Portfolio Risk and Correlation Impact

The assignment analyzes the effect of various correlation levels (0.15, +0.95) on a hypothetical portfolio consisting of two stocks: Stock D and Stock E. It calculates the actual risk of each stock based on their individual risks and investment percentages. The impact of negative correlation is also considered. The results demonstrate how different correlations significantly influence the overall portfolio risk.

Running Head: FINANCE
Finance
Name of the Student:
Name of the University:
Authors Note:

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Table of Contents
Answer to question 1:......................................................................................................................3
Answer to question 2:......................................................................................................................8
Answer to question 3:......................................................................................................................8
References:....................................................................................................................................13

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Answer to question 1:
Calculation of equivalent annual rate of interest earnings for the available projects:
Project A:
Annual interest earnings rate from project A is to be calculated using the following formula:
Assuming the principal amount of investment of $100.00. The Interest earnings over the period
of 10 years @ 11.56% per annum compounded annually will be calculated using the following
formula:
Year 1 = 100 X 111.56% = 111.56 – 100.00 = 11.56
Accordingly, the total interest earnings from the project A shall be as following:
Year 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00
100.00 111.56 124.46 138.84 154.89 172.80 192.78 215.06 239.92 267.66 298.60
Total interest earnings over the 10 years period = 298.60 – 100.00 = 198.60
Average interest earnings per year = 198.60 / 10 years = 19.86
Equivalent Annualized rate of interest earnings = 19.86 X 100 / 100 = 19.86% (Anderson et
al. 2015)
Project B:
The interest earning rate for the project is 12% per annum to be compounded monthly. Using the
following formula let us calculate the annualized rate of interest earnings for the project.

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Assuming the principal at $100.00, the annualized interest earning rate would be calculated using
the following formula:
Interest earning per month will be:
(100.00 X 12%) X 1/12 = 1.00
Accordingly, the annualized interest earning rate would be:
Month 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000
100.00 1.0000 1.0100 1.0201 1.0303 1.0406 1.0510
Month 7.0000 8.0000 9.0000
10.000
0 11.0000 12.0000
1.0615 1.0721 1.0829 1.0937 1.1046 1.1157
Annualized interest earnings rate would be:
(1+1.01+1.0201+1.0303+1.0406+1.0510+1.0615+1.0721+1.0829+1.0937+1.1046+1.1157)) =
12.68% per annum
Assuming the principal amount of investment of $100.00. The Interest earnings over the period
of 10 years @ 12.68% per annum compounded annually will be calculated using the following
formula:
Year 1 = 100 X 112.68% = 112.68 – 100.00 = 12.68
Accordingly, the total interest earnings from the project B shall be as following:
Year

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1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00
100.00 112.68 126.97 143.07 161.21 181.65 204.68 230.64 259.88 292.83 329.97
Total interest earnings over the 10 years period = 329.97 – 100.00 = 229.97
Average interest earnings per year = 229.97 / 10 years = 22.997
Equivalent Annualized rate of interest earnings = 22.997 X 100 / 100 = 22.99%
Project C:
Assuming the principal at $100.00, the annualized interest earning rate would be calculated using
the following formula:
Interest earning per month will be:
(100.00 X 5%) X 1/6 = 0.833
The annualized rate of interest earning will be as following:
Month 1 2 3 4 5 6
100
0.83333
3
0.84027
8 0.84728
0.85434
1 0.86146
0.86863
9
Month 7 8 9 10 11 12
0.87587
8
0.88317
7
0.89053
7
0.89795
8
0.90544
1
0.91298
6
(Miles 2015)
Annualized interest earnings rate would be:
(0.833+0.840+0.847+0.854+0.861+0.868+0.876+0.883+0.890+0.898+0.905+0.913) = 10.47%
per annum

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Assuming the principal amount of investment of $100.00. The Interest earnings over the period
of 10 years @ 10.47% per annum compounded annually will be calculated using the following
formula:
Year 1 = 100 X 110.47% = 110.47 – 100.00 = 10.47
Accordingly, the total interest earnings from the project C shall be as following:
Year 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00
100.00 110.47 122.04 134.81 148.93 164.52 181.75 200.78 221.80 245.02 270.67
Total interest earnings over the 10 years period = 270.67 – 100.00 = 170.67
Average interest earnings per year = 170.67 / 10 years = 17.067
Equivalent Annualized rate of interest earnings = 17.067 X 100 / 100 = 17.07%
Project D:
Annual rate of interest earning from project D is = 3.26 X 4 = 13.04%
Assuming the principal amount of investment of $100.00. The Interest earnings over the period
of 10 years @ 13.04% per annum compounded annually will be calculated using the following
formula:
Year 1 = 100 X 113.04% = 113.04 – 100.00 = 13.04
Accordingly, the total interest earnings from the project D shall be as following:
Year 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00
100.00 113.04 127.78 144.44 163.28 184.57 208.64 235.84 266.60 301.36 340.66

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Total interest earnings over the 10 years period = 340.66 – 100.00 = 240.66
Average interest earnings per year = 240.66 / 10 years = 24.066
Equivalent Annualized rate of interest earnings = 24.066 X 100 / 100 = 24.07% (Turner 2016)
Project D should be selected as the interest earnings from the project is highest at equivalent
annual rate of interest of 24.07%. Thus, the management if only has the option of making
investment in only one of the above four alternative investment proposals then the management
shall invest the money on project D as the rate of interest earning from the project is higher than
all the other projects (Titman and Martin 2014).
Part (ii):
Let us first have the relevant data of equivalent annual interest earnings rate of all the four
projects to assess the projects which have met the organizational criterion of investment:
Project Equivalent annual interest earnings rate
A 19.86%
B 22.99%
C 17.07%
D 24.07%
Since all the projects have a higher rate of interest earnings than 12.50%, i.e. conditional
rate of return to be earned by investment proposals for making investment, the management
should invest in all the four available projects in front of it.

