CHAPTER 4- RISK AND RETURN
Prices adjusted for bonus issues
Date
9/30/2009
10/30/2009
11/30/2009
12/31/2009
29/01/2010
2/26/2010
3/31/2010
4/30/2010
5/31/2010
6/30/2010
7/30/2010
8/31/2010
9/30/2010
10/29/2010
11/30/2010
12/31/2010
1/31/2011
2/28/2011
3/31/2011
4/29/2011
5/31/2011
6/30/2011
7/29/2011
8/30/2011
9/30/2011
10/31/2011
11/30/2011
12/30/2011
1/31/2012
2/29/2012
3/30/2012
ITC
233
256
258
251
250
234
264
266
284
306
308
327
356
340
343
350
326
339
366
385
386
406
417
401
395
427
401
401
408
416
452
Reliance
Industries
2202
1927
2116
2187
2092
1959
2149
2063
2093
2178
2018
1832
1975
2194
1973
2116
1840
1923
2103
1970
1905
1790
1656
1570
1611
1750
1567
1386
1635
1630
1496
Tata
Steel
509
472
578
617
569
575
632
619
500
486
536
522
652
588
586
681
639
609
622
616
590
612
563
468
415
480
383
334
453
474
469
WIPRO
602
610
631
681
648
673
707
671
674
578
618
597
678
629
628
737
662
656
714
675
671
626
586
502
510
551
571
597
620
654
658
NIFTY
5084
4712
5033
5201
4882
4922
5249
5278
5086
5313
5368
5402
6030
6018
5863
6135
5506
5333
5834
5750
5560
5647
5482
5001
4943
5327
4832
4624
5199
5385
5296
Monthly returns on
Month
Sep-09
Oct-09
Nov-09
Dec-09
Jan-10
Feb-10
Mar-10
Apr-10
May-10
Jun-10
Jul-10
Aug-10
Sep-10
Oct-10
Nov-10
Dec-10
Jan-11
Feb-11
Mar-11
Apr-11
May-11
Jun-11
Jul-11
Aug-11
Sep-11
Oct-11
Nov-11
Dec-11
Jan-12
Feb-12
Mar-12
Mean
return
ITC
R(ITC)(%)
Reliance
Industries
R(RIL)(%)
Tata Steel
R(TSL)(%)
WIPRO
R(WL)(%)
NIFTY
R(M)(%)
9.87
0.68
-2.48
-0.48
-6.66
12.89
0.72
6.78
7.80
0.74
6.25
8.68
-4.36
0.97
1.95
-6.89
3.99
7.85
5.28
0.31
5.18
2.73
-3.91
-1.35
7.99
-6.11
0.10
1.64
2.06
8.65
-12.49
9.81
3.34
-4.31
-6.39
9.72
-4.00
1.45
4.08
-7.36
-9.23
7.80
11.13
-10.09
7.26
-13.06
4.56
9.34
-6.31
-3.34
-6.01
-7.49
-5.19
2.61
8.62
-10.49
-11.51
17.95
-0.32
-8.22
-7.37
22.59
6.75
-7.76
0.97
10.03
-2.10
-19.26
-2.66
10.08
-2.45
24.81
-9.82
-0.33
16.13
-6.11
-4.76
2.20
-0.98
-4.21
3.73
-7.98
-16.90
-11.29
15.62
-20.26
-12.67
35.42
4.68
-1.02
1.28
3.42
8.02
-4.87
3.92
4.98
-5.03
0.39
-14.30
7.03
-3.35
13.55
-7.34
-0.12
17.32
-10.12
-0.95
8.90
-5.46
-0.67
-6.60
-6.37
-14.36
1.57
8.06
3.61
4.58
3.74
5.50
0.73
-7.32
6.81
3.35
-6.13
0.83
6.64
0.55
-3.63
4.45
1.04
0.65
11.62
-0.20
-2.58
4.64
-10.25
-3.14
9.38
-1.44
-3.29
1.57
-2.93
-8.77
-1.15
7.76
-9.28
-4.30
12.43
3.58
-1.66
ΣR(ITC)=70.89
ΣR(RIL)=-28.16
ΣR(TSL)=15.09
ΣR(WL)=17.04
ΣR(M)=9.18
R'(ITC)=2.36
R'(RIL)=-0.94
R'(TSL)=0.50
R'(WL)=0.57
R'(M)=0.31
b) The Arithmetic mean monthly return on ITC Ltd = 70.89/30= 2.36
The geometric mean monthly return on ITC Ltd =
[1.0987 X1.0068 X 0.9752 X 0.9952
X 1.0780 x1.0074 X 1.0625 X 1.0868
X 1.0399 x1.0785 X 1.0528 X 1.0031
X 1.0799 x0.9389 X 1.0010 X 1.0164
=(1.9412)(1/30) -1 = 0.0224 or 2.24 %
X 0.9334
X 1.1289
X 0.9564
X 1.0097
X 1.0518
X 1.0273
X 1.0206 x1.0865]1/30
X 1.0072 X 1.0678
X 1.0195 X 0.9311
X 0.9609 X 0.9865
-1
The Arithmetic mean monthly return on Reliance Industries Ltd =- 28.16/30= - 0.94
The geometric mean monthly return on Reliance Industries Ltd =
[0.8751X1.0981X 1.0334X 0.9569X 0.9361X 1.0972X 0.9600
X 1.014X 1.0408X 0.9264
X 0.9077X 1.0780X 1.1113X 0.8991X 1.0726X 0.8694X 1.0456X 1.0934X 0.9369X 0.9666
X 0.9399X 0.9251X 0.9481X 1.0261X 1.0862
X 0.8951X 0.8849X 1.1795X 0.9968
X 0.9178](1/30) - 1
= (0.6793)(1/30) -1 = -0.01281 or -1.28 %
The Arithmetic mean monthly return on Tata Steel Ltd =15.09/30= 0.50
The geometric mean monthly return on Tata Steel Ltd =
[0.9263 X1.2259 X 1.0675 X 0.9224
X 0.9734 x1.1008 X 0.9755 X 1.2481
X 0.9524 X1.0220 X 0.9902 X 0.9579
X 1.1562 X0.7974 X 0.8733 X 1.3542
= (0.9214)(1/30) -1 = - 0.00272 or -0.27 %
X 1.0097
X 0.9018
X 1.0373
X 1.0468
X 1.1003 X 0.9790 X 0.8074
X 0.9967 X 1.1613 X 0.9389
X 0.9202 X 0.8310 X 0.8871
X0.9898]1/30-1
The Arithmetic mean monthly return on Wipro Ltd =17.04/30 = 0.57 %
The geometric mean monthly return on Wipro Ltd =
[1.0128 X1.0342 X 1.0802 X 0.9513
X 0.8570 X 1.0703 X 0.9665 X 1.1355
X 0.9905 X 1.0890 X 0.9454 X 0.9933
X 1.0806 X 1.0361 X 1.0458 X 1.0374
=(1.0936)(1/30) -1 = 0.00299 or 0.299 %
X 1.0392
X 0.9266
X 0.9340
X 1.0550x
X 1.0498
X0.9988
X 0.9363
1.0073](1/30)-1
X0.9497
X 1.0039
X 1.1732 X 0.8988
X 0.8564 X 1.0157
The Arithmetic mean monthly return on Nifty =9.18/30 = 0.31
The geometric mean monthly return on Nifty =
[0.9268X1.0681X 1.0335X 0.9387X 1.0083X 1.0664X 1.0055X 0.9637X 1.0445X 1.0104X
