BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Portfolio management Q1
PRAVINN MAHAJAN
)
2
Year
X
(X-
(X- )
05
12
-3
9
06
18
3
9
07
-6
-21
441
08
20
5
25
09
22
7
49
10
24
9
81 __________
614
CA CLASESS
Ʃ =
= 15%
σ =
( ; )
=
=
=
=
10.11%
= 102.33
Q2
No.
Return (X)
Prob.
(X- )
P(X- )
1
12
0.05
-8.56
3.66
2
15
0.10
-5.56
3.09
3
18
0.24
-2.56
1.57
4
20
0.26
-0.56
0.082
5
24
0.18
3.44
2.13
6
26
0.12
5.44
3.55
7
30
0.05
9.44
4.46
2
18.542 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
σ
=
( )
1
=
= 20.56
18.542 18.
= 4.31%
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q3
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
2
Year
Return(X)
Prob.
PX
) (X-
P(X- )
1
-24
0.05
-1.2
-33.6
56.448
2
-10
0.15
-1.5
-19.6
57.624
3
0
0.15
0
-9.6
13.824
4
12
0.20
2.4
2.4
1.152
5
18
0.20
3.6
8.4
14.112
6
22
0.15
3.3
22.4
23.064
7
30
0.10
3.0
20.4
41.616
9.6 Expected return = σ =
207.84
9.6
Ʃ( ) = 207. 207.84 = 14.417 %
Q4 Year
Return =
− = X
Prob.
PX
(X- )
P(X- )
0.10
-3.33
-60.33
363.97
2
1
-33.33
PRAVINN
2
50
0.20
10.00
23
105.8
MAHAJAN
3
33.33
0.40
13.33
6.33
16.027
CA CLASESS
4
25
0.20
5
-2
0.8
5
20
0.10
2
-7
4.9
27
491.497
Expected Return = σ =
( ) = 491. 491.497
Q5 Year
27
Return =
= 22.169 %
:(−) = X
.:(;) = 4.73 .:(;) = 23.68 .:(;) = 23.33 .:(;) = -1.886 .:(;) = 27.2 .:(;) = 16.393
04-05 05-06 06-07 07-08 08-09 09-10
93.447
Expected Return = σ =
2
(X- )
(X- )
-10.845
117.614
8.105
65.691
7.755
60.140
17.461
304.886
11.625
135.140
0.818
0.669
93.4476 = 15.575%
684.14
( ; ) = . = 10.67%
2
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q6 Year
Return =
:(−) = X
.:(.;.) = - 28.7 . .:(.;.) = 56.19 . :(;.) = 123.44 . :(;) = 52.23 :(;) = 57
96 97 98 PRAVINN MAHAJAN
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
99
CA CLASESS 00
(X- )
-80.732
6517.65
4.158
17.288
71.408
5099.102
0.198
0.0392
4.968
24.681
260.16
Expected return
σ =
.
=
2
(X- )
11658.76 = 52.032
( ; ) = ,. = 48.28%
Q7 Market
probability
Dividend
Condition
Expected
Market
Expected
Dividend
price
Mkt. price
Good
0.25
9
9 x 0.25 = 2.25 115
115 x 0.25 = 28.75
Normal
0.50
5
5 x 0.5 = 2.5
107 x 0.5 = 53.5
Bad
0.25
3
3 x 0.25 = 0.75 97
107
97 x 0.25 = 24.25
5.5
=
Return of security
106.5
:(−) .:(.;∗∗) = 12% =
**
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)
Capital gain
0.25
)
Return(X)
P(X)
P(X-
115 – 100 = 15 9
15 + 9 = 24
6
0.25(24 – 12) = 36
0.50
107 – 100 = 7
5
7 + 5 = 12
6
0.50(12-12) = 0
0.25
97 – 100 = -3
3
0
0
0.25(0 – 12) = 36
12
72
σ =
Dividend
( ) = 7272
2
2
2
= 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.
3
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q8
Security X
)
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
)
X
P
PX
(X- P(X-
30
0.10
3
19
20
0.20
4
10
0.40
PRAVINN
5
MAHAJAN
-10
CA CLASESS
σ =
2
)
)
2
Y
P
PX
(Y-
P(Y-
36.1 3 6.1
-20
0.05
-1
-40.5
82.0125
9
16.2
10
0.25
2.5
-10.5
27.5625
4
-1
0.40
20
0.30
6.0
0.5 0 .5
0.75
0.20
1
-6
7.20
30
0.30
9.0
9.5 9 .5
27.075 27 .075
0.10
-1
-22
44.10
40
0.10
4
19.5
38.025
11
Return =
Security Y
104
= 11%
20.5
Return =
( ) = 104 104 = 10.19%
σ =
. = =
Coefficient of variation =
174.75
= 20.5%
( ) = 174. 174.75 = 13.21%
Coefficient of variation =
. = = .
= 0.644
= 0.926
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
Security X
Security Y
)
)
X
P
PX
(X- P(X-
-10
0.10
-1
-25
10
0.2
2
15
0.4
20 40
σ =
)
)
X
P
PX
(Y- P(Y-
62.5
2
0.2
0.4
-8
-5
5.0
7
0.2
1.4
-3
1.8
6
0
0
12
0.3
3.6
2
1.2
0.2
4
5
5.0
15
0.2
3.0
5
5.0
0.10 0 .10
4
25
62.5 6 2.5
16
0.1
1.6
6
3.6
15
Return =
2
135
= 15%
10
Return =
( ) = 135 135 = 11.618%
Coefficient of variation =
σ =
. = =
12.8
24.4
= 10%
( ) = 24. 24.4 = 4.93%
Coefficient of variation =
= 0.774
2
=
=
.
= 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
Portfolio
AAA bonds
Risk premium
1
29.5
13.4
16.1
2
-3.8
12.8
-16.6
3
26.8
10.5
16.3
4
24.6
8.9
15.7
5
7.2
9.2
-2.0
Average risk premium =
.
= 5.9%
29.5
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
Market return
Treasury Bill
Prob.
9.7 9.5 9.2
0.20 0.30 0.50
Expected Expected T.B market return Return
Risk Expected Premium Risk premium
PRAVINN MAHAJAN CA CLASESS
28.5 -5.0 17.9
5.7 -1.5 8.95 13.15
1.94 2.85 4.6 9.39
18.8 -14.5 8.7
3.76 -4.35 4.35 3.76
Q12 portfolio return is weighted average of re turn 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
. + . + 2. r. . . . 0). (1515)). (0.60)0).(20) = (0.40 ). (15 ) + (0.60 ). (20 ) + (2). (1). (0.40) =
σP
=
3 6+144+144 36+144+144
=
324 324
=
18%
Portfolio risk if r=0
. + . + 2. r. . . . 0). (1515)). (0.60)0).(20) = (0.40 ). (15 ) + (0.60 ). (20 ) + (2). (0). (0.40) 3 6+144 180 = = 180 36+144 =
σP
=
13.41%
Portfolio risk if r= -1
. + . + 2. r. . . . = (0.40 ). (15 ) + (0.60 ). (20 ) + (2). (1). (0.40). (15). (0.60).(20) σP
=
=
3 6+144144 36+144144 5
=
3636 =
6%
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q13 Weight of stock A and stock B is same. i. Expected Re Return of Po Portfolio – It is weighted average of return of each security in portfolio. RP = WARA + WBRB 15 x 0.50 + 25 x 0.50
=
20%
Risk of Portfolio is NOT weighted average of risk of individual securities in portfolio.
ii.
PRAVINN
=
MAHAJAN
CA CLASESS σP
Portfolio risk if r=+1
. + . + 2.r. . . . 0). (20) 20). (0.50)0).(50) = (0.50 ). (20 ) + (0.50 ). (50 ) + (2). (1). (0.50) 1 00+ 625+500 = 1225 1225 = 100+ = =
35%
Portfolio risk if r=0
. + . + 2.r. . . . = (0.50 ). (20 ) + (0.50 ). (50 ) + (2). (0). (0.50) 0). (20) 20). (0.50)0).(50) 1 00+ 625 = 725 725 = 100+ = =
σP
26.92%
σP
Portfolio risk if r=-1
. + . + 2.r. . . . = (0.50 ). (20 ) + (0.50 ). (50 ) + (2). (1) 1). (0.50)0). (20) 20). (0.50)0).(50) = 100+ 1 00+ 625500 = 225 225 = =
15%
Q14
)
)
Year
Return (X)
(X-
(X-
1 2 3
9 12 18 39
-4 -1 5
16 1 25 42
Expected Return =
σ =
( ; )
=
= = 13% =
Covariance =
2
)
Return (Y) (Y- 6 30 18 54
-12 12 0
(X;) (Y;) =
= 12
144 144 0 288
)
(X- (Y-) 48 -12 0 36
=
= 9.79%
Co-eff of correlation (r) r=
=
= 0.3277 = .
6
2
= 18% (;) σ =
3.74 %
)
(Y-
. .
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q15 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.
RP
Return of portfolio Risk of portfolio
i.
WBRB + WDRD
. + . + 2.r. . . .
=
σP
100% investment in B
RP
PRAVINN
=
=
WBRB + WDRD
=
12 X 1
=
12%
MAHAJAN
. + . + 2. r. . . . (1.00). (10) + (0.00). (18) + (2). (0.15)5). (1.00)0). (10) 10). (0.00)0).(18) 100 = = 10% 100
CA CLASESS
σP
ii.
=
50% of fund invested in B and D both
RP
=
WBRB + WDRD
=
0.50 X 12 + 0.50 X 20
=
16%
. + . + 2. r. . . . (0.50). (10) + (0.50). (18) + (2). (0.15)5). (0.50)0). (10) 10). (0.50)0).(18) = 25 3 2424 + 13.5 13.5 0.0.25 10000 + 0.25 = = 2 5+81+13.5 119.5 119. 25+81+13.5 σP
iii. ii.
=
=
10.93%
75% 75% of fund fund inv investe ested d in B and and rest rest 25% 25% in D
RP
=
WBRB + WDRD
=
0.75 X 12 + 0.25 X 20
=
14%
. + . + 2. r. . . . (0.75). (10) + (0.25). (18) + (2). (0.15)5). (0.75)5). (10) 10). (0.25)5).(18) 56.25+20.25+10.125 = 86. 86.625 = 56.25+20.25+10.125 σP
=
=
9.30%
Contd:
7
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Contd: iv.
25% of the fund invested in B and rest 75% in D RP
=
WBRB + WDRD
=
0.25 X 12 + 0.75 X 20
=
18%
. + . + 2. r. . . . (0.25). (10) + (0.75). (18) + (2). (0.15)5). (0.25)5). (10) 10). (0.75)5).(18) 6.25+182.25+10.125 = 198. 198.625 = 6.25+182.25+10.125 =
σP
PRAVINN MAHAJAN CA CLASESS
=
v.
14.093%
100% investment in D
RP
=
WBRB + WDRD
=
20 X 1
=
20%
. + . + 2. r. . . . (0.00). (10) + (1.00). (18) + (2). (0.15)5). (0.00)0). (10) 10). (1.00)0).(18) = = 18% 324 324 =
σP
Q16
)
X
(X- )
(X-
Y
(Y-)
(Y-
(X- ) (Y-)
1
12
-2.8
7.84
20
-1
1
2.8
2
8
-6.8
46.24
22
1
1
-6.8
3
7
-7.8
60.84
24
3
9
-23.4
4
14
-0.8
0.64
18
-3
9
+2.4
5
16
1.2
1.44
15
-6
36
-7.2
6
15
0.2
0.04
20
-1
1
-0.2
7
18
3.2
10.24
24
3
9
9.6
8
20
5.2
27.04
25
4
16
20.8
9
16
1.2
1.44
22
1
1
1.2
10
22
7.2
51.84
20
-1
1
-7.2
207.6
210
84 84
-8
148
= 14.8% (;) = . = 4.55% =
)
Year
= 21% (;) = = 2.89% =
ReturnSEC1 =
ReturnSEC2 =
σSEC1
σSEC2
8
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
COVSEC 1&2
=
Correlation (r) =
(;).(;)
COVSEC & .