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Answer to question 2:
Project E F G H
Required investment ($) 600,000.00 560,000.00 960,000.00 542,000.00
Down payment 0.20 0.10 0.40 -
Down payment ($) 120,000.00 56,000.00 384,000.00 -
(A) Amount to be financed by
loan 480,000.00 504,000.00 576,000.00 542,000.00
Borrowed rate
6% per
annum
4.2% per
annum
6.2% per
annum
5.6% per
annum
Monthly installment to repay the
loan ($) 6,000.00 5,800.00 8,800.00 7,100.00
(B) Annual installment 72,000.00 69,600.00 105,600.00 85,200.00
Factor for duration (A / B) 6.67 7.24 5.45 6.36
Loan repayment duration
(Approx.) based on the Present
Value table of appropriate
borrowed rate. 9 Years 9 Years 7 Years 8 Years
Thus, considering the management will invest in the project which will have the shortest
repayment duration of loan hence, project G should be selected and invested in by the
management as the loan repayment duration for the project is 7 years which is the shortest
amongst the four probable investment projects.
Answer to question 3:
Part (i):
According to normal dividend model the value of a share can be calculated by using the
following formula:
Value of a share = Dividend paid / Cost of capital

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Value of stock A = $8.56 / 0.12 = $71.33
According to Gordon’s dividend growth model the value of a share is calculated by using the
following formula:
Value of a share = Dividend paid / Cost of capital – growth rate
Value of stock B = $6.23 / 0.12 – 0.04 = $77.88
According to normal dividend model the value of a share can be calculated by using the
following formula:
Value of a share = Dividend paid / Cost of capital
Expected dividend at the end of 5th year:
Year Formula Yearend dividend
1.00 (6X109%) 6.54
2.00 (6.54X109%) 7.13
3.00 (7.13X109%) 7.77
4.00 (7.77X109%) 8.47
5.00 (8.47X109% 9.23
Value of stock C = $9.23 / 0.12 = $76.92
Since, all the shares have been offered at $80.00 none of the shares are valued above the prices at
which they are being offered by the broker at present. However, in case it is essential to acquire
one of the stock at any cost then stock B should be purchased as it has the highest value at

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$77.88 per share. However, the recommendation to the investor should be to not make any
investment in any of the stocks as none of the stock have been valued above the cost at which
they are being offered by the broker (Arrow and Lind 2014).
Part (ii):
Investment
Amount
($)
% of
investment Return Risk
Coefficien
t of
variation Rank
Stock D 325,000.00 65.00 14% 16% 1.14 1
Stock E 175,000.00 35.00 18% 24% 1.33 2
Note: Coefficient of variation is calculated by using the following formula:
= Standard deviation / Expected return
Since, the coefficient of variation is lower for stock D it shall be preferred by the management
over stock E.
Part (iii):
Diversification is an important element in maintaining a portfolio by managing the risk and
returns effectively. It is often alluring for the investors to invest in a single stock which is
providing higher return over the other stocks however, in case any disaster struck with the stock
of such company then the whole investment portfolio of an investor would be in jeopardy. Thus,
to manage the risk and returns effectively it is essential to use diversification strategy. The reason
the investor have invested in both Stock D and E instead of only E which has a higher return
compare to stock D is to manage the risk along with the return. Though the expected return of

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stock D is lower compare to stock E yet the investor has decided to make investment in stock D
as it has much lower rate of interest compare to stock E, standard deviation being 16% compare
to 24% of stock E. The overall risks associated with the investment portfolio have subsequently
reduced due to combining of investment in stock D and E (Peppard and Ward 2016).
Part (iv):
When correlation is – 0.89
Investment
% of
investment Risk
Actual risk
(Risk X %
of
investment) Correlation
Risk (Actual risk +
negative correlation
impact)
Stock D 65.00 16% 0.10 (0.89) 0.1966
Stock E 35.00 24% 0.08 (0.89) 0.1588
Risk of portfolio 0.36
When correlation is 0.15
Investment
% of
investment Risk
Actual risk
(Risk X %
of
investment) Correlation
Risk (Actual risk +
negative correlation
impact)
Stock D 65.00 16% 0.10 0.15 0.0884
Stock E 35.00 24% 0.08 0.15 0.0714
Risk of portfolio 0.16
When correlation is +0.95

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Investment
% of
investment Risk
Actual risk
(Risk X %
of
investment) Correlation
Risk (Actual risk +
negative correlation
impact)
Stock D 65.00 16% 0.10 0.95 0.0052
Stock E 35.00 24% 0.08 0.95 0.0042
Risk of portfolio 0.01
The above calculations have made the impact of different correlations on the investment
portfolio risks very clear (Hammond et al. 2015).

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References:
Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D. and Cochran, J.J., 2015. An
introduction to management science: quantitative approaches to decision making. Cengage
learning.
Arrow, K.J. and Lind, R.C., 2014. Uncertainty and the evaluation of public investment
decisions. Journal of Natural Resources Policy Research, 6(1), pp.29-44.
Hammond, J.S., Keeney, R.L. and Raiffa, H., 2015. Smart choices: A practical guide to making
better decisions. Harvard Business Review Press.
Miles, L.D., 2015. Techniques of value analysis and engineering. Miles Value Foundation.
Peppard, J. and Ward, J., 2016. The strategic management of information systems: Building a
digital strategy. John Wiley & Sons.
Titman, S. and Martin, J.D., 2014. Valuation. Pearson Higher Ed.
Turner, R., 2016. Gower handbook of project management. Routledge.

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