1.0065
X 1.1162X 0.9980X 0.9742X 1.0464X 0.8975X 0.9686X 1.0938X 0.9856X 0.9671X
1.0157
X 0.9707X 0.9123X 0.9885X 1.0776X 0.9072X 0.9570X 1.1243X 1.0358
X 0.9834](1/30)-1
= (1.0416)(1/30) -1 = 0.001359 or 0.14 %
c)
R(ITC)
R'(ITC)
7.51
-1.68
-4.84
-2.84
-9.02
10.53
-1.64
4.42
5.44
-1.62
3.89
6.32
-6.72
-1.39
-0.41
-9.25
1.63
5.49
2.92
-2.05
2.82
0.37
-6.27
R(RIL) R'(RIL)
-13.43
8.87
2.40
-5.25
-7.33
8.78
-4.94
0.51
3.14
-8.30
-10.17
6.86
10.19
-11.03
6.32
-14.00
3.62
8.40
-7.25
-4.28
-6.95
-8.43
-6.13
R(TSL)R'(TSL)
-7.87
22.09
6.25
-8.26
0.47
9.53
-2.60
-19.76
-3.16
9.58
-2.95
24.31
-10.32
-0.83
15.63
-6.61
-5.26
1.70
-1.48
-4.71
3.23
-8.48
-17.40
R(M) R'(M)
-7.63
6.50
3.04
-6.44
0.52
6.33
0.24
-3.94
4.14
0.73
0.34
11.31
-0.51
-2.89
4.33
-10.56
-3.45
9.07
-1.75
-3.60
1.26
-3.24
-9.08
[R(ITC)R'(ITC)]2
56.42
2.81
23.45
8.05
81.29
110.90
2.69
19.53
29.54
2.64
15.16
39.97
45.16
1.93
0.17
85.48
2.65
30.13
8.53
4.19
7.96
0.14
39.29
[R(RIL)R'(RIL)]2
180.33
78.64
5.77
27.59
53.80
77.11
24.38
0.26
9.83
68.87
103.37
47.00
103.76
121.76
39.93
196.07
13.07
70.61
52.56
18.36
48.26
71.09
37.54
[R(TSL)R'(TSL)]2
61.90
487.86
39.03
68.28
0.22
90.88
6.74
390.65
9.99
91.84
8.68
590.91
106.42
0.69
244.40
43.72
27.64
2.90
2.19
22.14
10.43
71.94
302.62
[R(M)R'(M)2]
58.25
42.29
9.21
41.53
0.27
40.06
0.06
15.54
17.12
0.53
0.11
127.83
0.26
8.33
18.72
111.45
11.87
82.35
3.08
12.98
1.59
10.49
82.52
-3.71
5.63
-8.47
-2.26
-0.72
-0.30
6.29
1.67
7.68
-11.43
-12.45
17.01
-1.26
-9.16
-11.79
15.12
-20.76
-13.17
34.92
4.18
-1.52
-1.46
7.45
-9.59
-4.61
12.12
3.27
-1.97
13.74
31.72
71.78
5.11
0.51
0.09
39.53
Σ[R(ITC)R'(ITC)]2
= 780.57
2.79
139.07
59.00
228.64
130.55
430.99
155.00
173.49
289.28
1219.59
1.58
17.50
83.94
2.32
Σ[R(RIL)R'(RIL)]2 Σ[R(TSL)=
R'(TSL)]2
2172.07 =4893.67
2.15
55.43
92.06
21.25
146.97
10.67
3.90
Σ[R(M)R'(M)]2
=1028.84
Standard deviation of the returns of ITC = [780.57/29]1/2 = 5.19 %
Standard deviation of the returns of RIL
= [2172.07/29]1/2= 8.65 %
Standard deviation of the returns of Tata Steel Ltd =
= [4893.67/29]1/2 = 12.99 %
Standard deviation of the returns of Nifty
= [1,028.84/29]1/2 = 5.96 %
CHAPTER 5: THE TIME VALUE OF MONEY
1. (i) 600,000 x PVIFA (10%, 20) X 1.10
=
600,000 X 8.514 X 1.10
=
Rs. 5619240
(ii)
Shyam needs Rs. 5,619,240 when he reaches the age of 60 His bank balance of
Rs. 200,000 will grow to:
200,000 (1.10)25 = 200,000 (10.835) = 2,167,000
This means that his periodic savings must grow to
5,619,240 - 2,167,000 = 3,452,240
His annual savings must be:
A
=
3,452,240
FVIFA (25, 10%)
=
3,452,240
=
98347
35,103
(iii)
74
75
500
500
500
500
Amount required for the charitable cause
500,000 x PVIFA (10%, 5 yrs) x PVIF (10% 14)
Amount required for bequeathing:
=
=
4,000,000 x PVIF (10%, 20)
500,000 x 3.791 x 0.263
4,000,000 x 0.149 = 596,000
Total requirement for the charitable cause as well as bequeathing
=
498,517
= 1,094,517
iv)
500
Working:
A (1+g) n
A (1+g)
0
1
n
n
(1+g)n
1–
PVGA =
(1+r)n
A (1+g)
r-g
(1.12)25
1–
=
(1.09)25
400000
=
Rs. 12,952,809
0.09 – 0.12
2
Re.1 deposit each at the end of month
0 1
becomes Rs.3.0402
2
3
4
5
6
9
12
40
44
Rs.3.0402Rs.3.0402Rs.3.0402Rs.3.0402Rs.3.0402
MBA expenses for year I at present = 20 lakhs. After 10 years it would be = 20(1+0.05)10 = 32.58 lakhs
MBA expenses for year II at present = 25 lakhs. After 11 years it would be = 25(1+0.05)11 = 42.76 lakhs
At the end of 3 months, each 1 Rupee deposited in the RD account becomes = FVIFA (0.08/12,3)
= [{(1+0.08/12)3 -1} / (0.08/12)] x (1+0.08/12) = {(1.00667)3-1}/0.00667 x 1.00667 = Rs.3.0402 which
when compounded quarterly becomes at the end of 10 years = 3.0402 x [(1+0.08/4)4x10 - 1]/ (0.08/4)
= 3.0402 x [(1.02)40 – 1] / 0.02 = Rs. 183.634
For a RD maturity value of Rs.183.634 if the deposit to be made is Rs.1, for a maturity value of
Rs.32.58 lakhs, the monthly deposit to be made will be = 32, 58,000/183.634 = Rs.17, 742
Similarly for a maturity value of Rs.42.76 lakhs the monthly deposit needed .will be
= 42, 76,000 / [3.0402 x {(1.02)44 – 1} / 0.02] = Rs. 20,236
2) Amount required for Jasleen’s marriage at the end of 20 years = Rs.300 lakh Cumulative fixed deposit
to be made now to get the above amount = 300, 00,000 / (1+0.08/4)4x20= Rs.61, 53,29
3)
Annuity Period
Year end 0
19 20
1
2 3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
What deposit?