Q17
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
=
;
=
;. . .
= -0.8 =
-0.0608
a. Retu Return rn of por portf tfol olio io RP
PRAVINN
=
WXRX + WYRY
=
0.50 X 24 + 0.50 X 19
=
12 + 9.5
MAHAJAN CA CLASESS
Risk of portfolio ( σP)
=
21.5
. + . + 2. r. . . .
=
(0.50). (28) + (0.50). (23) + (2). (0.6). (0.50)0). (28) 28). (0.50)0).(23)
196+132.25+193.2 196+132.25+193.2
= =
=
22.83%
521.45 521.
Correlation if investor wants to reduce portfolio risk to 15 (σP)
=
15
=
15
=
. + . + 2.r. . . .
28). (0.50)0).(23) (0.50). (28) + (0.50). (23) + (2). ( ). (0.50)0). (28) 1 96+132.25+322 196+132.25+322
Squaring both sides 225
=
X
=
X
=
196 + 132.25 + 322X
;. -0.32
b.
i.
Weight
Risk
Return
GM
0.40
15
15
GE
0.60
14
9
Portfolio Return
RP
9
=
WGMRGM + WGERGE
=
0.40 X 15 + 0.60 X 9
=
6 + 5.4 =
11.4
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
ii.
(σP) = =
iii.
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
. + . + 2. r. . . .
=
3 6+70.56+50.4 36+70.56+50.4
=
156.96 156.
=
=
MAHAJAN
13 13 4
= x.15 + (1-x). 9 = 15x + 9 – 9x = 6x X = 0.667, (1-x) = 0.333
CA CLASESS
12.52%
WGMRGM + WGERGE
Risk of portfolio according to above weight is
(σP) =
=
. + . + 2. r. . . .
=
100+21.78+46.67 100+21.78+46.67
168.45 168.
=
Risk
weight
Devta (X)
14
25
0.20
Shree (Y)
18
35
0.80
RP
=
67). (15) 15). (0.33)3).(14) (0.667). (15) + (0.33). (14) + (2). (0.5). (0.667)
Return
(σP)
Let the weight of GM be X and weight of GE be (1-x)
RP
Q18
(0.402). (152) + (0.602). (142) + (2). (0.5). (0.40). (15). (0.60).(14)
PRAVINN
iv.
= 12.97%
r = 0.42
=
WXRX + WYRY
=
0.20 x 14 + 0.80 x 18
=
17.2%
. + . + 2.r. . . .
25). (0.80)0).(35) (0.20). (25) + (0.80). (35) + (2). (0.42)2). (0.20)0). (25)
= =
2 5+784+117.6 = 926. 926.6 = 30.44% 25+784+117.6
If 10% is invested in Devta and 90% in shree RP
=
WXRX + WYRY
=
0.10 x 14 + 0.90 x 18
=
1.4 x 16.2
= 17.6%
. + . + 2. r. . . .
(σP)
=
=
6.25+992.25+66.15 = 1064. 1064.65 = 32.628% 6.25+992.25+66.15
25). (0.90)0).(35) (0.10). (25) + (0.90). (35) + (2). (0.42)2). (0.10)0). (25)
10
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q19
Security P
i.
Year
X
1 2
(X- )
MAHAJAN
σP =
CA CLASESS ii.
)
Y
(Y-)
(Y-
(X- ) (Y-)
11 -3
9
20
6
36
-18
17 3
9
8
-6
36
-18
28
18
28
72
-36
=
= = 14%
ReturnQ =
( ; ) = = 3%
COVPQ
σP =
=
Correlation (r)
iii iii.
)
(X-
ReturnP PRAVINN
security Q
(;).(;)
=
=
.
( ; ) = = 6%
; = -18 ; = -1
=
= = 14%
If P and and Q are are inves nveste ted d in in the the rat ratiio of of 2:1 2:1 (σPORTFOlio)
= =
=
. + . + 2. r. . . .
1). (0.667) 67). (3). (0.33)3).(6) (0.67). (3) + (0.33). (6) + (2). (1) 4 .04+3.927.924 = 0.0.04 = 0.2% 4.04+3.927.924
(since r = -1, so portfolio risk is equivalent to 0)
iv. iv.
If P and and Q are are inves nveste ted d in in the the rat ratiio of of 1:1 1:1 (σPORTFOlio)
. + . + 2. r. . . .
=
1). (0.50)0). (3). (0.50)0).(6) (0.50). (3) + (0.50). (6) + (2). (1) = 2.25+99 2 .25+99 = 1.5%
=
Since the correlation between two securities securities is -1, so portfolio risk can be 0. But for portfolio risk to be 0 weight of securities in portfolio should be in the ratio of 2:1. Since weight of each security in portfolio is changed and weight of low risk security P is reduced and high risk security is increased so portfolio risk is higher
Q20
i.
Inve Invest stme ment nt in A to to att attai ain n a min minimu imum ris risk k por portf tfol oliio WA =
; : ;
=
; . . . = = 0.711 :; . . . .
WB = 1 – WA = 1 – 0.711 = 0.289 For minimum risk portfolio portfolio investor will invest invest 71.1% i.e (5,00,000 X 0.711) 3,55,500 in A and 28.9% (5,00,000 X 0.289) 1,44,500 in B
11
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
ii.
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Return of portfolio RP
= =
MAHAJAN CA CLASESS
iii.
WARA + WBRB
=
0.711 x 17 + 0.289 x 16
=
16.711
σ ) = . + . + 2. r. . . . 11). (20) 20). (0.289) 89).(30) (0.711). (20) + (0.289). (30) + (2). (0.10)0). (0.711) 202.2+75.15+24.657 = 302 302 = 17.38% 202.2+75.15+24.657
Risk of portfolio ( PRAVINN
=
P
If r = -1, weight of A and B is
WA =
; : ;
=
;(;) . . = = 0.60 :; . (;) . .
WB = 1 – WA = 1 – 0.60 = 0.40
For minimum risk portfolio portfolio investor will invest 60% i.e (5,00,000 X 0.60) 3,00,000 in A and 40 % (5,00,000 X 0.40) 2,00,000 in B
X
Y
Risk (σ)
20%
25%
Return
10%
15%
Q21
r = + 0.5
Weight of each security for minimum risk portfolio WX = WY =
; :;
=
1 - WX
;(.) . . = = 0.71 :; . (.) . .
1 – 0.71 = 0.29 Return =
RP
=
WXRX + WYRY 0.71 x 10 + 0.29 x 15 = 11.45
Risk = (σP)
. + . + 2. r. . . .
=
(0.71). (20) + (0.29). (25) + (2). (0.5). (0.71)1). (20) 20). (0.29)9).(25)
357.1525 = 18.89% 357.
Q22
L
M
Risk
15%
18%
Return
20%
22%
r = -1
Weight of each security for minimum risk portfolio portfolio WL =
; ; :
=
;(;) . . = = 0.55 :; . (;) . .
WM = 1 – WL = 1 – 0.55 = 0.45
Contd. 12
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Contd. Return at the above weight RP PRAVINN Risk = (σP)
MAHAJAN
Q23
WLRM + WLRM
=
0.55 x 20 + 0.45 x 22
= 20.9
. + . + 2. r. . . .
=
CA CLASESS
=
(55) 55). (15) + (0.45). (18) + (2). (1) 1). (0.55)5). (15) 15). (0.45)5).(18) 0.0.0225 = 0.15% Risk of portfolio can be zero only if r = -1, weight of P and Q so that portfolio risk is Zero :WP =
=
:
= 0.55 :
WQ = 1- WP = 1 – 0.55 = 0.45 RP
=
WLRM + WLRM .54 x 16 + 0.45 x 18 = 16.82 %
RP Q24
=
WARA + WBRB
=
0.80 x 12 + 0.20 x 20
=
9.6 + 4 = 13.6
σ ) = . + . + 2. r. . . . 0). (3). (0.20)0).(7) = (0.80 ). (3 ) + (0.20 ). (7 ) + (2). (1). (0.80) = 5.76+1.96+6.72 = 14. 14.44 = 3.8% 5.76+1.96+6.72
Risk of portfolio (
ii.
WA =
P
; : ;
=
; (;) . . = = 0.70 :; . (;) . .
WB = 1 – 0.70 = 0.30 Q25
1
2
3
W
0.3
0.5
0.2
σ
6
9
10
. = 0 .4
.
= 0.6
.
= 0.7
σ )= . + . + . + 2. .. . . . + 2. .. . . . + 2. .. . . .
(
P
2. (0.4). (0.30)0). (6). (0.50)0).(9) (0.30). (6) + (0.50). (9) +(0.20) (10) + 2.( (0.6). (0.30). (6). (0.20). (10) + 2. (0.7). (0.50). (9). (0.20).(10) +2. .48 + 4.32 + 12.6 = 50. 50.89 = 7.13 % = 3.24 + 20.25 + 4 + 6.48 =
13
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q26
X1
x2
x3
x4
rx1.x2 = 0.3
rx1.x3 = 0.5
W
0.20
0.30
0.40
0.10
rx1.x4 = 0.2
rx2.x3 = 0.6
σ
4
8
20
10
rx2.x4 = 0.8
rx3.x4 = 0.4
σ )= . + . + . + . + 2. . . . . . +
(
P
2. . . . . . + 2. . . . . . + 2. . . . . . + 2. . . . . . + 2. . . . . .
PRAVINN MAHAJAN CA CLASESS
2. (0.3). (0.20)0). (4). (0.30)0).(8) (0.20). (4) + (0.30). (8) +(0.40) (20) +(0.10) (10) + 2.( +2. (0.5). (0.20). (4). (0.40). (20) + 2. (0.2). (0.20). (4). (0.10).(10) +2. (0.6). (0.30). (8). (0.40). (20) + 2. (0.8). (0.30). (8). (0.10).(10) (0.4). (0.40). (20). (0.10). (10) +2. = 0.64 + 5.76 + 64 + 1 + 1.152 + 6.4 + 0.32 + 23.04 + 3.84 + 6.4 =
=
112.552 = 10.61% 112.
Q27
Risk of portfolio (
σ ) = . + . + 2. r. . . . P
20). (0.30)0).(10) (0.70). (20) + (0.30). (10) + (2). (0.1). (0.70)0). (20) 1 96+9+8.4 = 213. 213.4 = 14.60% 196+9+8.4 Weighted average risk of portfolio
= WAσA + WBσB
= 0.70 x 20 + 0.30 x 10 = 17% Gain on portfolio is excess of weighted average risk over portfolio risk Weighted average σ – Portfolio σ 17 – 14.60 %age of gain = Weighted average average σ – Portfolio σ Weighted average σ
= 2.40 % =
17- 4.60 x 100 = 14.91 % 17 Contd.
