%

29.5 5

4

fb-id PRAVINN MAHAJAN CA CLASSES

BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH

PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854

Risk premium is excess of return on risky securities over risk free securities. Risk premium on risky securities can be negative in short term due to negative movement or reduction in price but over a long term risk premium cannot be negative

Q11 PRAVINN MAHAJAN CA CLASESS

Market return

Treasury Bill 9.7 9.5 9.2

Prob.

Expected Expected T.B market return Return 5.7 -1.5 8.95 13.15 1.94 2.85 4.6 9.39

Risk Expected Premium Risk premium 18.8 -14.5 8.7 3.76 -4.35 4.35 3.76

28.5 -5.0 17.9

0.20 0.30 0.50

Q12 portfolio return is weighted average of return of individual securities in portfolio RP = = WXRX + WYRY 12 x 0.40 + 15 x 0.60

=

13.8

Risk of Portfolio is NOT weighted average of risk of individual securities in portfolio. Portfolio risk if r=+1 P =2 2 2 . + 2 . + 2. r. . . .

= (0.402 ). (152 ) + (0.602 ). (202 ) + (2). (1). (0.40). (15). (0.60). (20)= P 36 + 144 + 144 = 324 = 18%

Portfolio risk if r=0 =2 2 2 . + 2 . + 2. r. . . .

= (0.402 ). (152 ) + (0.602 ). (202 ) + (2). (0). (0.40). (15). (0.60). (20) = P

36 + 144

=

180 =

13.41%

Portfolio risk if r= -1 =2 2 2 . + 2 . + 2. r. . . .

= (0.402 ). (152 ) + (0.602 ). (202 ) + (2). (1). (0.40). (15). (0.60). (20)= 36 + 144 144 = 36 = 6%

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fb-id PRAVINN MAHAJAN CA CLASSES

BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q13

PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854

Weight of stock A and stock B is same. i. Expected Return of Portfolio It is weighted average of return of each security in portfolio. RP = WARA + WBRB = 15 x 0.50 + 25 x 0.50 = 20%

PRAVINN MAHAJAN CA CLASESS

ii.

Risk of Portfolio is NOT weighted average of risk of individual securities in portfolio. P Portfolio risk if r=+1 =2 2 2 . + 2 . + 2. r. . . .

= (0.502 ). (202 ) + (0.502 ). (502 ) + (2). (1). (0.50). (20). (0.50). (50) = 100 + 625 + 500 P Portfolio risk if r=0 =2 2 2 . + 2 . + 2. r. . . .

=

1225

=

35%

= (0.502 ). (202 ) + (0.502 ). (502 ) + (2). (0). (0.50). (20). (0.50). (50) = 100 + 625 = P Portfolio risk if r=-1 =2 2 2 . + 2 . + 2. r. . . .

725

= 26.92%

= (0.502 ). (202 ) + (0.502 ). (502 ) + (2). (1). (0.50). (20). (0.50). (50) = 100 + 625 500 = 225 = 15%

Q14 Year 1 2 3 Return (X) 9 12 18 39

(X-) -4 -1 5

(X-) 16 1 25 42

2

Return (Y) (Y-) 6 -12 30 12 18 0 54

(Y-)2144 144 0 288

(X-) (Y-)48 -12 0 36

Expected Return =

=

39 3 42 3

= 13% = 3.74 %36 3

=

54 3

= 18%288 3

=

(;)2

=

=

(;)2

= 9.79%

Covariance =

(X;) (Y;)

=

= 12

Co-eff of correlation (r) r=12

=

12 3.74 9.79

= 36.615 = 0.3277

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fb-id PRAVINN MAHAJAN CA CLASSES

BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGHQ15

PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854

Return of portfolio is weighted average of return of each security in the portfolio. Risk of portfolio is not the weighted average of risk of each security in the portfolio. Return of portfolio RP = W B RB + W D RD Risk of portfolio P =2 2 2 . + 2 . + 2. r. . . .

i.

100% investment in B

PRAVINN MAHAJAN CA CLASESS

RP

= ==

W B R B + W D RD 12 X 1

=

12%

P

2 2 2 . + 2 . + 2. r. . . .

(1.002 ). (102 ) + (0.002 ). (182 ) + (2). (0.15). (1.00). (10). (0.00). (18) = ii. 100 = 10%

50% of fund invested in B and D both

RP

= = ==

W B R B + W D RD 0.50 X 12 + 0.50 X 20 16%2 2 2 . + 2 . + 2. r. . . .

P

(0.502 ). (102 ) + (0.502 ). (182 ) + (2). (0.15). (0.50). (10). (0.50). (18) = = = iii. 0.25 100 + 0.25 324 + 13.5 25 + 81 + 13.5 10.93% = 119.5