Annuity Payments
12L 12L12L12L12L12L12L12L12L12L
Annuity needed per annum at the beginning of each year in real terms after 10 years = Rs.12
lakhs
With inflation at 5 percent, in nominal terms, this may be considered as a growing annuity for
10 years at a growth rate of 5 percent and discount rate of 10 percent. Present value of the
annuity, as at the beginning of the 10th year from now
= 12, 00,000 x (1+0.05)[ 1 –(1+0.05)/(1+0.10)10 /(0.10-0.05)] = Rs.93,74,163
Amount to be deposited in cumulative fixed deposit now, to have a maturity value of
Rs.93, 74,163 at the end of 9 years = 93, 74,163/(1+0.08/4)4x9 = Rs.45,95,432
CHAPTER 6: FINANCIALSTATEMENT ANALYSIS
DUPONT CHART : INFOSYS
1.
Net Profit
4,470
/
/
Net Profit
Margin
28.57 %
Total Costs
11,861
Net Sales
15,648
X
Return on
Assets
Net Sales +/Non operating
Surplus/Deficit
16,331
_
Net Sales
15,648
Average
Fixed
Assets
3,519
DUPONT CHART: RELIANCE INDUSTRIES
Net Profit
Margin
14.582 %
Net Sales +/Non operating
Surplus/Deficit
139,072
Net Profit
19,459
/
_
/
Total Costs
119,613
Net Sales
133,443
X
Net Sales
133,443
Return on
Assets
17.35 %
Average
Fixed
Assets
78,039
+
Total
Assets
Turnover
1.19
Average
/
Total
Assets
112,288.5
Average
Investments
19,157.5
+
Average
Net
Current
Assets
15,092
2. Common Size Profit and Loss account statements for Infosys
Regular(Rs. In crores)
For year ending
31-3-07
31-3-08
Common Size(%)
31-3-07
31-3-08
Net sales/income
13,149
15,648
100
100
Cost of goods sold/Software
development expenses
7,278
8,876
55
57
Gross profit
5,871
6,772
45
43
Operating expenses
2,115
2,355
16
15
Operating profit
3,756
4,417
29
28
379
683
3
4
4,135
5,100
31
33
4,135
5,100
31
33
352
630
3
4
3,783
4,470
29
29
Non-operating surplus
Profit before interest and
tax
Interest
Profit before tax
Tax/Provision for tax
Proft after tax
Common Size Balance Sheets for Infosys
Regular(Rs. In crores)
As on
Common Size( %)
31-3-07
31-3-08
31-3-07
31-3-08
286
286
3
2
10,876
13,204
97
98
11,162
13,490
100
100
3,107
3,931
28
29
Investments
839
964
8
7
Deferred tax assets
79
99
1
1
Liabilities & Equity
Share capital
Reserves & surplus
Long-term debt
Deferred tax liabilities
Assets
Net fixed assets
Current assets, loans
& advances
Inventories
Common Size Profit and Loss account statements for Reliance Industries
Regular (Rs. In crores)
Common Size (%)
For year ending
31-3-07
31-3-08
31-3-07
31-3-08
Net sales/income
111,693
133,443
100
100
development expenses
85,876
104,197
77
78
Gross profit
25,817
29,246
23
22
Operating expenses
10,586
10,787
9
8
Operating profit
15,231
18,459
14
14
Non-operating surplus
478
5,629
0
4
Profit before interest and tax
15,709
24,088
14
18
Interest
1,189
1,077
1
1
Profit before tax
14,520
23,011
13
17
Tax/Provision for tax
2,577
3,552
2
3
Proft after tax
11,943
19,459
11
15
Cost of goods sold/Software
Common Size Balance Sheets for Reliance Industries.
Regular(Rs. In crores)
Common Size (%)
As on
Liabilities & Equity
Share capital
Reserves & surplus
31-3-07
31-3-08
31-3-07
31-3-08
1,453
62,514
3,136
78,313
1.5
63.3
2.5
62.3
Long-term debt
27,826
36,480
28.2
29.0
Deferred tax liabilities
6,982
98,775
7,873
125,802
7.1
100
6.3
100
Assets
Net fixed assets
Investments
71,189
16,251
84,889
22,064
72.1
16.5
67.5
17.5
Current assets, loans & advances
Inventories
Receivables
Cash & bank balance
Other current assets
12,137
3,732
1,835
3
14,248
6,228
4,280
73
12.3
3.8
1.9
0.0
11.3
5.0
3.4
0.1
Loans & advances
12,206
18,058
12.4
14.4
Less:
Current liabilities & provisions
18,578
24,038
18.8
19.1
Net current assets
11,335
18,849
11.5
15.0
98,775
125,802
100
100
CHAPTER 7: PORTFOLIO THEORY
Expected return on BPDL = 0.2x (-5) + 0.5 x 10 + 0.3x 35 = 14.5 %
Expected return on ONGD = 0.2x (-3) + 0.5 x 14 + 0.3x 22 = 13 %
Standard deviation of the returns on BPDL
=[ 0.2(-5-14.5 )2 +0.5(10-14.5 )2 +0.3(35-14.5 )2 ]1/2 = 14.57 %
Standard deviation of the returns on ONGD
=[ 0.2(-3-13)2 +0.5(14-13)2 +0.3(22-13)2 ]1/2 = 8.72 %
RB
Period
1
2
3
4
5
6
7
8
9
10
Sum
Mean
RB - RB RO - RO
RO
32
14
24
-8
-2
15
8
28
-7
-3
101
10.1
14
5
-6
12
22
14
5
-14
26
20
98
9.8
21.9
3.9
13.9
-18.1
-12.1
4.9
-2.1
17.9
-17.1
-13.1
(RB -RB)(RO -RO)
4.2
-4.8
-15.8
2.2
12.2
4.2
-4.8
-23.8
16.2
10.2
91.98
-18.72
-219.62
-39.82
-147.62
20.58
10.08
-426.02
-277.02
-133.62
-1139.8
Covariance of the two stocks = -1139.8/9 = -126.64
Coefficient of correlation = -126.64/ (14.57 x8.72) = - 1
(i)
If equal amounts are invested in each stock, the risk and returns are as follows:
Return = 0.5 x14.5 + 0.5 x 13 = 13.75 %
Portfolio risk= 0.5 x 14.57 -0.5 x 8.72 = 2.93 %
(ii)
Proportion of BPDL in the Minimum variance portfolio
= 8.72 / (14.57 + 8.72) = 0.374
Return from such a portfolio = 0.374 x 14.5 + 0.626 x 13 = 13.56 %
Portfolio risk= 0.374 x 14.57 – 0.626 x 8.72 = 0.00954 i.e. nil
(iii)
I would recommend going in for the minimum variance portfolio (MVP) which
gives an almost riskless return of 13.56 percent which is only slightly less than
the return from the other alternative.