14
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Contd. If r = -1 Risk of portfolio (
σ ) = . + . + 2. r. . . . P
1). (0.70)0). (20) 20). (0.30)0).(10) (0.70). (20) + (0.30). (10) + (2). (1) 1 96+984 = 121 121 = 11% 196+984
PRAVINN MAHAJAN CA CLASESS
Weighted average risk of portfolio
= WAσA + WBσB = 0.70 x 20 + 0.30 x 10 = 17%
Gain on portfolio is excess of weighted average risk over portfolio risk Weighted average σ – Portfolio σ 17 – 11
= 6%
%age of gain = Weighted average average σ – Portfolio σ
=
Weighted average σ
17- 11 x 100 = 35.29 % 17
Q28
A
B
σ
0.06
0.09
W
0.40
0.60
Risk of portfolio (
ra.b
= 0.06
σ ) = . + . + 2. r. . . . P
(0.40). (6) + (0.60). (9) + (2). (0.06)6). (0.40)0). (6). (0.60)0).(9) 5.76+29.16+1.5552 = 36. 36.4752 = 6.04% 5.76+29.16+1.5552 Weighted average risk of portfolio
= WAσA + WBσB = 0.40 x 6 + 0.60 x 9 = 7.8% 7.8%
Gain on portfolio is excess of weighted average risk over portfolio risk Weighted average σ – Portfolio σ
7.8 – 6.04 %age of gain = Weighted average average σ – Portfolio σ Weighted average σ
15
= 1.76 % =
7.8- 6.04 x 100 = 2.26 % 7.8
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q29
Rm = 10% , σM= 14% , R F = 6% (i)
If 10 100% is is in invest ested in ri risk fr free asset Return = 6% Risk = 0
PRAVINN
(ii) ii)
If 100% 100% is inv invest ested in mark market et por portfol tfoliio
MAHAJAN
Return = 10%
CA CLASESS
Risk = 14 (iii) (iii)
If invest investmen mentt in Risk Risk free free and market market portf portfoli olio o is is in in the the ratio ratio of 1:2 RP
=
WRf RRf + WMPRMP
=
(0.333) (6) + (0.667) (10)
=
8.67%
Risk of portfolio is weighted average risk
(iv) (iv)
=
WMPσMP
=
(0.667) (14) = 9.33%
Risk Risk of port portfo foli lio o is is wei weigh ghte ted d ave avera rage ge risk risk =
WMPσMP
=
(1.333) (14)
Return of portfolio =
=
Q30
; )σ ;) 18.67 6+(
RF + (
=
18.67% 18 .67%
=
11.33%
P
Ram buys 30,000 of stock X And sells short 10,000 of stock Y and buys more of stock X Return =
(1.333) (15) + (-0.333) (10)
Risk
=
(σP)
=
33). (10) 10). (0.333) 33).(12) (1.333). (10) + (0.333). (12) + (2). (0.45)5). (1.333)
=
=
=
16.667 %
. + . + 2. r. . . .
12.07%
16
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q31
RF = 7%, R M = 15%, σM = 20% (i) (i)
Risk Risk lev level el of of por portf tfol olio io cons constr truc ucted ted by A. Exp Expec ected ted rate rate of of retu return rn of of A is is 18% 18% Return of portfolio
PRAVINN
=
; )σ ; 7+( ) σ
RF + (
P
18
=
0.4 σP
=
18 – 7
σP
=
27.5
σP
=
WRf σRf + WMPσMP
27.5
=
WRF.0 + WMP. (20)
WMP
=
WRf
=
P
MAHAJAN Risk of portfolio
CA CLASESS
=
.
=
1 – 1.375
1.375 =
-0.375
A will shortsell 37.5% of risk free securities and invest 137.5% in Market portfolio for return of 18% and risk r isk at this level is 27.5%. (ii) (ii)
Expe Expect cted ed lev level el of retu return rn or or portf portfol olio io con const stru ruct cted ed by by B havi having ng a risk risk of of 15.8 15.81% 1% Risk of portfolio
=
σP
=
WRf σRf + WMPσMP
15.81
=
0
WMP
=
WRF
Q32
.
+ WMP. 20
=
0.7905
=
1 - WMP
=
1 – 0.7905
=
0.2095
Rm = 16% , σM= 10% , RF = 8% (i)
If 100% 100% is inv invest ested in mark market et por portfol tfoliio Return = 16% Risk = 10%
(ii) ii)
If 100% 100% is inv invest ested in ris risk fr free ass asset Return = 8% Risk = 0
(iii) (iii)
If inve investm stment ent in Risk Risk free free and and marke markett portf portfoli olio o is in the the rati ratio o of 40% : 60% 60% RP
=
WRf RRf + WMPRMP
=
(0.40) (8) + (0.60) (16)
=
12.8 %
Risk of portfolio is weighted average risk =
WMPσMP
=
(0.60) (10) = 6% Contd.
17
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH (iv) (iv)
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Risk Risk of port portfo foli lio o is weigh weighte ted d avera average ge risk risk =
WMPσMP
=
(1.20) (10)
Return of portfolio = =
Contd Contd..
; )σ ; 8+( ) 12
RF + (
=
12%
=
17.6%
P
Q33
Rf = 10%, RM = 18% , σM = 5% PRAVINN MAHAJAN
Return of portfolio
CA CLASESS
=
16
=
6
=
σP
=
; )σ ; 10 + ( )σ 1.6 σ . =
RF + (
P
P
P
3.75
Risk of portfolio is weighted average risk σP
=
WRf σRf + WMPσMP
3.75
=
WRf . 0 + W MP.5
WMP
=
WRF
=
.
=
0.75
1 – WMP = 1 – 0.75 = 0.25
If expected return is 20% Return of portfolio
=
; )σ ; 10 + ( )σ
RF + (
20
=
σP
=
σP
=
WRf σRf + WMPσMP
6.25
=
WRf (0) + W MP. (5)
WMP
=
WMP
=
WRF
=
.
=
P
P
6.25
1.25
1.25 1 - WMP = 1- 1.25
18
=
-0.25
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q34
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Between A and B – A dominates B, B is cancelled cance lled
Between A and C – there is no domination Between And D – A dominates D, D is c ancelled Between A and E – There is no domination Between A and F – there is no domination Between C and E – there is no domination Between E and F – E dominated F, F is c ancelled So A, C and E are efficient securities PRAVINN
Securities in ascending order of risk
MAHAJAN CA CLASESS
ii. a)
Risk
Return
A
4
8
E
5
9
C
12
12
75% in A and 25% in C RP
=
WARA + WCRC
ER
= 0.75 x 8 + 0.25 x 12
Risk
=
(σP)
=
=6+3 =9
. + . + 2. r. . . .
(0.75). (4) + (0.25). (12) + (2). (1). (0.75)5). (4). (0.25)5).(12) =
b)
100% in E
=
6%
Expected return 9 and risk = 5%
Investment in E gives return of 9 % with risk of 5% whereas investment in portfolio of A and C gives return of 9 with risk of 6%. So investment in E is better.
Q35
Between U and V = U dominates V , V is cancelled Between U and W = No domination Between U and X = U dominates and X is cancelled Between U and Y = No Dominance Between U and Z = U dominates and Z is cancelled Between W and Y = No domination U, Y and W are efficient securities Securities in Increasing order of Risk
ii)
Risk
Return
U
5
10
Y
6
11
W
13
15
80% in U and 20% in W RP
=
WURU + WWRW =
Risk
=
(σP)
=
0.80 x 10 + 0.20 x 15 = 11%
. + . + 2. r. . . .
(0.80). (5) + (0.20). (13) + (2). (1). (0.80)0). (5). (0.20)0).(13)
100% investment in Y
= 6.6%
ER = 11% and Risk 6%
Investment in Y gives return of 11% with risk of 6.6% whereas investment in portfolio of A and C gives return of 11% w ith risk of 6%. So investment in Y is bette r.
19
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q36
Dividend Cl. Price
M
N
10
3
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
220
290
, , = 300 :( − ) Return of security = :(;⬚ ) M = = 15% :(;⬚ ) N = = - 2.3%
Op. Price
, , ,
= 200
PRAVINN MAHAJAN CA CLASESS
Portfolio return(31.03.09) =
RP
= ii.
=
, , , ,
WMRM + WNRN
, , , ,
x 15 +
x (-2.3) = 7.63%
M
N
Dividend
20
3.5
Expected MP
220 x 0.2 +
290 x 0.2 + 310 x 0.5
250 x 0.5 +
+ 330 x 0.3 = 312
280 x 0.3 = 253 Opening Price
=
Return of security M
N
220
Portfolio return(31.03.09) =
RP =
iii.
290
:( − ) :(;⬚ ) = = 24.09% .:(;⬚ ) = = 8.79%
Standard Standard deviation of M
=
WMRM + WNRN
, ,
x 24.09 +
, ,
x 8.79 =
)
Probability
CG
Div
Return(X)
PX
P(X-
0.2
220 – 220= 0
20
20
4
217.8
0.5
250-220 = 30
20
50
25
4.5
0.3
280-220 = 60
20
80
24
218.7
Risk = Standard deviation of M
441
441 = 21% 441
)
Probability
CG
Div
Return(X)
PX
P(X-
0.2
290 – 290= 0
3.5
3.5
0.7
96.8
0.5
310-290 = 20
3.5
23.5
11.75
2
0.3
330-290 = 40
3.5
43.5
13.05
97.2
Risk =
20
196 = 14% 196
17.97%
196
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q37
RP
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
=
WPRp + WQ RQ + WRRR
=
0.33 x 25 + 22 x 0.33 + 20 x 0.33
(
σ )=
=
22.326%
P
. + . + . + . . . . . . + . . . . . . + . . . . . .
PRAVINN MAHAJAN CA CLASESS
=
(. ). ( ) + (. ). ( ) + (. ) ( ) + . (. ). (. ). (). (. ). () +. (. ). (. ). (). (. ). () + . (. ). (. ). (). (. ). ()
. + . + . . + . + . = . = = 17.2588%
Q38
Portfolio P and Q RP
Risk
=
WPRp + WQ RQ
=
0.5 x 11 + 0.5 x 20
=
(σP)
=
= 15.5%
. + . + 2. r. . . .
(. ). ( ) + (. ). (. ) + (). (). (. ). (). (. ). ()
= 16.80%
Portfolio Q and R
RP
Risk
=
WQ RQ + WRRR
=
0.5 x 20 + 0.5 x 14
=
(σP)
=
= 17%
. + . + . . . . .
(. ). ( ) + ( ). (. ) + (). (. ). (. ). (). (. ). ()
= 21.03%
Portfolio P and R RP
Risk
=
WPRp + WRRR
=
0.5 x 11 + 0.5 x 14
=
(σP)
=
= 12.5%
. + . + . . . . .
(. ). ( ) + (. ). ( ) + (). (. ). (. ). (). (. ). ()
.
=
= 17.017
Portfolio
Risk
Return coeff. of varition
PQ
16.8
15.5
1.083
Portfolio PQ is most efficient
QR
21.03
17
1.237
as it has least co.eff. of variation
PR
17.017 12.5
1.36
21
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q39
Probability
Stock A
PA
Stock B
PB
Stock C
PC
.25
14
3.5
15
3.75
33
8.25
.75
12
9.0
3
2.25
-6
-4.5
Expected return
12.5
6.0
3.75
Expected return of equally weighted portfolio = RP
ii.
=
WARA + WBRB + WCRC
=
0.33 x 12.5 +0.33 x 6 + 0.33 x 3.75
Standard deviation of A, B and C
)
)
)
=
) )
7.84%
) )
) )
probability P(A-
P(B- P(C-
P(A- (B-
P(C- (B-
P(A- (C-
0.25
0.5625
20.25
213.891
3.375
65.8125
10.969
0.75
0.1875
6.75
71.297
1.125
21.9375
3.656
0.75
27
4.5
87.75
14.625
.
285.188
σA = = 0.866% rA.B =
(
σ )=
.
.
.
=1
.
= 5.196% σB = rB.C =
.
.
.
= 16.88% σC =
=1
rC.A =
.
.
.
=1
P
. + . + . + . . . . . . + . . . . . . + . . . . . .
=
(. ). (. ) + (. ). (. ) + (. ) (. ) + . (). (. ). (. ). (. ). (. ) + . (). (. ). (. ). (. ). (. ) + . (). (. ). (. ). (. ). (. )
= . + . + . + . + . + . . =
= 12.725%
2
Variance = σ = 161.933
22
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q40
A
B
C
X 5,000
1500
2000
1500
Y 3,000
600
1500
900
2100
3500
2400
Weight of each stock ii.
