FINS5517_APPLIED PORTFOLIO MANAGEMENT & MODELLING_2005 Semester 2_w2_Ben78
Benninga Chapter 5 Problem 4
r w s
x10%0.30.30.02-0.05
y12%0.20.020.40.06
z14%0.5-0.050.060.6
0.03
0.024
0.07
Matrix algebra
r(p)0.1240.124
sum(w)1
v(p)0.1924=MMULT(TRANSPOSE(C2:C4),MMULT(E2:G4,C2:C4))
s(p)0.438634
TRANSPOSE(C5:C7)MMULT(E5:G cov(1,2)0.1106=MMULT(G18:I18,J17:J1
long cov(1,2)0.11060.153
0.30.20.50.176
0.059
w v(p)s(p)r(p) given x y z
-10.36120.6009990.10.70.6-0.3
-0.90.32920.573760.10120.680.58-0.26
-0.80.299680.547430.10240.660.56-0.22
-0.70.272640.5221490.10360.640.54-0.18
-0.60.248080.4980760.10480.620.52-0.14 Array -0.50.2260.4753950.1060.60.5-0.1
-0.40.20640.4543130.10720.580.48-0.06
-0.30.189280.4350630.10840.560.46-0.02
-0.20.174640.41790.10960.540.440.02
-0.10.162480.4030880.11080.520.420.06
-1.4E-160.15280.3908960.1120.50.40.1
0.10.14560.3815760.11320.480.380.14
0.20.140880.375340.11440.460.360.18
0.30.138640.3723440.11560.440.340.22
0.40.138880.3726660.11680.420.320.26
0.50.14160.3762980.1180.40.30.3
0.60.14680.3831450.11920.380.280.34
0.70.154480.3930390.12040.360.260.38
0.80.164640.4057590.12160.340.240.42
0.90.177280.4210460.12280.320.220.46
10.19240.4386340.1240.30.20.5
1.10.210.4582580.12520.280.180.54
1.20.230080.4796670.12640.260.160.58
1.30.252640.5026330.12760.240.140.62
1.40.277680.5269540.12880.220.120.66
1.50.30520.5524490.130.20.10.7
1.60.33520.5789650.13120.180.080.74
1.70.367680.6063660.13240.160.060.78
1.80.402640.6345390.13360.140.040.82
1.90.440080.6633850.13480.120.020.86
20.480.692820.1360.100.9
2.10.52240.7227720.13720.08-0.020.94
2.20.567280.753180.13840.06-0.040.98
2.30.614640.783990.13960.04-0.06 1.02
2.40.664480.8151560.14080.02-0.08 1.06
2.50.71680.846640.1420-0.1 1.1
2.60.77160.8784080.1432-0.02-0.12 1.14
2.70.828880.9104280.1444-0.04-0.14 1.18
2.80.888640.9426770.1456-0.06-0.16 1.22
2.90.950880.9751310.1468-0.08-0.18 1.26
3 1.0156 1.007770.148-0.1-0.2 1.3
3.1 1.0828 1.0405770.1492-0.12-0.22 1.34
3.2 1.15248 1.0735360.1504-0.14-0.24 1.38
3.3 1.22464 1.1066350.1516-0.16-0.26 1.42
3.4 1.29928 1.139860.1528-0.18-0.28 1.46
3.5 1.3764 1.1732010.154-0.2-0.3 1.5
3.6 1.456 1.2066480.1552-0.22-0.32 1.54
3.7 1.53808 1.2401940.1564-0.24-0.34 1.58
3.8 1.62264 1.2738290.1576-0.26-0.36 1.62
3.9 1.70968 1.3075470.1588-0.28-0.38 1.66
4 1.7992 1.3413430.16-0.3-0.4 1.7
4.1 1.8912 1.3752090.1612-0.32-0.42 1.74
4.2 1.98568 1.4091420.1624-0.34-0.44 1.78
4.3 2.08264 1.4431350.1636-0.36-0.46 1.82
Benninga Chapter 5 Problem 4
with efficient portfolios
r w s