No. of shares of BPDL to be purchased for the MVP
= 0.374 x 100, 00,000 / 500 = 7480
No. of shares of ONGD to be purchased for the MVP
= 0.626 x 100, 00,000 / 300 = 20,866
CHAPTER 8: CAPITAL ASSET PRICING MODEL AND ARBITRAGE PRICING THEORY
1 (a)
R(ITC)
R'(ITC)
(1)
7.51
-1.68
-4.84
-2.84
-9.02
10.53
-1.64
4.42
5.44
-1.62
3.89
6.32
-6.72
-1.39
-0.41
-9.25
1.63
5.49
2.92
-2.05
2.82
0.37
-6.27
-3.71
5.63
-8.47
-2.26
-0.72
-0.30
6.29
15.96
R(RIL) R'(RIL)
(2)
-13.43
8.87
2.40
-5.25
-7.33
8.78
-4.94
0.51
3.14
-8.30
-10.17
6.86
10.19
-11.03
6.32
-14.00
3.62
8.40
-7.25
-4.28
-6.95
-8.43
-6.13
1.67
7.68
-11.43
-12.45
17.01
-1.26
-9.16
-0.55
R(TSL)R'(TSL)
(3)
-7.87
22.09
6.25
-8.26
0.47
9.53
-2.60
-19.76
-3.16
9.58
-2.95
24.31
-10.32
-0.83
15.63
-6.61
-5.26
1.70
-1.48
-4.71
3.23
-8.48
-17.40
-11.79
15.12
-20.76
-13.17
34.92
4.18
-1.52
4.41
R(M) R'(M)
(4)
-7.63
6.50
3.04
-6.44
0.52
6.33
0.24
-3.94
4.14
0.73
0.34
11.31
-0.51
-2.89
4.33
-10.56
-3.45
9.07
-1.75
-3.60
1.26
-3.24
-9.08
-1.46
7.45
-9.59
-4.61
12.12
3.27
-1.97
0.04
[R(ITC)R'(ITC)] x
[R(M)R'(M)]
(1X4)
-57.33
-10.90
-14.70
18.29
-4.65
66.65
-0.39
-17.42
22.49
-1.18
1.32
71.48
3.45
4.01
-1.77
97.61
-5.61
49.81
-5.12
7.38
3.55
-1.21
56.94
5.43
41.93
81.29
10.42
-8.67
-0.98
-12.42
0.64
[R(RIL)R'(RIL)]
x [R(M)R'(M)]
(2X4)
102.49
57.67
7.29
33.85
-3.78
55.58
-1.19
-2.01
12.97
-6.03
-3.44
77.51
-5.23
31.84
27.34
147.82
-12.46
76.25
12.72
15.44
-8.75
27.31
55.66
-2.45
57.19
109.62
57.39
206.20
-4.11
18.09
-0.02
[R(TSL)R'(TSL)] x
[R(M)-R'(M)]
(3X4)
60.04
143.63
18.96
53.25
0.24
60.34
-0.62
77.91
-13.08
6.97
-1.00
274.84
5.29
2.40
67.63
69.81
18.12
15.44
2.60
16.95
4.07
27.47
158.03
17.27
112.58
199.19
60.71
423.37
13.67
3.01
0.18
[R(M)-R'(M)2]
((4)^2)
58.25
42.29
9.21
41.53
0.27
40.06
0.06
15.54
17.12
0.53
0.11
127.83
0.26
8.33
18.72
111.45
11.87
82.35
3.08
12.98
1.59
10.49
82.52
2.15
55.43
92.06
21.25
146.97
10.67
3.90
0.00
Σ[R(ITC)R'(ITC)]x
[R(M)R'(M)]
=400.32
Σ[R(RIL)R'(RIL)]x
[R(M)R'(M)]
= 1140.75
Beta of ITC
= (400.32/29) / (1028.84/29) = 0.39
Beta of RIL
= (1140.75/29) / (1028.84/29) = 1.11
Σ[R(TSL)R'(TSL)]x
[R(M)-R'(M)]
= 1899.26
Σ[R(M)-R(M)2]
= 1028.84
Beta of Tata Steel Ltd = (1899.26/29) / (1028.84/29) = 1.85
(b)
The beta of ITC is usually very low as it is a well entrenched defensive stock. There were no big
surprises from RIL during the period covered and so its beta of 1.11 reflected mostly the market
movement. The fortunes of the steel industry were rather volatile during the period and this is
reflected by the high beta of Tata Steel.
2.
(1) Calculation of beta of Century Limited stock from the historical data
Period
Return Return
Rc-Rc Rm-Rm (Rm-Rm)2 (Rc-Rc)
Rc ( % ) Rm( %)
x (Rm-Rm)
1
10
8
0
1
1
0
2
8
(6)
(2)
(13)
169
26
3
25
12
15
5
25
75
4
(8)
10
(18)
3
9
(54)
5
14
9
4
2
4
8
6
11
9
1
2
4
2
∑Rc=60 ∑Rm=42
Rc=10
∑ (Rm-Rm)2=212 ∑ (Rc-Rc)(Rm-Rm)=57
Rm=7 σm2 = 212/5 =42.4
Cov (c,m) = 57/5=11.4
Beta of Century Limited βc = 11.4/42.4 = 0.3
(2) Calculation of expected returns, standard deviations and covariance
E(A) =[ 0.2x(-)10] + [0.4x18] +[ 0.4x30] = -2+7.2+12=17.2
E(B)= [0.2x(-)8] + [0.4x12] + [0.4x20] = -1.6 +4.8+8 = 11.2
E(C)= [0.2x15] + [0.4x6] +[0.4x(-) 10] = 3+2.4- 4 = 1.4
E(M)= [0.2x(-)8]+ [0.4x15] + [0.4x25] = -1.6+6.0 +10=14.4
σA = [ 0.2(-10-17.2)2 +0.4(18-17.2)2+0.4(30-17.2)2 ]1/2
= [148 + 0.3+65.5]1/2 = 14.6
σB = [0.2(-8-11.2)2 + 0.4(12-11.2)2 +0.4(20-11.2)2]1/2
= [ 73.7 +0.3+31.0]1/2 =10.2
σc = [0.2(15-1.4)2+0.4(6-1.4)2 + 0.4(-10-1.4)2]1/2
= [ 37 +8.5+52]1/2 = 9.9
σM = [0.2(-8-14.4)2 +0.4(15-14.4)2+0.4(25-14.4)2]1/2
= [ 100.4 +0.1 +44.9]1/2 = 12.1
Calculation of covariances between the stocks
State of
the
Economy
Prob-
RA-RA
RB-RB
RC-RC
(3)
(4)
(5)
(2)x(3)x(4)
(2)x(4)x(5)
(2)x(3)x(5)
ability
(2)
(1)
Recession
0.2
(27.2)
(19.2)
13.6
104.4
(52.2)
(74.0)
Normal
0.4
0.8
0.8
4.6
0.3
1.5
1.5
Boom
0.4
12.8
8.8
(11.4)
45.1
σA,B =149.8
(40.1)
σB,C=(90.8)
(58.4)
σA,C= (130.9)
Expected return and standard deviations of the portfolio
E(P) = (0.5x17.2) + (0.4x11.2) +(0.1x1.4)=8.6+4.5+0.1=13.2%
σp= [ wA2 σA2 + wB2 σB2 + wC2 σC2 + 2 wAwBσA,B +2 wBwCσB,C +2 wAwCσA,C]1/2
= [ 53.3 + 16.6 +1.0 + 59.9-7.3-13.1]1/2 = 10.5
( 3) Determining overpricing and underpricing using CAPM
βA =1.2
βB =0.8 βC = 0.3
E(RM) = 14.4 Rf =6%
SML = 6 + (14.4 -6) x Beta
= 6 + 8.4 x Beta
Required return on Arihant Pharma = 6 + (8.44 x 1.2) = 16.1%
Required return on Best Industries = 6 + (8.44 x 0.8) = 12.7%
Required return on Century Limited= 6 + (8.44 x 0.3) = 8.5%
As the expected return of 17.2 % on Arihant Pharma is slightly more than the required
return of 16.1 %, its expected return can be expected to come down to the fair return
indicated by CAPM and for this to happen its market price should go up. So it is slightly
undervalued.