= 26%
= 44%
= 30%
Minimum variance of 3 security portfolio is computed by Critical line method Critical line =
WB = a + b.W A
Portfolio X
0.4 = a + b. (0.30)
….1
Portfolio Y
0.50=a + b (0.20)
…..2
Solving 1 and 2 b = -1 and = 0.70 So critical line is WB = 0.70 – 1(WA) Out of 8000, Rs 4,000 is invested in A, So weight of A = 0.50 WB = 0.70 – 1(0.50)
=
0.20
WC = 1 – WA - WB
=
1 – 0.50 – 0.20 = 0.30
Investment in
A = 4,000 B = 1600 C= 2400
23
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q41
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
A
B
C
X 2,000
480
1040
480
Y 1,000
(360)
720
640
120
1760
1120
Weight of each stock ii.
= 4%
= 58.67%
= 37.33%
Minimum variance of 3 security portfolio is computed by Critical line method Critical line =
WB = a + b.W A
Portfolio X
0.52 = a + b. (0.24)
….1
Portfolio Y
0.72=a + b (-0.36)
…..2
PRAVINN MAHAJAN
Solving 1 and 2 b = -0.333 and = 0.0.44
CA CLASESS
So critical line is WB = 0.44 – 0.33(WA) Out of 3000, Rs 1,500 is invested in A, So weight of A = 0.50 WB = 0.44 – 0.33(0.50) =
0.275
WC = 1 – WA - WB
1 – 0.50 – 0.275 = 0.225
Investment in
=
A = 1,500 B = 825 C= 675
Q42
i.
β = rM.S
0.7 X
= 1.283
Systematic risk β X = (1.283) X (12) =237.036 2
2
2
2
r X = (0.7) X (22)
2
2
or
= 237.16
Unsystematic risk of security = - systematic risk 2
= (22) – 237.16
24
=
246.84
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q43
)
)
) )
Year
S
(S-
M
(M-
(S- (M-
1
14
4
6
9
-6
2
21
81
8
1
-9
3
-6
324
-2
121
198
4
4
64
12
9
-24
PRAVINN
5
20
64
14
25
40
MAHAJAN
6
19
49
16
49
49
72
586
54
214
248
CA CLASESS ERS =
σS =
ii.
= 12%
ERM =
= 9.88%
βS.M = rM.S
σM =
= 5.97
COVS.M =
= 41.33
.
or
= 9%
=
. = 1.15 (. )
Q44
)
)
) )
Probability
S
SP
P(S-
M
MP
P(M-
P(S- (M-
0.30
30
9
50.7
-10
-3
172.8
-93.6
0.20
20
8
3.6
20
8
14.4
7.2
0.30
0
0
86.7
30
9
76.8
-81.6
17
141
14
264
168
ERS = 17
ERM = 14
= 11.87% σS = ΒS =
.
=
COVS.M = 168
= 16.24% σM =
= 0.636
25
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q45
)
)
)
) )
) )
Year
M
(M-
A
(A-
B
(B -
(M- (A-
(M- (B-
2002
12
1.7689
13
2.455
11
0.4489
2.084
0.8911
2003
11
0.1089
11.50 0.004
10.5
.0289
0.022
0.056
2004
9
2.7889
9.80
2.666
9.50
.6889
2.727
1.3861
32
4.6667
34.3
5.125
31
1.1667
4.833
2.3332
PRAVINN
.
= = 10.67
MAHAJAN CA CLASESS
σM =
COVM.A =
ΒA =
Q46
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
.
.
= 1.247
=
. .
= 1.30%
= 1.036
.
βB =
= = 10.33
σA =
= 1.611 COV M.B =
. .
= = 11.433
σB =
.
= 0.624%
= 0.777
.
)
=
. .
= 0.50
)
) )
Year
Probability
M
PM
P(M-
I
PI
P(I-
1
1/3
9
3
5.33
6
2
48
2
1/3
12
4
0.33
30
10
48
-4
3
1/3
18
6
8.33
18
6
0
0
13
13.99
18
96
12
= 13
.
= 18
P(M- (I- 16
= 3.740% σI = = 9.798% σM = COVM.I = 12 ΒI =
b.
.
βX.M = rM.X
=
.
= 0.8578
= 0.72 X
=
0.96
Q47
Vriability of returns of EML = σEML = 3.82% ΒEML.M = rM.EML
rM.EML = 1.2
σM = 7.6
=
.
=
1.2 x
=
0.603
.
26
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q48
Β of Portfolio is value weighted β of security constituting the portfolio
Weight
β
W Xβ
10,000
0.8
8000
20,000
1.2
24,000
16,000
1.4
22,400
14,000
1.75
24,500
60,000
78,900 βP
Q49
=
βP (5 securities) = 1.2
, ,
= 1.315
Required β = 0.90 β
W
Securities
1.2
W1
PRAVINN
RF
0
W2
MAHAJAN
β of Portfolio is value weighted β of security constituting the portfolio
CA CLASESS 0.90 W1 =
= 1.2 W1 + 0. W 2
. = 0.75 .
W2 = 1 – W1 = 1 – 0.25
= 0.75
75% of funds are to be invested in 5 securities and 25% in risk free investments.
Q50
Weight
, , = 0.28 , , , , = 0.32 , ,
Stock A Stock B
β 0.9 1.2
Stock C
?
1.6
RF
?
0
β of market is always equal to 1 . Portfolio β should be equal to market β, so required
portfolio β = 1. β of Portfolio is value weighted β of security constituting the portfolio
1 = 0.9 X 0.28 + 1.2 x 0.32 + 1.6 X WC + 0 X ( 1- 0.28 – 0.32 – WC) 1 = 0.252 + 0.384 + 1 .6 WC WC = 0.2275
WRF = 1 – 0.28 – 0.32 – 0.2275 = 0.1725
Investment in risk free investments is 17.25% of 5,00,000 = Rs 86,250
27
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q51
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Return
Risk (β)
Stock X
28%
1.6
Stock Y
16%
1.2
RF Security
7%
0
Required return of portfolio = 12.5%
Required β of portfolio = 80% of market portfolio i.e 80% of 1 = 0.8
PRAVINN
Return of portfolio is weighted average of returns of Individual securities in the portfolio
MAHAJAN 12.5 = 28. WX + 16. WY + 7. W RF
CA CLASESS
12.5 = 28WX + 16WY + 7(1 – WX – WY) 21WX + 9WY = 5.5
…………………………..(1)
β of Portfolio is value weighted β of security constituting the portfolio
0.8 = 1.6WX + 1.2WY + 0WRF 0.8 = 1.6WX + 1.2WY …………………………………………(2) Solving 1 and 2
WX = - 0.0555 WRF
WY = 0.740 = 1 – WX – WY = 1 + 0.0555 – 0.740
= 0.3155
Available funds of Rs 1,00,000 and funds acquired by short selling X i.e Rs 5,550 are invested in Y and risk free security. 0.740 x 1,00,000 = Rs 74,000 in Y and 0.3155 X 1,00,000 = Rs 31,550 In Risk free security.
Q52
1)
2)
Market
Prob.
S1
PS1
P(S1 -
S2
PS2
P(S2-
Recession
0.20
9
1.8
107.648
-30
-6
320
Normal
0.60
42
25.2
57.624
12
7.2
2.4
Irrational
0.20
26
5.2
7.688
44
8.8
231.2
32.2
172.96
10
553.6
σS1 = σS2 =
) ( . ) ( .
=
= 13.15%
=
= 23.52% Stock 2 is more riskier
contd.
28
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Contd. Expected return = RF + β (RM – RF) Stock1
32.2 = 4 + β (10) β = 2.82
Stock2
10 = 4 + β (10) β = 0.6
since β of stock 1 is higher and β is index of systematic risk so systematic risk of stock 1 is higher Since β of stock 2 is lower and β is index of systematic risk, so systematic risk of stock 2 is lower and unsystematic risk is higher Since σ of stock 2 is higher so stock 2 is more riskier
Q53
Return of security
=
:(−)
Returns from market index % of index appreciation
2003
:( ; ) X 100 = 25.62% : ( ; ) X 100 = 20.07% : ( ; ) X 100 = 17.05%
Year
S
(S-
M
(M-
(S- (M-
2001
25.62
22.1841
12.62
0.3844
- 2.9202
2002
20.07
0.7056
21.79
73.1025
- 7.182
2003
17.05
14.8996
5.32
62.7264
30.5712
62.74
37.7893
39.73
136.2133
20.469
2001 2002
σM = βS =
.
)
.
=
= 6.738%
. .
COV S.M =
)
.
Div yield
; X 100 = 7.62% ; X 100 = 15.79% ; X 100= (1.68%)
Total
5%
12.62%
6%
21.79%
7%
5.32%
) )
6.823
= 0.15
This is a low β stock
29
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q54
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Systematic Risk = x X Y
=
(0.71) x 2.25
2
=
1.134225
=
2
=
0.164025
(0.27) x 2.25
Unsystematic Risk = - Systematic risk of security X
=
6.30 - 1.134
=
5.166
Y
=
5.86 - 0.164
=
5.696
PRAVINN MAHAJAN
β of Portfolio is value weighted β of security constituting the portfolio
CA CLASESS
= WX. βX + WY. βY
βP
= (0.50 X 0.71) + (0.50 X 0.27) = 0.49 Portfolio Variance = Systematic Risk of Portfolio + Unsystematic Risk of P ortfolio
. + Weighted average unsystematic unsystematic Risk of each security in the portfolio 2
=(0.49) . (2.25) (2.25) + (0.50) (0.50)2 X 5.166 + (0.50)2 X 5.696 =0.5402 + 1.2915 + 1.424 =3.2557
Q55
i.
βS = rS.M x
A = 0.60 x
B = 0.95 x C = 0.75 x ii.
= 0.80
= 1.14
= 0.60
Covariance of 2 securities = βSECURITY 1 X β(SECURITY 2)
(NEW CONCEPT)(CHECK DERIVATION)
X 2
COVA.B = 0.80 X 1.14 x (15) = 205.20 2
COVB.C = 1.14 X 0.60 X (15) = 153.90 2
COVC.A = 0.60 X 0.80 X (15) = 108 iii. (
=
P
= . + . + . + .
)
.
. . . + . . . . + . . . . .
( ) . ( ) + ( ) . ( ) + ( ) ( ) + . . . (. ) + . . . (. ) + . . . ()
=
.
=
. =
14.151
Portfolio Variance = 200.244
30
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
iv.
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
β of Portfolio is value weighted β of security constituting the portfolio βP = WAβA + WBβB + WCβC
= x 0.80 + x 1.14 + x 0.60
= 0.847
PRAVINN MAHAJAN
v.
Portfolio Systematic Risk = X 2
CA CLASESS
2
= (0.847) X (15)
= 161.417
Unsystematic Risk = Variance of portfolio – systematic Risk of Portfolio = 200.244 200.244 - 161.417 = 38.827 Q56
Required Return = RF + r.
(RM – RF)
= 5.2 + 0.8 X = 10.21%
Q57
βS.M = rM.S
( 9.8 – 5.2) .
= 0.8 X
.
= 1.364
Required Return = R F + β (RM – RF) = 5.2 + 1.364( 9.8 – 5.2) = 11.474%
Q58
βS.M = rM.S
= 0.8 X
.
= 1
Required Return = R F + β (RM – RF)
= 13 + 1( 15 – 13) = 15% b.
Required Return = RF + β (RM – RF) = 10 + 0.5 (15 – 10) = 12.5
31
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q59
Expected Return = 16.14% , R F = 4.95% , (R M – RF) = 8.88% i.
ii.
PRAVINN
Expected Return = RF + β(RM - RF) 16.14
= 4.95 + β (8.88)
β
= 1.260
Risk Risk prem premiu ium m of stoc stock k
= Retu Return rn of secu securi rity ty – Risk free return
MAHAJAN
= 16.14 - 4.95
CA CLASESS
= 11.19 iii. ii.
