The optimal combination of Kalama and Adelphia is 53% and 47%, respectively. This results in a risky
Question:
The optimal combination of Kalama and Adelphia is 53% and 47%, respectively. This results in a risky portfolio return of 18.74% and a standard deviation of 17.65%. As Andrea wants to earn a return of 19%, she will need to borrow money at the risk-free rate.
I know the answers are correct I just don't know how they figure those exact numbers (53% and 47%) to be the optimal combination out of 98 possibilities.
Info/questions:
Andrea Corbridge is considering forming a portfolio consisting of Kalama Corp. and Adelphia Technologies. The two corporations have a correlation of -0.1789, and their expected returns and standard deviations are as follows:
Kalama Corp. | Adelphia Technologies | |
Expected return (%) | 14.86 | 23.11 |
Standard Deviation (%) | 23.36 | 31.89 |
Calculate the frontier for all possible investment combinations of Kalama Corp. and Adelphia Technologies (from 0% to 100%, in 1% increments). Determine the optimal risky portfolio if the risk-free rate is 3%.
Andrea has $50,000 and wants to earn a 19% expected return on her investment. What is the optimal manner in which to structure her portfolio-both in dollar amounts and in weights relative to her $50,000-based on the preceding information?
Answers
#1
Weight/Kalama | Weight/Adelphia | Standard Deviation | Expected Return |
99% | 1% | 23.07% | 14.94% |
98% | 2% | 22.79% | 15.03% |
97% | 3% | 22.51% | 15.11% |
96% | 4% | 22.23% | 15.19% |
95% | 5% | 21.96% | 15.27% |
94% | 6% | 21.70% | 15.36% |
93% | 7% | 21.44% | 15.44% |
92% | 8% | 21.18% | 15.52% |
91% | 9% | 20.94% | 15.60% |
90% | 10% | 20.69% | 15.69% |
89% | 11% | 20.46% | 15.77% |
88% | 12% | 20.23% | 15.85% |
87% | 13% | 20.00% | 15.93% |
86% | 14% | 19.78% | 16.02% |
85% | 15% | 19.57% | 16.10% |
84% | 16% | 19.37% | 16.18% |
83% | 17% | 19.18% | 16.26% |
82% | 18% | 18.99% | 16.35% |
81% | 19% | 18.81% | 16.43% |
80% | 20% | 18.64% | 16.51% |
79% | 21% | 18.47% | 16.59% |
78% | 22% | 18.32% | 16.68% |
77% | 23% | 18.17% | 16.76% |
76% | 24% | 18.03% | 16.84% |
75% | 25% | 17.90% | 16.92% |
74% | 26% | 17.78% | 17.01% |
73% | 27% | 17.67% | 17.09% |
72% | 28% | 17.58% | 17.17% |
71% | 29% | 17.49% | 17.25% |
70% | 30% | 17.41% | 17.34% |
69% | 31% | 17.34% | 17.42% |
68% | 32% | 17.28% | 17.50% |
67% | 33% | 17.23% | 17.58% |
66% | 34% | 17.19% | 17.67% |
65% | 35% | 17.16% | 17.75% |
64% | 36% | 17.14% | 17.83% |
63% | 37% | 17.14% | 17.91% |
62% | 38% | 17.14% | 18.00% |
61% | 39% | 17.16% | 18.08% |
60% | 40% | 17.18% | 18.16% |
59% | 41% | 17.22% | 18.24% |
58% | 42% | 17.26% | 18.33% |
57% | 43% | 17.32% | 18.41% |
56% | 44% | 17.39% | 18.49% |
55% | 45% | 17.47% | 18.57% |
54% | 46% | 17.55% | 18.66% |
53% | 47% | 17.65% | 18.74% |
52% | 48% | 17.76% | 18.82% |
51% | 49% | 17.87% | 18.90% |
50% | 50% | 18.00% | 18.99% |
49% | 51% | 18.14% | 19.07% |
48% | 52% | 18.28% | 19.15% |
47% | 53% | 18.43% | 19.23% |
46% | 54% | 18.60% | 19.32% |
45% | 55% | 18.77% | 19.40% |
44% | 56% | 18.94% | 19.48% |
43% | 57% | 19.13% | 19.56% |
42% | 58% | 19.32% | 19.65% |
41% | 59% | 19.53% | 19.73% |
40% | 60% | 19.73% | 19.81% |
39% | 61% | 19.95% | 19.89% |
38% | 62% | 20.17% | 19.98% |
37% | 63% | 20.40% | 20.06% |
36% | 64% | 20.64% | 20.14% |
35% | 65% | 20.88% | 20.22% |
34% | 66% | 21.12% | 20.31% |
33% | 67% | 21.38% | 20.39% |
32% | 68% | 21.64% | 20.47% |
31% | 69% | 21.90% | 20.55% |
30% | 70% | 22.17% | 20.64% |
29% | 71% | 22.44% | 20.72% |
28% | 72% | 22.72% | 20.80% |
27% | 73% | 23.00% | 20.88% |
26% | 74% | 23.29% | 20.97% |
25% | 75% | 23.58% | 21.05% |
24% | 76% | 23.88% | 21.13% |
23% | 77% | 24.18% | 21.21% |
22% | 78% | 24.84% | 21.30% |
21% | 79% | 24.79% | 21.38% |
20% | 80% | 25.10% | 21.46% |
19% | 81% | 25.41% | 21.54% |
18% | 82% | 25.73% | 21.63% |
17% | 83% | 26.05% | 21.71% |
16% | 84% | 26.38% | 21.79% |
15% | 85% | 26.70% | 21.87% |
14% | 86% | 27.03% | 21.96% |
13% | 87% | 27.36% | 22.04% |
12% | 88% | 27.70% | 22.12% |
11% | 89% | 28.04% | 22.20% |
10% | 90% | 28.38% | 22.29% |
9% | 91% | 28.72% | 22.37% |
8% | 92% | 29.06% | 22.45% |
7% | 93% | 29.41% | 22.53% |
6% | 94% | 29.76% | 22.62% |
5% | 95% | 30.11% | 22.70% |
4% | 96% | 30.46% | 22.78% |
3% | 97% | 30.82% | 22.86% |
2% | 98% | 31.17% | 22.95% |
1% | 99% | 31.53% | 23.03% |
#2
The optimal combination of Kalama and Adelphia is 53% and 47%, respectively. This results in a risky portfolio return of 18.74% and a standard deviation of 17.65%. As Andrea wants to earn a return of 19%, she will need to borrow money at the risk-free rate.
0.19 = (1- wm) ´ .03 + wm ´ .1874
wm = 101.65%
Of the $50,000 Andrea has, she should place 101.65%, or $50,825.92 in the optimal portfolio of Kalama and Adelphia. Thus, she needs to borrow $825.92 at the risk-free rate.
Expert Answer:
rf 3 Rk 1486 Ra 2311 SDk 2336 Sda 3189 wKalama wAdelphia E r Portfolio Std Dev 99 1 14942500 230715 98 2 15025000 227873 97 3 15107500 225077 96 4 151... View the full answer