In the case of Best Industries stock, as the expected return is slightly less than the required
return of 12.7 %, its expected return can be expected to go up and for this to happen its
market price should go down. So it is slightly undervalued.
Century Limited can be considered as overvalued as its required return is far in excess of the
expected return which is likely to drive the market price downwards.
3. For stock A:
Expected return
= (0.2 x -18) + (0.5 x 20) + (0.3 x 42) = 19
Standard deviation = [ 0.2 ( -18 -19)2 + 0.5 (20-19)2 + 0.3 (42 – 19)2 ] 1/2
= [273.8 + 0.5 + 158.7]1/2 = 20.07
For stock B:
b.
State of the
Economy
Probability (p)
Return on
A (%) (RA)
Return
B (%) (RB)
RA-E(RA)
RB-E(RB)
p
x [RA-E(RA)]
x[RB-E(RB)]
Recession
Normal
Boom
0.2
0.5
0.3
-18
20
42
25
5
-12
-37.0
1.0
23.0
21.1
1.1
-15.9
total =
-156.14
0.55
- 109.71
- 265.30
RA-E(RA)
RC-E(RC)
p
x [RA-E(RA)]
x[RC-E(RC)]
-37.0
1.0
-20.1
0.9
148.74
0.45
Covariance between the returns of A and B is (-) 265.3
State of the
Economy
Recession
Normal
ProbReturn on A
ability (p)
(%) (RA)
0.2
0.5
-18
20
Return C
(%) (RC)
- 6.0
15.0
Expected return of the portfolio = (0.2 x 3.5) + (0.5 x 12.5) + (0.3 x 15.0)
= 0.7 + 6.25 + 4.5 = 11.45
Standard deviation of the portfolio
= [ 0.2 (3.5 – 11.45)2 + 0.5 (12.5 – 11.45)2 + 0.3 (15.0 – 11.45)2]1/2
= [ 12.64 + 0.55 + 3.78] ½ = 4.12
Portfolio in which weights assigned to stocks A, B and C are 0.4, 0.4 and 0.2 respectively.
Expected return of the portfolio = (0.4 x 19.0) + (0.4 x 3.9) + 0.2 x 14.1)
= 7.6 + 1.56 + 2.82 = 11.98
For calculating the standard deviation of the portfolio we also need covariance between B
and C, which is calculated as under:
State of the
Economy
Probability (p)
Recession
Normal
Boom
0.2
0.5
0.3
Return on
B (%) (RB)
Return on
C (%)
(RC)
RB-E(RB)
RC-E(RC)
- 6.0
15.0
26.0
21.1
1.1
(-)15.9
-20.1
0.9
11.9
total =
25
5
(-)12
Covariance between the returns of B and C is (-)141.08
We have the following values:
WA = 0.4
WB = 0.4
σA = 20.07
σB = 12.86
σAB= (-)265.3
σAC = 231.3
WC = 0.2
σC = 11.12
σBC = (-) 141.08
Standard deviation
= [ (0.4 x 20.07)2 + (0.4 x 12.86)2 + (0.2 x 11.12)2 + [ 2 x 0.4 x 4 x (-) 265.3 ] +
+ [2 x 0.4 x 0.2 x 231.3] + [2 x 0.4 x 0.2 x (-) 141.08]1/2
= (64.45 + 26.46 + 4.95 – 84.90 + 37.01 – 22.57)1/2 = 5.04
p
x[RB-E(RB)]
x[RC-E(RC)]
(-) 84.82
0.50
(-) 56.76
(-)141.08
e. (i) Risk-free rate is 6% and market risk premium is 15 – 6 = 9%
The SML relationship is
Required return = 6% + β x 9%
(ii) For stock A:
Required return = 6 % + 1.3 x 9 % = 17.7 %; Expected return = 19 %
Alpha = 19 – 17.7 = 1.3%
For stock B:
Required return = 6 % - 0.60 x 9 % = 0.6%; Expected return = 3.9 %
Alpha = 3.9 – 0.6 = 3.3 %
For stock C:
Required return = 6% + 0.95 x 9 % = 14.55 %; Expected return = 14.1%
Alpha = 14.1 – 14.55 = (-) 0.45 %
f.
_
Period RD (%)
1
-15
2
7
3
14
4
22
5
5
∑RD = 33
_
RM (%)
-5
4
8
15
9
∑ RM = 31
_
RD-RD
-21.6
0.4
7.4
15.4
-1.6
_
_
RM-RM
-11.2
-2.2
1.8
8.8
2.8
_
(RM-RM)2
125.44
4.84
3.24
77.44
7.84
_
_
(RD-RD) (RM-RM)
241.92
-0.88
13.32
135.52
- 4.48
_
∑(RM-RM)2 = 218.80 ∑ (RD-RD) (RM-RM) = 385.4
_
RD = 6.6
RM = 6.2
σ2m = 218.8/4 = 54.7 Cov (D,M) = 385.4/4 = 96.35
ß = 96.35 / 54.7 = 1.76
Interpretation: The change in return of D is expected to be 1.76 times the expected
change in return on the market portfolio.
CAPM assumes that return on a stock/portfolio is solely influenced by the market
CHAPTER 11- BOND PRICES AND YIELDS
a.
Value of a bond is calculated as the present value of all future cash flows
associated with it.
Value of a bond (V) carrying an annual coupon payment of C (in rupees) maturing
after n years with maturity value of M is given by
n
C
M
V = -------- + -------t=1 ( 1+r)t
(1+r)n
where r is the required periodic rate of return and t is the time period for receipt of
periodic payments.
b.
V
=
=
c.
d.