Expe Expect cted ed retu return rn of Ma Marrket ket port portffolio olio (RM) = RM – RF = 8.88 RM – 4.95 = 8.88
RM = 13.83% Iv
Expected return of stock if RM = 8% Expected Return = RF + β(RM - RF) = 4.95 + 1.26 (8 - 4.95) = 8.793%
Q60
Required Return = RF + β(RM - RF) If Expected return > Required Return = Security is under under priced If Expected return < Required Return = Security is over priced If Expected return = Required Return = Security is correctly priced Required return of X = 7 + 1.8(15.3 - 7) = 21.94% Expected Return of X = 22.00% ER > RR = Security X is Under Under priced
Required return of Y = 7 + 1.6(15.3 - 7) = 20.28% Expected Return of Y = 20.40% 20 .40% ER > RR = Security Y is Under Under priced RF if securities are correctly Priced
If Security Is correctly Priced ER = RR If RR of X is 22% 22 = RF + 1.8 1.8 (15.3 – RF) RF = 6.925% If RR of Y is 20.40% 20.40 = RF + 1.6 (15.3 – RF) RF = 6.89%
32
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q61
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
)
(1.5)
)
106.953
) )
5
1.25
31.641
12.656
0.0875
20
7
4.922
0.656
4
6.05
25
5
15.313
9.625
3.75
16.5375
30
4.5
28.359
21.656
14.5
87.25
16.25
187.188
124.374
(P)
Market(M)
P(M)
P(M-
Project(S)
P(S)
P(S- P(M- (S-
0.05
(20)
(1)
59.5125
(30)
0.25
10
2.5
5.0625
0.35
15
5.25
0.20
20
0.15
25
PRAVINN MAHAJAN
i.
CA CLASESS
79.781
ERM = 14.5 ERS = 16.25
ii.
βM = 1 βS =
iii.
.
=
. = 1.425 .
Required Return
= RF + β(RM - RF) = 8 +1.425 (14.5 – 8) = 17.2625
iv.
Since Since Requ Require ired d retu return rn is more more than than expecte expected d retur return n so so proj project ect should should not be expecte expected d Systematic Risk =
2
β .
(1.425)2. (87.25) (87.25) = 177.172 Unsystematic risk =
- Systematic Risk of Security 187.188 – 177.172 = 10.016
Q62
Required Return Security
= RF + β(RM - RF)
Expected Return
Required return
A
13
8 + 0.8(14 – 8) = 12.8
B
14
8 + 1.05 (14 – 8)= 14.3 ER < RR
Over Priced
C
17
8 + 1.25 (14 – 8) = 15.5 ER > RR
under priced
D
13
8 + 0.90 (14 – 8) = 13.4 ER < RR
over priced
33
ER > RR
under priced
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q63
Required Return Security
Expected Return
Required return
A
18
9 + 1.7(14 – 9) = 17.5
ER > RR
under priced
B
11
9 + 0.6 (14 – 9)= 12
ER < RR
Over Priced
C
15
9 + 1.2 (14 – 9) = 15
ER = RR
correctly priced
A ltd
B Ltd.
Expected Return
22
24
Standard deviation
40
38
β
0.86
1.24
Q64
PRAVINN
= RF + β(RM - RF)
i.
Coefficient of variation =
rA.B = 0.72
Risk
MAHAJAN
Return
CA CLASESS
= 1.82
Altd ii.
B Ltd.
=
= 1.583
70 % in A and 30% in B RP =
WARA + WBR =
0.7 x 22 + 0.3 x 24
Risk
=
(σP)
=
( . ). ( ) + ( . ). ( ) + ( ). ( . ). ( . ). ( ). ( . ). ( ) .
. + . + . . . . .
=
= 22.6 %
= 37.0622
iii.
Expected Return A
= RF + β(RM - RF)
22 = RF + 0.86 (R M – R – RF) 22 = 0.14RF + 0.86RM
B
24 = RF + 1.24 (R M – R – RF ) 24 = - 0.24R F + 1.24RM
Solving 1 and 2 vi.
……………….(1)
RM = 22.736
…………………(2) RF = 17.469%
β of Portfolio is value weighted β of security constituting constituting the portfolio βP = WAβA + WBβB 0.70 X 0.86 + 0.30 X 1.24 = 0.974
34
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q65
Required Return Security
Q66
= RF + β(RM - RF)
Expected Return
Required return
A
22
10 + 1.5(18 – 10) = 22 ER = RR
correctly priced
B
17
10 + 0.7 (18 – 10)= 15.6 ER > RR
under Priced
)
) P(M-)(C-)
(P)
Market(M)
P(M)
P(M-
(C)
P(C)
P(C-
0.2
10
2.0
12.8
15
3
3.2
0.4
16
6.4
1.6
14
5.6
10.0
4.0
0.4
24
9.6
14.4
26
10.4
19.6
16.8
18
28.8
19
32.8
27.2
PRAVINN MAHAJAN
ERM = 18
CA CLASESS
ERC = 19 βM = 1
.
βC =
=
6.4
. = 0.944 .
Required Return
= RF + β(RM - RF) = 9 +0.944 (18 – (18 – 9) = 17.496 2
β .
Systematic Risk =
2
(0.944) . (28.8) = 25.665
- Systematic Risk of Security
Unsystematic risk =
32.8 – 32.8 – 25.665 = 7.135
If Investor Is Aggressive RF = 4.6% Q67
Required Return
= RF + β(RM - RF)
15.5
=
4.6 + β (12 - 4.45)
β
= 1.444
=
If Investor is conservative RF = 4.3% Required Return
= RF + β(RM - RF)
15.5 = 4.3 + β (12 – (12 – 4.3) 4.3) β=
1.455
If Investor is moderate Risk free return = Required Return 15.5 β
. : .
=
4.45
= RF + β(RM - RF) =
4.45 + β (12 – (12 – 4.45) 4.45)
= 1.464
35
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q68
RM = 12% , β = 2 , RR = 18%, g = 5% , P 0 = Rs 30 i.
P0
= 30 =
PRAVINN
=
; .; .
3.9
d1 = d0 ( 1 + g )
MAHAJAN
3.9 = d0 (1 + .05 )
CA CLASESS
D0 = 3.71 ii.
combined ef effect on on pr price of of sh share Required Return
= RF + β(RM - RF)
18
= RF + 2 (12 – RF) RF = 6%
If inflation increases by 2%, R F = 2% , So new RF = 8% , Existing Risk Premium = 12 – 6 = 6%
New Risk Premium = 6 –( X 6) = 4% New growth rate = 4% and β = 1.8 Required Return
= RF + β(RM - RF) = 8 + 1.8 (4) = 15.2%
P0
=
;
=
3.71(1.04)
Rs 34.45
.152 – .152 – 0.04 0.04 Q69
RM = 9% , β = 1.2 , RM = 13%, g = 7% , d0 = Rs 2 i.
Required Return
= RF + β(RM - RF) = 9 + 1.2 (1- 9)
P0
ii.
=
= 13.8%
; ( . ) = . ; .
31.47
If in inflation pr premium in incre creases by 21 21%, RF and RM shall increase by 2% Risk premium shall remain same. Required Return
= RF + β(RM - RF) = 11
P0 =
( . ) = 24.31 % . ; .
1.2 (15 – (15 – 11) = 15.8%
Contd.
36
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
ii.
increases by 3% RR
= 13.8
P0
=
iii.
;
PRAVINN MAHAJAN
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Required Return
CA CLASESS
=
( . ) = 57.89 . ; .
= RF + β(RM - RF) = 9 + 1.3 (13 – (13 – 9) = 14.2
P0
= =
;
. . ; .
= 29.72
Q70
RF = 10% , β = 1.4 , RM = 15%, g = 8% , P1 = Rs 36 d0 = 4 Required Return
= RF + β(RM - RF) = 10 + 1.4 (15 – 10) 10) = 17%
P0
=
; ( . ) = Rs 48 = 48 . ;.
Equilibrium Price is Rs 8 whereas share is currently traded at Rs 36. So share must be purchased
Q71
Required Return RM =
= RF + β(RM - RF)
:( ; ) :(, ;, ) = = 0.158 or 15.8% ,
Expected Rate X
=
Required Return
= RF + β(RM - RF) = 15 + 0. (15.8 – 15) = 15.64%
Y
=
Required Return
= RF + β(RM - RF) = 15 + 0.7 (15.8 – 15) = 15.56%
Z
=
Required Return
= RF + β(RM - RF) = 15 + 0.5 (15.8 – 15) = 15.4%
Bonds =
Required Return
= RF + β(RM - RF) = 15 + 1 (15.8 – 15) = 15.8%
Average Return =
. : .: . : .
37
= 15.6%
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q72
RM =
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
:( ; ) :(, ;, ) = = 0.167 or 16.7% ,
Average Return 0.157 =
: .(. ; ):: .(. ; ): : .(. ; ): : (. ; )
RF = 12.7% PRAVINN
Required Return
MAHAJAN
CA CLASESS
= RF + β(RM - RF)
Gold
= 12.7 + .6 ( 16.7 -12.7) -12 .7) = 15.1
Silver
= 12.7 + .8 ( 16.7 -12.7) = 15.9
Bronze = 12.7 + .6 ( 16.7 -12.7) = 15.1 GOI
Q73
RM =
= 12.7 + 1 ( 16.7 -12.7) = 16.7
:( ; ) :; = 26.33%
Required Return
= RF + β(RM - RF)
Cement Ltd.
= 14 +0.8 (26.33 – 14) = 23.864%
Steel Ltd.
= 14 + 0.7 (26.33 – 14) = 22.631%
Liquor Ltd
= 14 + 0.5 (26.33 -14) = 20.165%
GOI Bonds
= 14 + 0.99 (26.33 – 14) = 26.207%
Average Return =
. : . : . : .
38
= 23.217%
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q74
β of Portfolio is value weighted β of security constituting the
portfolio Investment
β
Value weight
β X Weight
I
1.6
2,57,400
2,98,584
II
2.28
2,3,600
5,32,608
IiI
0.90
2,17,000
1,95,300
IV
1.50
3,92,500
5,88,750
11,00,500
16,15,242
ΒP
,, = 1.467 = ,,
PRAVINN MAHAJAN
CA CLASESS Required Return
= RF + β(RM - RF)
I
= 11 + 1.16 (19 -11)
= 20.28%
II
= 11 + 2.28 (8)
= 29.24%
Iii
= 11 + 0.90 (8)
= 18.2%
IV
=11 + 1.5 (8)
= 23%
Change in the composition of portfolio
Q75
ER
RR
Value
Action
I
19.50
20.28
overvalued
Sale
II
24
29.24
overvalued
Sale
Iii
17.50
18.2
overvalued
Sale
IV
26
23
undervalued
Hold
D0 = 2 P0 = 25 Required Return
= RF + β(RM - RF) = 12 + 1.4 (6)
P0
=
= 20.4%
; ( . ) = R 13.63 = . ;.
Existing price is more than equilibrium price, so currently share is overvalued Revised RR
Required Return
= RF + β(RM - RF) = 10 + 1.25(4)
P0
=
(. ) = = 36.33 ; ( . ; . )
= 15%
Existing price is less than revised equilibrium price, so currently share is undervalued, Investor should hold the share.
39
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q76
WP = 0.75
WQ = 0.25
β = 1.40
(RM – RF)= 10%
Portfolio risk premium is return of portfolio over risk free rate which is market risk premium times β. Portfolio risk premium = (RM – RF) β = 10 X 1.4 = 14%
Q77
RM = 0.095, σM = 0.035, RF = 0.025
Market Return- Risk trade off = βS.M = rM.S
= 0.75 X
Required Return
;
=
.
