1 A B C D E F G H I J K L MN
2
3 IDS 270/371: BUSINESS STATISTICS I/II (Sclove) latest revision:
4 PORTFOLIO ANALYSIS Copyright (C) 2001 Stanley Louis Sclove 7-Oct-01
5
6 TABLE. Characteristics of rates of return of two stocks (annual %)
7 Change them and see what happens.
8
9 Stock weight rate of return mean SD Correlation The criterion to be maximized here is
10 A a X 20 25 Prob(Return > c),
11 -0.3 where c= 5 % per year.
12 B b Y 7 3
13 s m
14 a^2* b^2* 2ab* Var. of SD of Exp Val of z = P( return > 0 )
15 a b Var(X) Var(Y) Cov(X,Y) aX+bY aX+bY aX+bY a (c-m)/s = 1-N(z)
16 0.000 1.000 0.00 9.00 0.0 9.00 3.00 7.000 0.000 -2.333 0.9902
17 0.025 0.975 0.39 8.56 -1.1 7.85 2.80 7.325 0.025 -2.615 0.9955
18 0.050 0.950 1.56 8.12 -2.1 7.55 2.75 7.650 0.050 -2.785 0.9973
19 0.075 0.925 3.52 7.70 -3.1 8.09 2.85 7.975 0.075 -2.803 0.9975
20 0.100 0.900 6.25 7.29 -4.1 9.49 3.08 8.300 0.100 -2.694 0.9965
21 0.125 0.875 9.77 6.89 -4.9 11.73 3.43 8.625 0.125 -2.518 0.9941
22 0.150 0.850 14.06 6.50 -5.7 14.83 3.85 8.950 0.150 -2.324 0.9899
23 0.175 0.825 19.14 6.13 -6.5 18.77 4.33 9.275 0.175 -2.141 0.9839
24 0.200 0.800 25.00 5.76 -7.2 23.56 4.85 9.600 0.200 -1.978 0.9760
25 0.225 0.775 31.64 5.41 -7.8 29.20 5.40 9.925 0.225 -1.837 0.9669
26 0.250 0.750 39.06 5.06 -8.4 35.69 5.97 10.250 0.250 -1.716 0.9569
27 0.275 0.725 47.27 4.73 -9.0 43.02 6.56 10.575 0.275 -1.612 0.9465
28 0.300 0.700 56.25 4.41 -9.5 51.21 7.16 10.900 0.300 -1.523 0.9361
29 0.325 0.675 66.02 4.10 -9.9 60.24 7.76 11.225 0.325 -1.446 0.9259
30 0.350 0.650 76.56 3.80 -10.2 70.13 8.37 11.550 0.350 -1.379 0.9161
31 0.375 0.625 87.89 3.52 -10.5 80.86 8.99 11.875 0.375 -1.321 0.9067
32 0.400 0.600 100.00 3.24 -10.8 92.44 9.61 12.200 0.400 -1.269 0.8978
33 0.425 0.575 112.89 2.98 -11.0 104.87 10.24 12.525 0.425 -1.223 0.8893
34 0.450 0.550 126.56 2.72 -11.1 118.15 10.87 12.850 0.450 -1.182 0.8814
35 0.475 0.525 141.02 2.48 -11.2 132.27 11.50 13.175 0.475 -1.146 0.8740
36 0.500 0.500 156.25 2.25 -11.3 147.25 12.13 13.500 0.500 -1.113 0.8670
37 0.525 0.475 172.27 2.03 -11.2 163.07 12.77 13.825 0.525 -1.083 0.8605
38 0.550 0.450 189.06 1.82 -11.1 179.75 13.41 14.150 0.550 -1.055 0.8544
39 0.575 0.425 206.64 1.63 -11.0 197.27 14.05 14.475 0.575 -1.031 0.8486
40 0.600 0.400 225.00 1.44 -10.8 215.64 14.68 14.800 0.600 -1.008 0.8432
41 0.625 0.375 244.14 1.27 -10.5 234.86 15.33 15.125 0.625 -0.987 0.8382
42 0.650 0.350 264.06 1.10 -10.2 254.93 15.97 15.450 0.650 -0.968 0.8334
43 0.675 0.325 284.77 0.95 -9.9 275.84 16.61 15.775 0.675 -0.950 0.8289
44 0.700 0.300 306.25 0.81 -9.4 297.61 17.25 16.100 0.700 -0.933 0.8247
45 0.725 0.275 328.52 0.68 -9.0 320.22 17.89 16.425 0.725 -0.918 0.8207
46 0.750 0.250 351.56 0.56 -8.4 343.69 18.54 16.750 0.750 -0.904 0.8169
47 0.775 0.225 375.39 0.46 -7.8 368.00 19.18 17.075 0.775 -0.890 0.8133
48 0.800 0.200 400.00 0.36 -7.2 393.16 19.83 17.400 0.800 -0.878 0.8099
