Portfolio Risk and Return Analysis

This assignment involves calculating the beta for a portfolio consisting of shares in companies like CBA and RIO. It then compares these betas to determine which security offers the lowest risk and highest return. The calculations were made using specific formulas, with results indicating that investing in RIO would be the most beneficial due to its lower risk and higher returns.

Financial Mathematics

Table of Contents
Introduction......................................................................................................................................1
Question 1........................................................................................................................................1
A).................................................................................................................................................1
B). ...............................................................................................................................................1
C). ...............................................................................................................................................1
D).................................................................................................................................................2
E). ...............................................................................................................................................2
Question 2........................................................................................................................................2
A: ................................................................................................................................................2
B): ...............................................................................................................................................3
Question 3........................................................................................................................................3
1...................................................................................................................................................3
2...................................................................................................................................................6
3...................................................................................................................................................8
4...................................................................................................................................................8
6...................................................................................................................................................9
7...................................................................................................................................................9
8...................................................................................................................................................9
Conclusion.....................................................................................................................................10
References .....................................................................................................................................11

Introduction
In the business there are various decisions which will have to be made and for that
different calculations should be made. All of that will be covered under business mathematics.
The main aspect which is involved in this is calculations which are made in terms of fianancial
factors. In this report different values will be identified with the use of several fianacial methods
which are present in relation to financial management (Cole, Paulson and Shastry, 2016). There
are calculations which will be made in respect of the manner in which present values and other
calculations about annuity will be made. Also the concept of capital asset pricing model will be
used by that the cost of capital will be determined. The calculation for the returns which will be
earned on monthly basis will be identified that will further be used to know the average rate of
return made by the organisation. All of these will be understood with the help of solutions which
are provided in the report provided below.
Question 1
A).
B).
Couple invest their lottery amount of 1,80,000. for the 4 years with the intention to get
the equal monthly amount for 180 months. Hence, he invested their $180000 for the 4 years.
Then they will get of $262538 after investing of $180000 for 4 years. They will get of $1464.1
for 180 equal payment.
Future Value= Present value( 1.10)^4
Fv=180000(1.1)^4=$262538.
C).
Future Value of annuity= Present value[(1+r)^number of year-1]
Rate of return
Fv=4000[(1+0.05)^10-1]
0.05
In December 2017, She will get $50311.55.
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D).
Present value= Annuity[(1+0.06)^10-1] * (1.06)^10
0.06
20000[(1.06)^10-1]
0.06 (1.06)^10
=$1,47,200
Hence, Mary tone will take the lump sum payment of $1,50,000.
E).
Present value= Annuity/ Rate- Growth=hence cost of annuity = 1000/.12-.10= $50000.
Question 2
A:
The concept of shareholder wealth maximisation is based on the rule which states that the
direct operating goals and the objectives of a public business firm and that should help to gain
maximum return on equity. Shareholder wealth is said to be present values of what is expected
future return will be gain to its owners of the firm (Chavez-Demoulin and McGill, 2012).
Generally those return which are made in terms of periodic form of dividend and continued from
the sale of inventory. Shareholder is associated with the business context which is based on that
concepts that ultimately influence company success up to the extent to enrich shareholder
interest. There are various aspect of business which are used by the company in order to generate
more profit and make the company profitable in coming future. These are:
 Wealth maximisation: The main objectives of this concept is to increase the market
value and share as well. Another is to maximise net present value of shareholder that are
related with company growth. Under this company generated profit in terms of cash
flows. The advantage of wealth maximisation is to create shareholder interest as well as
creditors interest and so on. It also ensures that company should work in to create
effective return to the shareholders through building reserves for growth and maintain
financial discipline in an organisation.
 Maximisation of profit to the notion: It is associated with the profit that is earned by an
organisation during the period of time. It measure goals which are implies that
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investment, financing and making effective decision that should generated maximum
profit to the organisation. There are some advantages that are related with profit
maximisation are to create effective decision making process, utilisation of resources in
most effective manner. Although it said to be unrealistic and difficult but can be more
effective in most of the situations.
B):
Risk aversion is a statement of an investor who faced with two situation of investments
with a similar return but they are going to select that risk which is very less. It is said to be major
factors that are based on psychology and financial professional (Tsekouras and Tsimikas, 2013).
It is that kind of situation under which people react to a conditions in which there is uncertainty
and has lot of implications. According the statements that risk aversion is states that only those
risk free investments are under taken by the managers which are less risky or generate maximum
profit. According to my opinion it is very true that most of manager of the company are
appointed with the motive to provide that kind of ideas though which company make there
investments in more effective those are having less risks.
There are different types of risk that a manager need to go through in there daily course
of businesses. As the major objective of a manager is to provide right direction to the
investors those are going to invests in our business. So they first of all look in to all the
financial aspects of the company on the basis of that various decision are being made by
investors regarding investments. The risk free rate is a annual return on a assets as any
investments are more risky than the risk free return which is major task of the company.
Risk and return are varies both ways as in every investments that are made by people in
any part of business are highly risky (Tan and Touzi, 2013). To calculate the holding
period formula is: ). So manager need to plan such kind of plan which are generating
more return with minimum risk associated with the company. So risk aversion should be
recommend to the investors in order to make profitable decision in an organisation.
Question 3
1.
Commonw
ealth Bank
3