V
12 PVIFA8%,8yrs+ 100 PVIF8%, 8yrs
12 x 5.747 + 100 x 0.540
=
Rs. 122.96
=
6 PVIFA 4%, 16 + 100 PVIF 4 %, 16
=
6 x 11.652 +100 x 0. 534
=
Rs. 123.31
Let the YTM be r %. We have
13 PVIFA r, 5yrs + 100 PVIFr, 5 yrs= 95
Trying r = 15%, LHS = 13 x 3.352 + 100 x 0.497 = 93.28
Trying r = 14%, LHS = 13 x 3.433 + 100 x 0. 519 = 96.53
By linear interpolation
r= 14 % + (96.53 - 95) / (96.53 – 93.28) = 14.47 %
( e)
Approximate YTM
13+ (100- 95)/5
= -----------------------------
= 14.43 %
0.4 x 100 + 0.6 x 95
f.
Let r be the yield to call. We then have
13 PVIFA r%, 2yrs +105 PVIF r%, 2yrs =95
Trying r= 18%, LHS = 13 x 1.566 + 105 x 0. 718 =95.75
Trying r=19%, LHS = 13 x 1.547 + 105 x 0.706 = 94.24
By linear interpolation,
(95.75- 95)
r= 18% + ----------------------- = 18.50 %
(95.75- 94.24)
g.
If future cash flows are reinvested at 15 % p.a. the terminal value will be
13 FVIFA15%, 4 yrs+ 100
=
13x 4.993 + 100
=
164.91
Let r* be the realized yield to maturity.
We have 95 (1+ r *)5 =
164.91
(1+r*) 5
=
1+r*
= 1.1166
r*
=
164.91/ 95 = 1.736
11.66 %
h.
13 + (100 – 95) / 5
Stated YTM
=
-------------------------------0.4 x 100 + 0.6 x 95
= 14.43 %
13+ (90 – 95)/ 5
Expected YTM
= ----------------------------
= 12.90 %
0.4 x 90 + 0.6 x 95
Difference between the expected and stated YTM = 1.53
CHAPTER 12- BOND PORTFOLIO MANAGEMENT
a.
Yield to maturity is the value of r that satisfies the following equation:
5
80
1000
1020 = 
--------- + -----t=1
(1+r)t
(1+r)5
Trying
r
=
7 % the right hand side (RHS) of the above equation is:
=80 x PVIFA (7%, 5 years) + Rs.1000 x PVIF (7%, 5 years)
=
Rs.80 x4.100 + Rs.1000 x 0.713
=
Rs. 1041
As this value is higher than 1020, let us try a higher value for r.
Trying
r
=
8 %. The right hand side (RHS) of the above equation is:
80 x PVIFA (8 %, 5 years) + Rs.1000 x PVIF (8%, 5 years)
=
80 x 3.993 + Rs.1000 x 0.681
=
1000.44
By linear interpolation, r = 7+ (1041-1020)/(1041-1000.44) = 7.52%
b.
The duration of a coupon bond is:
1+y
(1 + y) + T(c –y)
------
- -----------------------
y
c [(1 +y)T – 1] + y
y = 7.52 %, c = 8 %, T = 5 years
So, the duration of the bond is:
1.0752
(1.0752) + 5 (0.08 – 0.0752)
-------- 0.0752
- -----------------------------0.08 [(1.0752)5 – 1] + 0.0752
= 4.32 years
(t2+t) x Ct
n
c.
(1+y)t
Convexity = Σ
-------------
t=1 P x (1+y)2
(12+1)x80
(22+2)x80
------------
------------
(1.0752)1
=
------------------- +
1020 x (1.0752)2
(1.0752)2
(32+3)x80
-----------(1.0752)3
------------------- + ------------------1020 x (1.0752)2
(42+4) x 80
(52+5) x 80
-----------------
------------------
(1.0752)4
1020 x (1.0752)2
(1.0752)5
+ ------------------- + ------------------1020 x (1.0752)2
1020 x (1.0752)2
=
0.1262 + 0.3521 + 0.6550 + 1.0153 + 1.4164
=
3.565
d. The modified duration of the bond is:
Duration
=
4.32
----------- = ----------- = 4.018
(1+ yield)
(1.0752)
The percentage change in the price of the bond, if the yield increases by 0.25 percent is:
∆P/ P =
=
- Modified duration x 0.25
- 4.018 x 0.25 = - 1 percent
The bond price decreases by 1 percent.
e. Price after two years
=
80 PVIFA (9 %, 3 years) + 1,000 PVIF (9 %, 3 years)
=
80 x 2.531 + 1,000 x 0.772
=
974.48
Future value of reinvested coupon
=
80 (1.11) + 80
= 168.80
168.80 + (974.48 -1,020)
Two year return =
---------------------------------------- = 12.09 %
1,020
The expected annualised return over the two year period will be
(1. 1209)1/2 – 1 = or 5.87 %
CHAPTER 13 EQUITY VALUATION
Dr
a.
The general formula is P0 =  -----------------t=1
( 1+ r)t
where Dt = dividend expected t years hence
r
= expected return
D1
b.
Value of a constant growth stock P0 = -----------r- g
where D1 is the dividend expected a year hence, r the expected return and g the growth
rate in dividends.
c.
Required rate of return
=
=
6 % + 1.4 x 7 %
15.8 %
3 x 1.15 x 1.15
d.
(i) Expected value of the stock a year hence =
0.158 – 0.15
(ii) Expected dividend in the first year
=
3 x 1.15
=
Rs. 3.45
= Rs. 495.94
3x 1.15
Intrinsic price of the stock at present = P0 = ------------ = Rs. 431.25
0.158- 0.15
3.45
Expected dividend yield = ---------- = 0.8 %
431.25
495.94-431.25
Capital gains yield in the first year = ------------------- = 15 %
431.25
e
Let r be the expected rate of return on the stock. We then have
3x1.15/(r-0.15) =400
So r = 3x1.15/400 + 0.15 = 15.86 %
f.
Year
Expected dividend
PV factor @16%
PV of dividend
1
3 x 1.35
= 4.05
0.862
3.49
2
3 x (1.35)2 = 5.47
0.743
4.06
3
3 x (1.35)3 = 7.38
0.641
4.73
4
3 x (1.35)4 = 9.96
0.552
5.50
5
3 x (1.35)5 = 13.45
0.476
total =Rs. 24.18
6.40
(A)
Price of the stock at the beginning of the 6th year
13.45 x 1.15
= ---------------- = Rs. 1546.75
0.16- 0.15
Present value of the above is 1546.75 x 0.476
= Rs. 736.25
(B)
Present value of the stock = A+B = 24.18 + 736.25 = Rs. 760.43
The expected dividend in the third year
= Rs. 7.38
Expected price of the stock at the beginning of the third year:
7.38
9.96
= --------
+ --------(1.16)2
1.16
=
+
13.45
1546.75
--------- +
---------------
( 1.16 )3
( 1.16 )3
1013.32
Dividend yield in the third year
=
7.38/ 1013.32
=
0.00728
Expected price of the stock at the end of the third year,
9.96
=
------- + ------(1.16)
=
13.45
1546.75
+ --------
(1.16)2
(1.16)2
1168.07
1168.07 – 1013.32
Capital gain in the third year = --------------------------- = 0. 1527
1013.32
The total return for the third year
=0.00728 + 1527
= 16 %
Expected dividend in the sixth year = 13.45x1.15 = Rs 15.47
Expected price of the stock in the beginning of the 6th year = Rs.1546.75
Expected dividend yield in the 6th year =
15.47/1546.75
=
1%
Expected price of the stock at the end of 6th year
15.47
-------------
=
1547
0.16-0.15
Expected capital gains yield in the 6th year = (1547-1546.75)/1546.75
= 0.016%
g.