49 0.825 0.175 425.39 0.28 -6.5 419.17 20.47 17.725 0.825 -0.866 0.8067
50 0.850 0.150 451.56 0.20 -5.7 446.03 21.12 18.050 0.850 -0.855 0.8036
51 0.875 0.125 478.52 0.14 -4.9 473.73 21.77 18.375 0.875 -0.844 0.8007
52 0.900 0.100 506.25 0.09 -4.0 502.29 22.41 18.700 0.900 -0.834 0.7980
53 0.925 0.075 534.77 0.05 -3.1 531.69 23.06 19.025 0.925 -0.825 0.7953
54 0.950 0.050 564.06 0.02 -2.1 561.95 23.71 19.350 0.950 -0.816 0.7928
55 0.975 0.025 594.14 0.01 -1.1 593.05 24.35 19.675 0.975 -0.808 0.7904
56 1.000 0.000 625.00 0.00 0.0 625.00 25.00 20.000 1.000 -0.800 0.7881
57 min z = -2.803 0.997
Frontier
25.000
20.000
15.000
Expected Return
10.000
5.000
0.000
0.00 5.00 10.00 15.00 20.00 25.00 30.00
Volatility
Return= rate of Return= rate of
price + return price + return
TABLE. Two stocks: t Year price dvd dvd Xt price dvd dvd Yt
price series, 0 1955 9 1 10 45 5 50
returns, 1 1956 14 1 15 50.0 49 5 54 8.0
means, 2 1957 20 1 21 40.0 48 5 53 -1.9
standard devs., 3 1958 19 1 20 -4.8 47 5 52 -1.9
correlation 4 1959 19 1 20 0.0 52 5 57 9.6
5 1960 20 1 21 5.0 55 5 60 5.3
Share prices 6 1961 21 1 22 4.8 59 5 64 6.7
not adjusted 7 1962 22 1 23 4.5 63 5 68 6.3
for splits. 8 1963 20 1 21 -8.7 68 5 73 7.4
9 1964 26 1 27 28.6 74 5 79 8.2
Stock A (risky): 10 1965 23 2 25 -7.4 81 5 86 8.9
price series Pt 11 1966 33 2 35 40.0 86 5 91 5.8
returns Xt 12 1967 47 2 49 40.0 93 5 98 7.7
13 1968 57 3 60 22.4 95 10 105 7.1
Stock B (conservative): 14 1969 69 3 72 20.0 103 10 113 7.6
price series Qt 15 1970 45 3 48 -33.3 110 12 122 8.0
returns Yt 16 1971 42 3 45 -6.3 123 12 135 10.7
17 1972 27 3 30 -33.3 129 12 141 4.4
18 1973 19 3 22 -26.7 142 12 154 9.2
19 1974 18 3 21 -4.5 162 12 174 13.0
20 1975 27 3 30 42.9 173 12 185 6.3
21 1976 41 3 44 46.7 168 12 180 -2.7
22 1977 61 3 64 45.5 177 12 189 5.0
23 1978 90 5 95 48.4 189 12 201 6.3
24 1979 126 5 131 37.9 202 12 214 6.5
25 1980 175 5 180 37.4 215 12 227 6.1
26 1981 238 5 243 35.0 230 12 242 6.6
27 1982 323 10 333 37.0 246 12 258 6.6
28 1983 434 10 444 33.3 263 12 275 6.6
29 1984 610 10 620 39.6 253 40 293 6.5
30 1985 775 25 800 29.0 270 40 310 5.8
31 1986 1061 50 1111 38.9 300 40 340 9.7
32 1987 1184 50 1234 11.1 330 40 370 8.8
33 1988 1517 50 1567 27.0 350 40 390 5.4
34 1989 2142 80 2222 41.8 374 40 414 6.2
35 1990 1487 80 1567 -29.5 434 40 474 14.5
36 1991 2122 100 2222 41.8 467 40 507 7.0
37 1992 2655 100 2755 24.0 499 40 539 6.3
38 1993 3356 100 3456 25.4 533 40 573 6.3
39 1994 3840 200 4040 16.9 577 40 617 7.7
40 1995 4367 200 4567 13.0 621 40 661 7.1
41 1996 4689 200 4889 7.1 707 40 747 13.0
42 1997 5820 280 6100 24.8 753 40 793 6.2
43 1998 7377 400 7777 27.5 789 40 829 4.5
44 1999 9054 500 9554 22.8 838 40 878 5.9
45 2000 10400 1000 11400 19.3 908 40 948 8.0
46 2001 13020 1000 14020 23.0 958 40 998 5.3
mean 19.5 mean 6.8
std.dev.: 22.8 std.dev. 3.2
Correlation: -0.35