=
. ; . .
=
.
= 2
PRAVINN MAHAJAN
1.5
CA CLASESS
= RF + β(RM - RF) = 8 + 1.5 (6) = 17%
Q78
RM = 10 %, σM = 4%, RF = 3%
Market Return- Risk trade off = βS.M = rM.S
= 0.85 X
Required Return
;
=
=
;
=
= 1.75
1.70
= RF + β(RM - RF) = 9 + 1.7 (7) = 20.9%
40
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q80
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
)
)
) )
Period Security(s)
(S-
Market(M)
(M -
(S- (M-
1
20
25
22
100
50
2
22
49
20
64
56
3
25
100
18
36
60
4
21
36
16
16
24
5
18
9
20
64
24
6
-5
400
8
16
80
7
17
4
-6
324
-36
8
19
16
5
49
-28
9
-7
484
6
36
132
10
20
25
11
1
-5
120
706
357
150 ERS = βS =
.
= 15
=
ERM =
.
(. )
= 12
COVS.M =
= 35.7
σM =
= 8.40%
= 0.5059
characteristic line = RS = α + β (RM) When market return is 12%, security return is 15% 15 = α + 0.5059 (12) α = 8.929
Characteristic Line is RS = 8.929 8.929 +0.5059 (RM)
Q80
)
)
) )
Period Security(A)
(A-
Market(M)
(M -
(A- (M-
1
12
32.1489
8
5.0625
12.7575
2
15
75.1689
12
39.0625
54.1875
3
11
21.8089
11
27.5625
24.5175
4
2
18.7489
-4
95.0625
42.2175
5
10
13.4689
9.5
14.0625
13.7625
6
-12
335.9889
-2
60.0625
142.0575
38
497.3334
34.5
240.875
289.5
ERA = βS =
= 6.33%
.
=
.
ER M =
(. )
.
= 5.75%
COVS.M =
.
= 48.25
σM =
.
= 6.336%
= 1.20
characteristic line =
RS = α + β (RM)
When market return is 5.75%, security return is 6.33% S
6.33 = α + 1.20 (5.75)
ystematic Risk
α = - 0.57
Characteristic Line is
RS = -0.57 +1.20 (RM)
41
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
β . 2
Systematic Risk =
2
(1.20) . (40.145) = 57.8088
- Systematic Risk of Security
Unsystematic risk =
=
( ; ) – β . = . - 57.8088
=
82.8889 - 57.8088
=
25.0801
.
Q81
2
β of Portfolio is value weighted β of security constituting the portfolio
i.
W
β
Wβ
A
0.20
0.40
0.08
B
0.50
0.50
0.25
C
0.30
1.10
0.33 0.66
ii.
Residual variance or Unsystematic Risk
A
Total Variance
Systematic Risk
0.015 X 100 X 100 = 150
0.40 X 10 = 16
Unsystematic Risk ( )
2
2
134
2
2
225
2
2
879
B
0.025 X 100 X 100 = 250
0.50 X 10 = 25
C
0.1 X 100 X 100
1.10 X 10 = 121
iii.
Portfolio Variance =
= 1000
2
β + USRA + USRB + USRC 2
2
2
2
2
(.66) .(10) + (0.20) . (134) + (0.50) . (225) + (0.30) .(879) = 184.28
iv.
Expected Return of Portfolio RP = WARA + WBRB + WCRC (0.20)(14) + (0.50)(15) + (0.30)(21)
σ=
=
16.6%
v.( P)
. + . + . + .
. . . + . . . . + . . . . . = (. (. ) . () + (. ) . () + (. ) () + . (). (. ). (. ) + . (). (. ). (. ) +. (). (. ). (. ) = 19.039433
.
Portfolio variance = = (19.039433)
42
2
= 362.5
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q82
RM = 15%
Variance M = 320
σM = 17.88%
ER of Portfolio =
α + β (RM)
W
α
W.α
β
W.β
A
.25
2.10
0.525
1.65
0.4125
B
0.15
3.60
0.54
0.55
0.0825
C
.35
1.55
.54
0.75
0.2625
D
.25
0.70
0.175
1.40
0.35
1.78 ER
1.1075
=
1.78
+ 1.1075 (15)
=
18.395%
Portfolio variance according to Sharpe Model β + USRA + USRB + USRC + USRD 2
2
2
2
2
2
=
(1.10) (320) + (.25) (380) + (.15) (140) + (.35) (310) + (.25) (385)
=
476.1375
Q83
W
α
W.α
β
W.β
A
.25
0.50
0.125
0.90
0.225
B
.25
2.50
0.625
1.30
0.325
C
.25
1.50
0.375
1.40
0.35
D
.25
2.50
0.625
2.10
0.525
1.78
1.425
ER of Portfolio =
α + β (RM)
ER
=
1.75
=
16%
+ 1.425 (10)
Portfolio variance according to Sharpe Model 2
β + USRA + USRB + USRC + USRD 2
2
2
2
2
=
(1.425) (27) + (.25) (45) + (.25) (130) + (.25) (199) + (.25) (53)
=
81.5075
43
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q84
Systematic RiskSECUITY
=
A
=
B
=
C
=
D
=
W
α
A
.25
B
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
=
. . . .
=
1.01
=
0.663
=
0.8124
=
0.80
W.α W.α
β
W.β W.β
-0.08
-0.02
1.01
0.2525
.25
0.11
0.0275 0.663
C
.25
0.02
0.005
D
.25
-0.15
-0.0375 0.80
0.20
-0.025
0.82135
0.16575
0.8124 0.2031
ER of Portfolio =
α + β (RM)
ER
=
-0.025 + 0.82135 (10)
=
8.18875%
Portfolio variance according to Sharpe Model 2
β + USRA + USRB + USRC + USRD 2
=
2
2
2
2
(0.82135) (5) + (.25) (3) + (.25) (5.5) + (.25) (1.10) + (.25) (2.30) =
3.3731 + 0.74375
Q85
Market Price of risk
;
=
Or slope of CMl
.;
=
Q86
=
Rf = 8% R M = 18%, σM = 6% Required Return
= RF + (
15
= 8 +(
σP
= 4.2
Risk of Portfolio
2.5
;
)
; )σ
P
σP = WMP σMP + WRFσRF 4.2 = WMP (6) WMP =
.
= 0.7
Market portfolio 70%, Rf = 30%
44
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q87
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Between A and B
=
B dominates , A is cancelled
Between B and C
=
No Dominance
Between B and d
=
No Dominance
Between B and E
=
No Dominance
Between B and F
=
No Dominance
Between B and G
=
No Dominance
Between B and H
=
no Dominance
Between C and D
=
No Dominance
Between C and E
=
no Dominance
Between C and F
=
No Dominance
Between C and G
=
C Dominates and G is cancelled
Between C and H
=
No Dominance
Between D and E
=
E Dominates and D is cancelled
Efficient Portfolios in increasing order of Risk
ii.
Risk
Return
21
12.5
25
15.0
29
17.0
32
18.0
45
20.0
out of efficient portfolios best portfolio is that in which risk premium per unit of risk is highest Risk
Return
Risk Premium
Risk Premium per unit
If RF is 12%
of Risk
B
21
12.5
0.5
0.023
C
25
15
3
0.120
E
29
17
5
0.172
F
32
18
6
0.187
H
45
20
8
0.177
Since Risk Premium per unit of Risk of F is highest. So it is the Best Portfolio if Lending and Borrowing is allowed at 12%. Iii
If Lending and Borrowing is not allowed then σ of 25% is at portfolio C which gives return of 15%. So maximum return at risk r isk of 25% is 15%.
Required Return
= RF + (
;
)
If borrowing and lending is allowed 12% then F is best portfolio, so market portfolio is F 12 + = Risk of Portfolio
; X 25 16.68%
σP = WMP σMP + WRFσRF
25 = WMP (32) + WRF(0) WMP = 0.78125 WRF = 0.21875 If borrowing and lending is allowed then optimal strategy is t o invest 78.125% in F and 21.875% in Risk free and return at optimal strategy is 16.68%
45
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q88
Given the level of σ of security the Expected Rate of Return Prediction by CML is
10 + Actual return of security is
;
Required Return
= RF + (
( ; ) 40
)
=
; x 100
33%
= 14%
Actual return of security of 14% is well below 33%. Thus this venture does not constitute an efficient portfolio. It bears some risk that does not contribute to the expected rate of return Sharpe ratio is used as performance measure. Closer the sharpe ratio to CML, better is the performance of fund in terms of ret urn against risk.
Slope of CML = Sharpe ratio =
( ; ) = 0.583
;
= 0.1
Sharpe ratio of security is less than slope of CML, so it is not an efficient portfolio.
Q89
If securities are correctly priced ER = RR Required Return βS
βB
B
=
2
=
3
= Systematic Systematic Risk + Unsystematic Unsystematic Risk =
A
; ; ; = ; ; = ;
=
βA
Security variance
= RF + β(RM - RF)
2 β 2
+
USR
2
=
2 . (.40 ) + 0.0475
=
4.2075
=
Standard deviation of A
=
3 . (.40 )
=
1.505
=
Standard deviation of B
2
46
2
= .
= 2.0512
+ 0.0650
= .
= 1.227
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Required Return
Q90
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
= RF + β(RM - RF)
In case of security 1 .24
= RF + 2.50 (R M - RF)
.24
= 2.50 RM – 1.50 – 1.50 R F
………………….(i)
In case of security 2 .18
= RF + 1 (R M - RF)
.18
= RM
Security variance
From (i)….. R F
= .14
= Systematic Risk + Unsystematic Risk 2
β
=
+
USR
From security 2 2 2 (0.30 ) = (0.5) + 0.06
= 0.12
For Security 1 2 = 2.5 (0.12) + 0.10
= 0.85 Standard deviation of Security 1 = 2
= 1 (0.12) + 0.17
For Security 3
= .29 Standard deviation of Security 3 =
Q91
)
)
.
= 0.922
.
= 0.5385
)
)
)
A
(A-
M
(M-
D
(D-
4
324
7
81
9
20.25
40
324
25
81
18
20.25
162
40.5
44
648
32
162
27
40.50
324
81
ERM = = 16
ERD = = 13.5
COVAM =
ERA = = 22 COVDM =
= 40.5
σM =
βA =
ii.
ERA = 0.5 X 4 + 0.5 X 40 = 22
iii.
RM = 7 X 0.5 + 25 X 0.5 = 16
(D-)(M -
162
40.5
= 162
=9
i.
=
(A- )(M )(M -
= 2
βD =
=
.
= 0.5
ERD = 0.5 X 9 + 0.5 0.5 X 18 = 13.5
(RM – RF) = (16 - 9) = 9 SMl = RF + (RM – RF)β 7 + 9β iv. iv.
Alph Alpha a of stoc stock k = Expec Expecte ted d Retu Return rn - Requi Require red d Retu Return rn A
=
22
-
7 + 2(16 – 7)
=
-3 overpriced
D
=
13.5
-
7+ .5(16 – 7)
=
2 underpriced
47
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q92
i.
SMl
= RF + (RM – RF)β
RM = 0.30 X 12 + 0.40 X 8 + 0.30 X(-4)
= 5.6
SML = 8 + (5.6 – 8)β = 8 - 2.4 β ii.
Market price at risk is co-efficient of SML. In this case, market price at risk is negative which provides that if risk decreases, return will increase which does not happen
PRAVINN
normally
MAHAJAN CA CLASESS
III.
S
P. S
P(S-)
2
M
PM
P(M -)
0.30
18
5.4
38.988
12
3.6
12.288
21.888
0.40
9
3.6
2.304
8
3.2
2.304
2.304
0.30
-8
-2.4
63.948
-4
-1.2
27.648
42.048
5.6
42.24
66.24
6.6
ERs = 6.6 βSEC =
iv.
ER M = 5.6 =
. .
