MIFI 563_MATHEMATICS FOR FINANCE AND INVESTMENT
ASSIGNMENT TWO
Question one
I.
Earning per share of Coastal Bank and
A&B Bank
7
6
5
4
Earning per share of
Coastal Bank and A&B
Bank
3
2
1
0
0
1
2
3
From the scatter plot there is a positive relationship between the earnings per share of
the two banks.
II.
The correlation coefficient (r) = 0.84
From the data the Correlation coefficient is 0.84 which indicate a strong positive
linear relationship between earning per share of A & B Bank and Coastal Bank.
Thus, as A & B Bank’s earnings per share increases so does Coastal Bank
earnings per share also increase.
III.
The regression model computed resulted in a P value of 0.00066 which is less
the significant level of 0.05. This means that the null hypothesis that there is no
relationship between the earnings per share of A&B bank and Coastal bank is
rejected. Therefore there is a statistical significant relationship between the
earning per share of A & B Bank and Coastal Bank.
IV.
Earnings per share of Coastal bank = -0.637+0.426(A&B bank). From this, if the
earnings for A&B bank is 3.2 then we can predict that the earnings per share of
Coastal Bank will be 0.73. This means that if we increase A&B bank earnings by
3.2 unit it will lead to increase of 0.73 earnings of Coastal bank shares
V.
The coefficient of determination for the model is 0.7024. This means that up to
70% of the variation in the earnings of Coastal bank is determined or explained
by A&B bank earnings per share.
Question Two
0.2
0.3 r
0.5
W
I.
II.
r*w
0.24 0.048
0.51 0.153 V
0.37 0.185
0.386
wT*V wT*V*w
0.06 0.05 0.01 0.033
0.0065
0.05 0.2 0.03 0.086 0.025725
0.01 0.03 0.02 0.022 0.011125
0.04335
The expected portfolio return is =wT*r=0.386
The standard deviation is =√ wT*V*w=√.04335=.20821
Question Three
I.
II.
The four unknown variables are the percentage associated with each investment type
and these are:
a. Percentage of Bonds (Variable B)
b. Percentage of CD’s (Variable C)
c. Percentage of Mutual funds (Variable M)
d. Percentage of Bonds (Variable B)
The four equations associated with each investment are as follows:
B+C+M+A=100
B+C=20
0.8B+0C+1.2M+2A=2
5.40B+4.80C+7.60M+9.60A=8
III.
The percentage of each investment are as follows:
1. Bonds
2. CDs
3. Mutual Funds
4. Aggressive stocks
Total
329.2857
-309.286
526.7857
-446.786
100