YearExpected dividend PV factor @16%
PV of dividend
1
3.00
0. 862
2.59
2
3.00
0. 743
2.23
3.
3.00
0.641
1.92
---------------------
total =
Rs. 6.74
(A)
-------------------Expected price of the stock at the beginning of the 4th year
3x 1.15
=
----------
= Rs. 345
0.16-0.15
Present value of which is 345 x 0.641
=
Rs. 221.14
Present value of the stock
=
A+B = 6.74 + 221.14
=
Rs. 227.88
(B)
3 [ ( 1+ 0.15) + 3 ( 0.35- 0.15 ) ]
h.
Present value of the stock = ---------------------------------------- = Rs. 525
0. 16-0.15
3x (1- 0.06)
i.
3x0.94
Present value of the stock= --------------- = --------- = Rs. 12.82
0.16- (-) 0.06
Dividend expected after one year
Dividend yield per year
0.22
=
3 x 0.94
=
Rs. 2.82
=
2.82/12.82
=
22 %.
Expected price of the stock at the end of the first year
3x0.94x0.94
= ------------------ =
Rs.12.05
0.16-(-)0.06
Capital gains yield per year = -( 12.82-12.05) / 12.82 = - 6%
(i)
Year
Expected dividend
1
3 x 1.35
2
3 x (1.35)2 = 5.47
0. 743
4.06
3
3 x (1.35)3 = 7.38
0.641
4.73
= 4.05
PV factor @16%
0.862
PV of dividend
3.49
----------totalRs. 12.28
(A)
-----------
Expected price of the stock at the beginning of the 4th year
7.38 [ ( 1+ 0.15) + 2.5 ( 0.35- 0.15) ]
= ------------------------------------------- =
Rs. 1217.7
0. 16 – 0. 15
Present value of this is 1217.7 x 0.641
=
Rs. 780.55
Present value of the stock
=
A+ B
=
12.28 + 780.55
=
Rs 792.83
CHAPTER 15: COMPANY ANALYSIS
(B)
CHAPTER 17: OPTIONS
1. 1)
Calls with strike prices 360 and 380 are out –of –the- money.
2) (i)If the firm sells Feb/380 call on 5000 shares, it will earn a call premium of
Rs.25,000 now. The risk however is that the firm will forfeit the gains that it would
have enjoyed if the share price rises above Rs. 380.
(ii) If the firm sells March 320 calls on 5000 shares, it will earn a call premium of
Rs.215,000 now. It should however be prepared to forfeit the gains if the share
price remains above Rs.320.
3) Let s be the stock price, p1 and p2 the call premia for March/ 340 and March/ 360
calls respectively. When s is greater than 360, both the calls will be exercised and
the profit will be { s-340-p1} – { s-360- p2 } = Rs. 15
The maximum loss will be the initial investment , i.e. p1-p2 = Rs.5
The break even will occur when the gain on purchased call equals the net premium
paid
i.e.s-340 = p1 – p2 =5 Therefore s= Rs. 345
4) If the stock price goes below Rs.320, the firm can execute the put option and
ensure that its portfolio value does not go below Rs. 320 per share. However, if
stock price goes above Rs. 380, the call will be exercised and the stocks in the
portfolio will have to be delivered/ sold to meet the obligation, thus limiting the
upper value of the portfolio to Rs. 380 per share. So long as the share price hovers
between R. 320 and Rs. 380, the firm will gain by Rs. 8 (net premium received) per
pair of call and put.
5)
Long straddle makes sense when the stock price is expected to move a lot in
either direction.. The cost of buying February 340 straddle is the total premia
paid for the 340 call and 340 put viz. Rs.31. This straddle will be profitable when
the stock price is either below (340-31) = 309 or above (340 + 31) = 371
6)
S0 = 350
E =360 t =0.25 r = 0.07 σ =0.40
(0.40)2
350
ln
+ 0.08 +
x 0.25
360
2
d1 =
0.40 x  0.25
= (-0.0282 + 0.0375) / 0.2 = 0. 00465
d2 = 0.0465 -0.40 √0.25 = - 4.535
Using normal distribution table
N (d1)
= N (0.0465) = 0.5185
N (0.00)
= 1 – 0.5000 = 0.5000
N (0.05)
= 1 – 0.4801 = 0.51999
N (0.0465) = 0.5000 + 0.0465/0.05 x 0.0199
= 0.5185
N (d2)
= N (-1.535)
N(-0.20) = 0.4207
N (-0.15) = 0.4404
N (-.1535) = 0.4207 + 0.0465/0.05 + 0.01977
= 0.4390
E / ert
C0
= E/ e0.07 x 0. 25 = 360 / 1. 01765 = 353.75
= 350 x 0.5185 – 353.75 x 0.4390
= 181.480 – 155.30 = Rs. 26.18
7) If put- call parity is working, we have P0 = C0 – S0 + E/ert
Value of the March/360 put = 16 -350 + 360/e0.08x0.25
= 16 -350 +360/1.0202 = Rs.18.87
CHAPTER 18-FUTURES
1.
The bet is on ICICI Bank stock attaining a new high by June. That is, that the June 2012
futures as it stands now is underpriced. So, buy the underpriced June futures and sell
the May futures to form a calendar spread at the calendar spread margin of 1.02
percent. For one pair of contracts, the margin would be, 898.85 x 250 x 0.0102 =
Rs.2292
So the no. of spreads would be = 40, 00,000 / 2292 = 1746 (in round figures)
The actual margin would be 1746 x 250 x 898.85 x 0.0102 = Rs. 40, 01,950
2.
To protect from any possible market downside, short Nifty futures by an equal amount.
So buy ICICI and sell Nifty futures for equal values in the June 2012 series.
Rs.100 worth of ICICI futures and Nifty futures can be bought with a margin of Rs.16.26 and
Rs.10.16 resply. So to obtain equal value of futures , we have to invest Rs.40,00,000 x
(16.26/26.42)= Rs.24,61,771 as margin in ICICI futures and 40,00,000 - 24,61,771 = Rs.
15,38,229 in Nifty futures.
No. of contracts to be bought of bank futures =[24,61,771 x100) /16.26]/(250 x 898.85) = 67
No. of contracts to be bought of index futures =[15,38,229 x100) /10.16]/(50 x 5342.95) = 57
2. On the calendar spread:
Reverse the open positions by selling the June futures and buying the May futures on 18th May.