=
σM
P(M P(M )2 42.24 = 6.49% 42.
2
Prob.
P(S - )(M )(M - )
COVSM = 6.4
= 1.573
Alpha of stock = Expected Return - Required Return
6.6
-
48
[8 – 2.4(1.573)] = 2.3752 underpriced
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q93
β
;
S
R
A
15 1.5
40
B
12 2.0
C
;
(
5.333
1
A
0.30
0.05625
0.30
20
2.5
3
F
0.35
0.075
0.65
0.13125
10 2.5
30
1.2
5
B
0.50
0.20
1.15
0.33125
D
9
1
10
2
4
D
0.20
0.10
1.35
0.43125
E
8
1.2
20
0.833
6
C
0.25
0.208
0.45
0.63925
F
14 1.5
30
4.67
2
E
0.06
0.072
0.51
0.71125
)β
( )
S
Ʃ(
Ʃ
Rank
)β
;
0.05625
− ) Ʃ( C= ) : Ʃ(
:
.
.
= 1.92
.
:
.
= 2.81
:
.
.
:
.
.
= 2.67
= 2.54
. =0.61 : .
:
.
.
=0.63
Highest of all cut off rates is cut-off rate of portfolio i.e 2.81. so securities A & F are selected Z
=
A
=
B
=
X [
; - C ]
. X [5.33 – [5.33 – 2.81 2.81 ] = 0.0945
. X [ 4.66 – 4.66 – 2.81 2.81 ] = 0.0925
0.187 Proportion of each security A
=
B
=
. . . .
= 0.51 = 0.49
49
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q94
R
β
1 19
1
20
S
;
;
;
(
14
1
1
1.7
0.05
0.7
0.05
)β
( )
S
Ʃ(
Ʃ
Rank
)β
2
23 1.5
30
12
2
2
0.9
0.075
1.6
0.125
3
11 0.5
10
12
3
3
0.3
0.025
1.9
0.15
4
25 2.0
40
10
4
4
1.0
0.10
2.9
0.25
5
13 1.0
20
8
5
5
0.4
0.05
3.3
0.30
6
9
0.5
50
8
6
6
0.04
0.005
3.34
0.305
1.5
30
6
7
7
0.45
0.075
3.79
0.38
7 14
− ) Ʃ( C= : Ʃ( ) . = 4.67 : . . = 7.11 : . . = 7.6 : . . = 8.28 : . . = 8.25 : . . = 8.24 : . . = 7.90 : .
Highest of all cut off rates is cut-off rate of portfolio i.e 8.82. so securities 1 to 4 are selected Z
=
1
=
2
=
3
=
4
=
X [
; - C ]
X (14 – (14 – 8.28) =
0.286
. X (12 – (12 – 8.28) =
0.186
. X (12 – (12 – 8.28)=
0.186
X (10 – (10 – 8.28) =
0.086 0.744
Proportion of each security in optimum portfolio 1
=
2
=
3
=
4
=
. . . . . . . .
= 0.38 = 0.25 = 0.25 = 0.12
50
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q95
i.
Risk Premium on each of 3 stocks Β1 x Market Risk Premium
+
β2 x
For β1
ii.
Market Risk Premium for β2
Security A =
1.75 X 4 + 0.25 x 8
= 9%
Security B =
-1 x 4 + 2 x 8
= 12%
Security C =
2 x 4 + 1 x 8
= 16%
, , , , :, ;, , , , , :, ;, , ; , , , , : , ;, ,
WA
=
WB
=
WC
=
β1 =
1.75 x2 + (-1) (0.5) + (-1.5) (2)
β2 =
0.25 x 2 + 2 x 0.5 + (- 1.5) (1)
=
2
=
0.5
=
- 1.5
= 0 = 0
Risk Premium is 0 Portfolio β1 and β2 is 0. This implies that by selecting the given Proportion of the portfolio of the Portfolio, investor has designed 0 risk port folio So, risk premium of Portfolio will be 0 & return of Portfolio will be equal to Risk free rate of Return.
Q96
If overall portfolio is insensitive to changes in factor 2 , β2 of Portfolio = 0 Portfolio β2
ii.
= WA X β2 of A +
WB X β2 of B
0
=
WA X 0.80 + (1 - WA) x 1.40
0
=
- 0.6 WA + 1.40
WA
=
2.33
WB
=
( 1 – W – WA)
=
1 – 2.33
=
Portfolio β1
=
1
Portfolio β2
=
0
Portfolio β1 1 Portfolio β2 0 Solving (i) and (ii)
-1.33
= WA X β1 of A + =
+
WRF X β1 of RF
WA (0.50) + W B (1.50) + 0……………….(i)
= WA X β2 of A + =
WB X β1 of B
WB X β2 of B
+
WRF X β2 of RF
WA (0.80) + W B (1.40) + 0……………….(ii)
WA = - 2.8
WB = 1.6
WRF = ( 1 – 1 – (-2.8) (-2.8) – – 1.6) =
51
2.2
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q97
i.
, , , , ; , ; , , , ;,
WA = WB
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
=
1.5
=
- 0.5
β1
β2
A
0.80
0.60
B
1.50
1.20
W
β1
Wβ1
β2
Wβ2
1.5
0.80
1.2
0.60
0.9
- 0.5
1.50
-0.75
1.20
-0.6
0.45 β1 = 0.46 ii.
=
a.
0.3 β2 = 0.3
Fund other than funds from short selling of B
=
1,00,000
Funds from Short selling of B
=
50,000
( 50% of funds other than from short selling selling of B) b.
Funds other than B owned funds
=
1,00,000
Short selling RF =
1,00,000
2,00,000
Short selling of B = 50% of funds other than from B 0.50 x 2,00,000 Investment in A
3,00,000
Investment in B
1,00,000
Short selling of R F
1,00,000
, , , , ;, , ;, , ; , , , , ;, , ;, , ; , , , , ;, , ;, ,
=
1,00,000
=
3
=
-1
=
-1
WA
=
WB
=
WRF
=
β1
=
3 X 0.80 + (-1)(1.5) + (-1)(0)
=
0.9
β2
=
3 X 0.60 + (-1) (1.20) + (-1)(0)
=
0.60
52
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
ER
= RF + β1 (RM1 – RF ) + β2 (RM2 – RF )
15
=
10 + 0.80 (RM1 – 10) + 0.6 (R M2 – 10)
15
=
-4 + 0.80 RM1 + 0.6 RM2
19
=
0.80 RM1 + 0.60 RM2
ER
= RF + β1 (RM1 – RF ) + β2 (RM2 – RF )
20
= 10 + 1.5 (RM1 – 10) + 1.20 (R M2 – 10)
20
= - 17 + 1.5 RM1 + 1.20 RM2
37
= 1.5 RM1 + 1.20 RM2
……………………………………………..(i)
…………………………………………(ii)
From (i) and (ii) RM1
=
10
RM2
=
18.33
Risk Premium of Factor 2 = R M2 – RF = 18.33 – 10 = 8.33%
Q98
ER
= RF + β1 (RM1 – RF ) + β2 (RM2 – RF )
Security A
14
=
RF + 0.8 RP1 +0.8 RP2
………..(i)
Security B
10.8
=
RF + 0.6 RP1 +0.4 RP2
…………(ii)
Security C
11.2
=
RF + 0.4 RP1 +0.6 RP2
…………(iii)
Solving (i) and (ii)
RF + 0.4 RP1
Solving (ii) ad (iii)
0.5 RF + 0.5 RP1 = 5
Solving (iv) and (v)
RP 1 = 4
Substituting values in (i) ER
= 7.60 ……..(iv) ……..(v)
RF = 6 RP2 = 6
= RF + β1 (RP1) + β2 (RP2 ) =
RF + 4β1 + 6β2
Required Return of Portfolio D =
Expected return of D
RF + 4β1 + 6β2
=
6 + 4(0.5) + 0.7 (6)
=
12.2%
=
14%
Since ER > RR, so Portfolio D is underpriced Investor will short sell securities yielding 12.2% and buy portfolio D If investor invests Rs 1,00,00 in portfolio D Return from D 14% of 1,00,000
= 14,000
Amount payable or return lost
= 12,200
Gain
1,800
53
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Required Return of Portfolio E = = Expected Return of Portfolio F =
R F + 4β1 + 6β2 6 + 4(0.8) + 6(1)
=
15.2%
=
11.40%
15.2%
Since ER = RR, so Portfolio E is correctly Priced. No Arbitrage. Required Return of Portfolio F = = Expected Return of Portfolio F =
RF + 4β1 + 6β2 6 + 4(0.6) + 6(0.5) 9%
Since ER < RR, So Portfolio F is Overpriced Investor will short sell Portfolio Portfolio F and invest in securities yielding yielding 11.40% If investor short sell Rs 1,00,00 of portfolio D Return from securities =
11.4% of 1,00,000
Loss of Return from Portfolio F
= 11,400 = 9,000
Loss
2,400
Q99
ER
= RF + β1 (RM1 – RF ) + β2 (RM2 – RF ) + β3(RM3 – RF) =
RF + RP1 β1 + RP2 β2 + RP3 β3
Small Cap value =
4.5 + (0.90 x 6.85) + (0.75 x – 3.5) + (1.25 x 0.65) = 8 .857
Small Cap growth=
4.5 + (0.80 x 6.85) + (1.39 x -3.5) + (1.35 x 0.65) = 5.9925
Large Cap value =
4.5 + (0.85 x 6.85) + (2.05 x -3.5) + 6.75 x 0.65) = 7.535
Large Cap Growth =
4.5 + 91.165 x 6.85) + (2.75 x -3.5) -3.5) + (8.65 x 0.65) = 8.48
Average Expected Return = 8.857 x 0.10 + 5.9925 x 0.25 + 7.535 x 0.15 + 8.48 x 0.50 Required Return
= RF + β. (Risk Premium)
Small Cap value
= 4.5 + (0.90 x 6.85)
= 10.665
Small Cap growth
= 4.5 + (0.80 x 6.85)
= 9.98
Large cap value
= 4.5 + (1.165 x 6.85)
= 12.48
= 7.754
Average return = (10.665 x 0.10) + (9.98 x 0.25) + (10.3225 x 0.15) + (12.48 x 0.50) = 11.35%
54
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q100
RF = 7% RM = 11% βEQUITY = 1.3 Since its an all equity firm so β of equity is β of Asset.
RRPRIOJECT
ΒASSET
= 1.3
=
RF + β(RM – RF)
=
7 + (11 – 7)1.3 = 12.2%
Q101
P.E Ratio = = 5
Ke =
= = 0.20
RF = 10%
Before Buy Back βEQUITY = 0.6, Since No Debt βASSET = 0.6 After Buy Back βASSET will be same ΒASSET = βEQUITY x 0.6 =
+ βDEBT x
: : . . β x + 0 x . (after Buy back) = = 1.2 .
EQUITY
ΒEQUITY ii.
Before Buy Back βE = .06 Before Buy – Buy –Back Back PE ratio = 5
Ke = = 20%
ii.
Risk Premium on Equity before Buy Back KE
= RF + β (RM – R – RF )
20
= 10 + Security Premium
Security Premium = 10% β (RM – R – RF) = 10 0.6 (RM – 10) – 10) = 10 RM = 26.67%
iii.
After Buy Back RR = RF + β (RM – R – RF) = 10 + 1.2 ( 26.67 – 26.67 – 10) = 30% Security Risk Premium = RR - RF = 30 – 30 – 10
iv.
=
20%
Return on Debt = Risk Free rate == 10%
55
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
v.
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Before Buy back PE ratio = 5 Assume MP = 100 PE = 5=
EPS = 20
After Buy back back KE = 30% PE ratio = PE ratio = 3.33 =
=
= 3.33 .
EPS = 30
Increase in EPS = vi.
