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- w_m) ´ .03 + w_m ´ .1874

w_m = 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.