The net gain per pair would be:
(905- 898.85) + (888.55 – 890) = Rs. 4.7
For 1746 contract pairs, the gain would be 1746x 250 x 4.7 = Rs.20, 51,550
On the hedged position:
Gain on the bank futures = (925 -898.85) x 250 x 67 = Rs. 438,012
Loss on Nifty futures = (5450 – 5342.95) x50 x 57 = Rs. 305,093
Net gain = Rs. 1,32,91
CHAPTER 22-PORTFOLIO MANAGEMENT FRAMEWORK
Stock prices adjusted for stock splits and bonus issues:
Closing
Nifty
HDFC Bank
TCS
Godrej
Consumer
Products
Tata Motors
31-3-09
3021
973
539
133
180
31-3-10
5249
1933
1562
261
758
31-3-11
5834
2346
2368
365
1248
31-3-12
5296
2600
2320
480
1375
price
Team Choksi:
As they do not believe in beating the market and paying anything other than the minimum by
way of brokerage commissions, they would be investing in Nifty index for the whole of the
three years.
Final portfolio value of Nifty investment = 75 x 5296/3021 = Rs. 131.48 lakhs
CAGR =(131.48/75)1/3 – 1 = 20.6 %
Team Ritesh:
Investment in each stock = 37.5 / 4 = Rs. 9.375 lacs
No. shares initially bought of:
HDFC Bank
TCS
Godrej Consumer Products Tata Motors
=9,37,500/973 =9,37,500/539 =9,37,500/133
=9,37,500/180
= 963
=5208
= 1739
=7048
Total investment in shares = 973 x 963 + 539 x 1739 + 133 x 7048 + 180 x 5208
= Rs. 37.49 lacs. Investment in bonds = Rs. 37.50 lacs
31-3-2010 Equity portfolio value before rebalancing
= 1933 x 963 + 1562 x 1739 + 261 x 7048 + 758 x 5208= Rs. 103.65 lacs
Investment in bonds = Rs. 37.50 lacs .
Total portfolio value = Rs. 141.15 lacs
As the portfolio has made a profit switch to CPPI strategy.
Investment in stocks = 1.4(141.15 – 60) = Rs.113.61 lacs.
So transfer (113.61 – 103.65) = Rs.9.96 lakhs from bonds to stocks to purchase additional stocks
of Tata Motors which was the highest performer during the year.
Stock
HDFC Bank TCS Godrej Consumer Products Tata Motors
Appreciation percentage 98.7
189.8 96.2
321.1
No. of Tata Motors stocks to be purchased = 9.96,000 / 758 = 1314
31-3-2011 Equity portfolio value before rebalancing
= 2346 x 963 + 2368 x 1739 + 365 x 7048 + 1248 x 6522 = Rs. 170,89,126 lacs
Investment in bonds = (37.5 -9.96)=Rs. 27.54 lacs.
Total portfolio value = Rs. 198.43 lacs
As per the CPPI policy, stock investment = 1.4(198.43 - 60) = Rs. 193.80 lacs
So further investment of Rs.(193.80 -170.89) = Rs.22.91 lacs has to be made in stocks.
Stock
HDFC Bank TCS Godrej Consumer Products Tata Motors
Appreciation percentage 21.4
51.6 39.8
64.6
Tata Motors once again being the best performing stock during the year , buy 22,91,000/1248
= 1835 share of the same.31-3-2012
Equity portfolio value before rebalancing
= 2600 x 963 + 2320 x 1739 + 480 x 7048 + 1375 x 8357 = Rs. 214,12,195 lacs ( as we have
already adjusted the stock prices for the bonus and stock splits, there is no need to correct the
number of stocks for our calculation purposes)
Investment in bonds = (27.54 – 22.91) = Rs.4.63 lacs. Total portfolio value = Rs. 218.75 lacs
CAGR = (218.75/75)1/3 -1 = 42.9%
CHAPTER 25 GUIDELINES FOR INVESTMENT DECISIONS
He will retire in 25 years. His post retirement goals are (i) An annual income equal to 50 percent
of his last drawn salary inflation adjusted. (ii) Bequeath Rs. 20 million to daughter at the age of
75
1.
His salary at the time of retirement
Fifty percent thereof 8,126,029 x 0.50
=
750,000 x (1.10)25
=
8,126,029
=
4,063,015
To have an annuity of Rs. 4,063,015 for 20 years, the amount that should be accumulated at
the time of retirement is
=
4,063,015 PVIFA (Real rate of interest, 20 yrs)
=
4,063,015 PVIFA [{(1.09/1.05)-1}, 20 yrs]
=
4,063,015 PVIFA (3.81 %, 20 yrs)
=
4,063,015 x [ 1-1/(1.0381)20 ] /0.0381
=
4,063,015 x 13.8219 = 56,158,587
To bequeath Rs. 20 million at the age of 75 years, the amount that should be accumulated at
the time of retirement is
=
20,000,000 PVIF (9 %, 20 yrs)
=
20,000,000 x 0.178 = 3,560,000
Therefore the total amount that should be accumulated
=
56,158,587+ 3,560,000
=
59,718,587
Out of the above the amount contributed by the investment of the financial asset of
Rs.2,000,000 for 25 years = 2,000,000 x (1.09)25 = 17,246,161
So the salary savings alone should cumulate to
59,718,587- 17,246,161
= 42,472,426
Present value of an annuity for 25 years with a terminal value of 42,472,426
=
42,472,426/FVIFA (9%, 25yrs)
=
42,472,426/ 84.701
=
501,439
So the proportion of his salary income that George should save till he retires so that he can
meet his post-retirement financial goals
2.
=
501,439/ 750,000
=
66.86 %
If he retires at the age of 50, his last drawn salary would be
=
750,000 x (1.10)20
=
5,045,625
Fifty percent thereof
=
5,045,625x 0.50
=
2,522,813
To have an annuity of Rs. 2,522,813 for 25 years, the amount that should be accumulated at the
time of retirement is
=
2,522,813 PVIFA (Real rate of interest, 25 yrs)
=
2,522,813 PVIFA (3.81 %, 25 yrs)
=2,522,813 [ 1-1/(1.0381)25 ] /0.0381
=
2,522,813 x15.9406= 40,215,153
To bequeath Rs. 20 million at the age of 75 years, the amount that should be accumulated at
the time of retirement is
=
20,000,000 PVIF (9 %, 25 yrs) = 20,000,000 x 0.116
=
23, 20,000
Therefore the total amount that should be accumulated
=
40,215,153+ 23, 20,000
=
42,535,153
Out of the above the amount contributed by the investment of the financial asset of
Rs.2, 000,000 for 20 years
=
2,000,000 x (1.09)20
= Rs. 11,208,821
So the salary savings alone should cumulate to
42,535,153 - 11,208,821
= 31,326,332
Present value of an annuity with a terminal value of 31,326,332
=
31,326,332/FVIFA (9%, 20 yrs)
=
31,326,332/ 51.160
=
612,321
So the proportion of his salary income that George should save till he retires so that he can
meet his post-retirement financial goals
=
612,321/ 750,000
=
81.64 %