;
= 50%
New PE ratio = 3.33
Q102
A
B
C
Weight
0.5
0.3
0.2
β
1.3
1.0
0.8
i.
R F = 8%
RM = 12%
Expected return of each project RF + (RM – R – RF)β
II. ii.
A = 8 + (12 – (12 – 8) 1.3
= 13.2%
B = 8 + (12-8) 1
= 12%
C = 8 + (12 – (12 – 8) 0.8
= 11.2%
Return OF Company = 0.5 x 13.2 + 0.3 x 12 + 11.2 x 0.2 = 12.44% Cost of capital i.e KE = 12.44%
56
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q103
Market value of East , West and Central Division is in the ratio of 1:2:1,I.e there weights are @25% , 50% and 25% Let Risk of Division West is X, Risk of East is 1.5X and risk of central is 0.75X i.
Since it it is an all equity company, So So βASSET = βEQUITY = 1.24 ΒASSET is Weighted average of β of Individual assets in the portfolio ΒASSET = WEAST βEAST + WWEST βWEST + WCENTRAL βCeNtRAL
1.24 = 0.25 x (1.5X) + 0.50 x (X) + 0.25 x (0.75X) (0.75X) X = 1.167 Thus βEAST = 1.167 x 1.5 ΒWEST
= 1.167 x 1
=
1.7505
=
1.167
ΒCENTRAL = 1.167 x 0.75 =
ii.
βASSET of PQR Ltd.
= Asset βWEST x
PRAVINN MAHAJAN CA CLASSES 9871255244
0.87525
x
. . = 1.167 x x
= 1.575545
iii.
βASSET of XYZ before acquisition = WEIGHTED β
(0.25 x 1.7505) + (0.50 x 1 .167) + (0.25 x 0.87525) = 1.24 βASSET of XYZ after acquisition=
(0.25 x 1.750) + (0.50 x 1.575545) + (0.25 x 0.87525) = 1.44 iv. iv.
Requi Required red rate rate of retu return rn of new new proj project ect is disc discou ount nt rate rate of new new pro proje ject ct RR = RF + (RM – R – RF)β 11 + 1.575545 (24 – 11) = 31.48%
57
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q104
Debt
Equity
Weight
0.30
0.70
β
0.2
Project β = 1.2 ΒASSET = βEQUITY x
:
+ βDEBT x
1.2 = 0.30 x 0.20 + 0.70 x βE
:
βEQUITY = 1.62 ii.
Debt – Debt – Equity Equity = 40 : 60 After re financing βASSET will remain same ΒASSET = βEQUITY x 1.2 =
:
+ βDEBT x
:
βEQUITY x 0.60 + 0.30 x 0.40
βEQUITY = 1.8
Q105
i.
Required r et eturn on Equity RRE = RF + β (RM – R – RF) = 6 + 1.40 (6) = 14.4%
ii.
ΒASSET = βEQUITY x = 1.40 x
+0x
:
+ βDEBT x
:
= 0.8 iii.
Cost of capital = RF + β (RM – R – RF) = 6 + 0.8 (6)
= 10.8%
iv. iv.
Disco iscou unt ra rate = Cost ost of of ca capita ital = 10.8%
v.
RR = RF + β (RM – R – RF) = 6 +1.5 (6) = 15%
58
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q106
i.
Required r et eturn on Equity RRE
= RF + β (RM – R – RF) = 8 + 1.5 (10) = 23%
ii.
ΒASSET
= βEQUITY x =
+ βDEBT x
:
x 1.5 +
:
x 0
= 0.9 iii.
Company’s cost of capital 8 + 0.9 (10) = 17%
iv.
Any new busin busines esss shoul should d yield yield more more tha than n cost cost of cap capita itall of compa company. ny. So, discou discount nt rate shall be Cost of capital i.e 17%
v.
D: E = 1: 9 Asset β will remain same ΒASSET 0.9 = 0 x
= βEQUITY x
+ βEQUITY x
:
+ βDEBT x
:
βEQUITY = 1 vi.
Since βASSET is same so cost of capital will remain same i.e 17%
vii.
β = 1.2 RR = RF + β (RM – R – RF) = 8 + 10 (1.2) = 20%
59
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH Q107
ΒASSET
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
(; ) :(; ) :(; ) . . (;. ) = 1.40 x +0x .: . (;. ) .: . (;. )
= βEQUITY x
+ βDEBT x
= 1.08
After change in Debt equity ratio, Asset β will remain same ΒASSET
= βEQUITY x
+ βDEBT x
:(; ) . x .: . (;. )
1.08 = βEQUITY
(; ) :(; )
βEQUITY = 1.584
Q108
AE is an all equity company therefore Asset β shall be equal to βEQUITY So βASSET = 1 ΒASSET
= βEQUITY x
1
= βEQUITY
βEQUITY =
.
+ βDEBT x
:(; ) x : (;. )
(; ) :(; )
= 1.62
Q109
i.
Food division ΒASSET
= βEQUITY x
+ β : . = 0.9 x + 0 x . .
DEBT
x
:
= 0.642
Chemical division ΒASSET
= βEQUITY x = 1.2 x
.
:
+ βDEBT x
:
+ 0
= 0.96 Machine Tools ΒASSET
= βEQUITY x = 1.4 x
+ βDEBT x
:
. + 0
= 0.933 ii.
:
βASSET for midland as a whole shall be average of βASSET of all its division (0.643 x 0.5) + (0.960 x 0.3) + (0.933 x 0.20) ΒASSET
= βEQUITY x
0.7961 = βEQUITY x βEQUITY = 0.9951
:
+ βDEBT x
= 0.7961
:
.
60
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
iii.
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
The cost of capital of each division may be calculated as required return on assets of division
iv.
Cost of capital
= RF + βASSET (RM – RF)
Food division
= 10 + 0.643 (18 – 10) = 15.144%
Chemical division
= 10 + 0.960 (18-10) = 17.68%
Tools Divisions
= 10 + 0.933 (18 – 10) = 17.464%
It is assumed that Amalgamated foods fairly represent Food Industry and studge chemicals and Chunky tools fairly represent chemical and tool industry. Further it is also assumed that Food, chemical and machine tools division of Midland Industry fairly Represent Amalgamated foods, Studge chemicals and chunky tools respectively So, each division of Midland Industry fairly represents their respective I ndustry. So above calculations are reliable
Q110
Since each company in the Industry r epresents overall industry so, β of one firm of t hat industry is equal to β of other firm of the same industry. So βAsset of Gamma is equal to βASSET of Alpha Ltd. Asset β of Alpha βASSET
= βEQUITY x
+ βDEBT x
(; ) :(; )
+ βDEBT x
(; ) :(; )
:(; ) = 1.30 x : (;.) + 0
= 1.13 asset β of Gamma shall also be 1.13 βASSET
= βEQUITY x
1.13
= βEQUITY
βEQUITY = 1.582
:(; ) x + 0 : (;.)
61
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q111
βASSET
= βEQUITY x
= 1.32 x
.
+ β :
DEBT
x
:
+0
= 1.1
βASSET of Birla Motors Motors will be equal to βASSET of Industry because it is assumed that Birla Motors is representing industry βASSET
= βEQUITY x
1.1
= βEQUITY
βEQUITY = 1.43 i.
ii.
Q112
RR
+ βDEBT x
: x + 0 .
=
RF + βASSET (RM – R – RF)
=
12 + 1.1(9)
=
21.9%
RREQUITY =
:
RF + βEQUITY (RM – R – RF)
=
12 + 1.43(9)
=
24.87%
βASSET of B Ltd. will be equal to to βASSET of A Ltd. A Ltd.
βASSET
= βEQUITY x
:
= 1.50 x
+ 0.30 x
.
= 1.1
+ βDEBT x
:
. .
βASSET of B Ltd. Will be same same as βASSET of A Ltd. βASSET
= βEQUITY x
1.1
= βEQUITY
βEQUITY = 1.62
Q113
+ βDEBT x
: : . x + 0.45 x . .
βASSET ofXY Ltd. will be equal to βASSET of AB Ltd. AB Ltd.
βASSET
= βEQUITY x
+ βDEBT x
:(; ) = 1.1 x + 0 :(;. )
(; ) :(; )
= 0.94
βASSET of XY Ltd. Will be same same as βASSET of AB Ltd. βASSET
= βEQUITY x
0.94
= βEQUITY
βEQUITY = 1.43
:(; x :(;. )
62
+ βDEBT x
)
(; ) :(; )
+0
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q114
βASSET
= βEQUITY x
+ βDEBT x
:(; ) = 1.35 x :. (;. )
(; ) :(; )
= 0.92
βASSET of A Ltd. Will be same as βASSET of shoe co. βASSET
= βEQUITY x
0.92
= βEQUITY
βEQUITY = 1.219
+ βDEBT x
:(; ) x :. (;. )
Debt equity Ratio = 4 : 6
Q115
(; ) :(; )
βEQUiTY = 1.25
Tax rate = 34% βASSET
= βEQUITY x
+ βDEBT x
:(; ) 1.25 x + 0 : (;. )
= =
RF = 6%
(R M – R – RF) = 3%
(; ) :(; )
0.8681
Asset β of other company will be same i.e 0.8681, Since other company company is all equity company so Asset β is equal to equity β. RREQUITY = RF + βEQUITY (RM – R – RF) = 6 + 0.8681(3) = 8.6043
Q116
i.
Asset β of Adhesive business βASSET
= βEQUITY x
+ βDEBT x
:(; ) = 1.15 x :. (;. )
(; ) :(; )
=1
If XYZ enters into Adhesive Business, its Asset β will be same as asset β of PQR Ltd. i.e 1 ii.
Rate of return on XYZ’s Adhesive business βASSET
= βEQUITY x
1
= βEqUITY
ΒEQuITY
=
1.32
+ βDEBT x
:(; ) x + 0 :(. )(;. )
(; ) :(; )
RREQUITY = RF + βEQUITY (RM – R – RF) = 10 + 1.32(15 – 1.32(15 – 10) 10) = 16.60% RR of XYZ Ltd. = kEQUITY .
+ KDEBT.
: : . = 16.60 x + 14(1-0.60) . .
63
=
11.71%
fb-id PRAVINN MAHAJAN CA CLASSES
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH
PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q117
Proxy β of Excellent Ltd. For Electronic business is average of Asset β of other companies in Electronic business Asset β of other companies Superior Ltd βASSET
= βEQUITY x
+ βDEBT x
:(; ) . = 1.33 x + 0 . :. (;. )
=
0.806
Admirable Ltd. βASSET
(; ) :(; )
= βEQUITY x
:(; ) + β . = 1.30 x + 0 . :. (;. )
DEBT
x
(; ) :(; )
= 0.907
Asset β = weighted average of β of Individual projects = WELECTRONIC BS. ΒELECTRONIC BS + WOTHER BS . βOTHER BS 0.907
=
βELECTrONIC BS
0.8 x βELECTrONIC BS + 0.2 x 1.4 = 0.784
Meritorious Ltd. βASSET
= βEQUITY x
+ βDEBT x
:(; ) . = 1.05 x + 0 . :. (;. )
(; ) :(; )
= 0.78
ΒELECTRONIC Bs for Excellent Ltd. =
. :. :.
= 0.79
ΒEQUItY of Security 1 is 1.2 Q118
ΒEQuItY of security 2 is 1.6 Since return on shares of British bank is equal to R M i.e return on market (12%). So β of shares of British bank is equal to β of Market i.e 1. β of security Y is 0 β of Invetment Portfolio of these 4 securities is Weighted average of β of securities in the portfolio βP = 0.3 x 1.2 + 0.3 x 1.6 + 0.20 x 1 + 0.20 x 0
= 1.04
RRP = RF + βP (RM – R – RF) = 5 + 1.04(12-5) = 12.28%
64
fb-id PRAVINN MAHAJAN CA CLASSES