ACST 816 Assignment
Question 1
Risk free rate
0.40%
Maximise Sp
0.116802642
ER1
1.50%
SD1
10%
ER2
0.80%
SD2
5%
Covariance
0.20%
Correlation
40%
Possible Portfolio Sets:
Proportion
in Asset 1 (w1)
Proportion
in Asset 2 (w2)
Expected Return (Y-axis)
Standard Deviation (X-axis)
-500%
600%
-2.70%
46.90%
-150%
250%
-0.25%
15.21%
-80%
180%
0.24%
9.35%
-70%
170%
0.31%
8.58%
-60%
160%
0.38%
7.85%
-50%
150%
0.45%
7.16%
-40%
140%
0.52%
6.53%
-30%
130%
0.59%
5.97%
-20%
120%
0.66%
5.51%
-10%
110%
0.73%
5.18%
0%
100%
0.80%
5.00%
10%
90%
0.87%
4.98%
20%
80%
0.94%
5.14%
30%
70%
1.01%
5.45%
40%
60%
1.08%
5.88%
50%
50%
1.15%
6.42%
60%
40%
1.22%
7.04%
70%
30%
1.29%
7.72%
80%
20%
1.36%
8.45%
90%
10%
1.43%
9.21%
100%
0%
1.50%
10.00%
110%
-10%
1.57%
10.81%
120%
-20%
1.64%
11.64%
250%
-150%
2.55%
23.05%
750%
-650%
6.05%
68.78%

Caculating the optimal risky portfolio:
By constructing the Sharpe ratio
Maximise the ratio using the Excel function SOLVER by varying w1, we can get
W1=52% and w2=1-w1=48%.
Or we can use formula to calculate w1 directly,
Which gives the same result w1=52%, w2=48%.
Then we can calculate the expected return and standard deviation of optimal portfolio.
E(Rp)=52%*1.5%+48%*0.8%=1.16%
σ(Rp)=sqrt(w12 σ 12+w22 σ 22+2w1w2Cov)=6.54%
The capital allocation line is a straight line passing through the risk free return on y-axis and the optimal portfolio, which is tangent to the effective frontier line.
Intercept = risk free rate =0.4%
Slope=(1.16%-0.4%)/(6.54%-0)=0.1168
Then CML equation is E(Rp)=0.1168σ+0.004.
The graph is as below:

The set of portfolios of different correlations
Sd when corr= -100%
Sd when corr=-20%
Sd when corr=50%
Sd when corr=100%
0.8

0.632 0.43589 0.2 0.275 0.214 0.13919 0.025 0.17 0.132 0.08544 0.01 0.155 0.12 0.07858 0.015 0.14 0.109 0.07211 0.02 0.125 0.098 0.06614 0.025 0.11 0.087 0.06083 0.03 0.095 0.077 0.05635 0.035 0.08 0.067 0.05292 0.04 0.065 0.058 0.05074 0.045 0.05 0.05 0.05 0.05 0.035 0.044 0.05074 0.055 0.02 0.041 0.05292 0.06 0.005 0.041 0.05635 0.065 0.01 0.045 0.06083 0.07 0.025 0.051 0.06614 0.075 0.04 0.059 0.07211 0.08 0.055 0.069 0.07858 0.085 0.07 0.079 0.08544 0.09 0.085 0.089 0.0926 0.095 0.1 0.1 0.1 0.1 0.115 0.111 0.10759 0.105 0.13 0.122 0.11533 0.11 0.325 0.275 0.2222 0.175 1.075 0.875 0.65144 0.425

Graph is as below:

Question 2
(i) The means and standard deviations:

Average Monthly Return
Standard Deviation
Stock
Barrick
0.70%
10.31%
Stock
Hanson
1.17%
10.00%
Stock
IBM
1.26%
9.39%
Stock
Nokia
2.44%
13.74%
Stock
Telefonos
2.08%
9.09%
Stock
YPF
1.56%
10.34%
US Portfolio
Small-Growth
0.71%
8.03%
US Portfolio
Small-Neutral
1.39%
5.22%
US Portfolio
Small-Value
1.54%
5.03%
US Portfolio
Big-Growth
0.72%
4.83%
US Portfolio
Big-Neutral
1.01%
4.36%
US Portfolio
Big-Value
0.99%
4.39%
Country Port
Australia
1.15%
5.00%
Country Port
Hong Kong
0.79%
7.83%
Country Port
Italy
1.36%
6.33%
Country Port
Japan
0.42%
5.91%
Country Port
Norway
1.40%
6.78%
Country Port
US
0.82%
4.60%
US Riskfree
US Riskfree
0.30%
0.15%

The correlations and covariance:

(ii) ER
Standard Deviation
Australia
1.15%
5.00%
Hong Kong
0.79%
7.83%
Italy
1.36%
6.33%
Japan
0.42%
5.91%
Norway
1.40%
6.78%
US
0.82%
4.60%

Australia
Hong Kong
Italy
Japan
Norway
US
Australia
0.250%
0.239%
0.155%
0.169%
0.221%
0.157%
Hong Kong
0.239%