x10%0.8990380.30.02-0.05
y12%0.2019230.020.40.06
z14%-0.10096-0.050.060.6
0.089904v(x)v(y)v(z)
0.0242310.5477230.6324560.774597
-0.01413
r(p)0.1
sum(w)1
v(p)0.278798=MMULT(TRANSPOSE(C2:C4),MMULT(E2:G4,C2:C4))
s(p)0.528013
cov(1,2)-0.00036MMULT(G18:I18,J17:J19)TRANSPOSE(C5:C7)MMULT(E5:G
-0.00036
-0.000360.8990380.201923-0.100960.179808
0.359976
w v(p)s(p)r(p) efficient x y z -0.60.7919830.8899340.1480.620.52-0.14 -0.550.7333660.8563680.14650.610.51-0.12 -0.50.6774970.8231020.1450.60.5-0.1 -0.450.6243750.7901740.14350.590.49-0.08 -0.40.5739990.7576280.1420.580.48-0.06
00.2698920.5195110.130.50.40.1
0.050.244240.4942070.12850.490.390.12
0.10.2213350.4704630.1270.480.380.14
0.150.2011780.4485290.12550.470.370.16
0.20.1837670.4286810.1240.460.360.18
0.250.1691040.4112220.12250.450.350.2
0.30.1571870.3964690.1210.440.340.22
0.350.1480180.3847310.11950.430.330.24
0.40.1415960.3762920.1180.420.320.26
0.450.137920.3713760.11650.410.310.28
0.50.1369920.3701250.1150.40.30.3
0.550.1388110.3725740.11350.390.290.32
0.60.1433770.3786510.1120.380.280.34
0.650.150690.3881880.11050.370.270.36
0.70.160750.4009360.1090.360.260.38
0.750.1735570.4166020.10750.350.250.4
0.80.1891110.4348690.1060.340.240.42
0.850.2074120.4554250.10450.330.230.44
0.90.228460.4779750.1030.320.220.46
0.950.2522560.5022510.10150.310.210.48
10.2787980.5280130.10.30.20.5
1.050.3080870.5550560.09850.290.190.52
1.10.3401240.5832010.0970.280.180.54
1.150.3749070.6122970.09550.270.170.56
1.20.4124380.6422130.0940.260.160.58
1.250.4527160.6728410.09250.250.150.6
1.30.495740.7040880.0910.240.140.62
1.350.5415120.7358750.08950.230.130.64
1.40.5900310.7681350.0880.220.120.66
1.450.6412970.800810.08650.210.110.68
1.50.6953090.8338520.0850.20.10.7
1.550.7520690.8672190.08350.190.090.72
1.60.8115760.9008750.0820.180.080.74
1.650.873830.9347890.08050.170.070.76
1.70.9388320.9689330.0790.160.060.78
1.75 1.00658 1.0032840.07750.150.050.8
1.8 1.077075 1.0378220.0760.140.040.82
1.85 1.150317 1.0725280.07450.130.030.84
1.9 1.226307 1.1073870.0730.120.020.86
1.95 1.305043 1.1423850.07150.110.010.88
2 1.386526 1.1775090.070.100.9 2.05 1.470757 1.2127480.06850.09-0.010.92
r w s
x10%0.50.30.02-0.05 y12%0.40.020.40.06 z14%0.1-0.050.060.6
0.05
0.048
0.014
r(p)0.112
sum(w)1
v(p)0.1528=MMULT(TRANSPOSE(C2:C4),MMULT(E2:G4,C2:C4)) s(p)0.390896
E5:G7,L5:L7)
r w s
x10%0.0697120.30.02-0.05 y12%0.3605770.020.40.06 z14%0.569712-0.050.060.6
0.006971
0.043269
0.07976
r(p)0.13
sum(w)1
v(p)0.269892=MMULT(TRANSPOSE(C2:C4),MMULT(E2:G4,C2:C4)) s(p)0.519511
E5:G7,L5:L7)