Date Open Close* Return
28/08/17 77.49 76.68
-
1.04529616
72
01/08/17 83.92 76.68
-
8.62726406
1
01/07/17 82.83 83.73
1.08656283
96
01/06/17 79.5 82.81
4.16352201
26
01/05/17 87.09 79.65
-
8.54288666
9
31/03/17 85.43 87.4
2.30598150
53
28/02/17 81.98 85.91
4.79385215
91
31/01/17 81.66 82.32
0.80822924
32
31/12/16 82.41 81.66
-
0.91008372
77
30/11/16 78.8 82.41
4.58121827
41
31/10/16 72.77 78.65
8.08025285
14
01/10/16 72.94 73.39
0.61694543
46
4

01/09/16 71.62 72.4
1.08908126
22
Rio Tinto
Date Open Close* Return
28/08/17 66.66 66.5
-
0.24002400
24
01/08/17 66.33 66.5
0.25629428
61
01/07/17 63.19 65.79
4.11457509
1
01/06/17 61.9 63.27
2.21324717
29
01/05/17 60.44 62.81
3.92124420
91
31/03/17 60.1 60.44
0.56572379
37
28/02/17 61.25 60.46
-
1.28979591
84
31/01/17 67 61.99
-
7.47761194
03
31/12/16 59.9 66.68
11.3188647
746
30/11/16 58.45 59.9 2.48075278
5

02
31/10/16 54.02 57.75
6.90485005
55
01/10/16 51.6 54.18 5
01/09/16 47.3 51.61 9.11205074
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-10
-5
0
5
10
15
Commonwealth Bank Return
Rio Tinto Return
2.
Commonw
ealth Bank
Date Open Close* Return
28/08/17 77.49 76.68
-
1.04529616
72
01/08/17 83.92 76.68
-
8.62726406
1
01/07/17 82.83 83.73
1.08656283
96
01/06/17 79.5 82.81 4.16352201
6

26
01/05/17 87.09 79.65
-
8.54288666
9
31/03/17 85.43 87.4
2.30598150
53
28/02/17 81.98 85.91
4.79385215
91
31/01/17 81.66 82.32
0.80822924
32
31/12/16 82.41 81.66
-
0.91008372
77
30/11/16 78.8 82.41
4.58121827
41
31/10/16 72.77 78.65
8.08025285
14
01/10/16 72.94 73.39
0.61694543
46
01/09/16 71.62 72.4
1.08908126
22
Average
return
0.70000957
98
Rio Tinto
Date Open Close* Return
28/08/17 66.66 66.5 -
0.24002400
7

24
01/08/17 66.33 66.5
0.25629428
61
01/07/17 63.19 65.79
4.11457509
1
01/06/17 61.9 63.27
2.21324717
29
01/05/17 60.44 62.81
3.92124420
91
31/03/17 60.1 60.44
0.56572379
37
28/02/17 61.25 60.46
-
1.28979591
84
31/01/17 67 61.99
-
7.47761194
03
31/12/16 59.9 66.68
11.3188647
746
30/11/16 58.45 59.9
2.48075278
02
31/10/16 54.02 57.75
6.90485005
55
01/10/16 51.6 54.18 5
01/09/16 47.3 51.61 9.11205074
Average Return
3.07334758
68
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3.
There is a strong technique to assist fred fried answers, this is the holding period return. This is
the normal period return from income and the assets enhancement over a long period of
time which is expressed like percentage (Hirsa and Neftci, 2013
HPR- [{Income+(end of period value- original value)}/real value]*100
Annualised holding period return: Under this, there is a need to implement the annualised HPR
formula and emphasis the % return in the decimal form. To calculate the Annualised
HPR= [{(HPR+1)^1/T}]-1 where t= number of years.
4.
The expected return by using the Capital asset pricing method is calcualted by using this
formula.
Expected return= Rf+Beta(Rm- Rf)
Here,
Rf= risk free rate return
Rm= Market return
By putting the value, the expected return of the commonwealth bank=
3.25+1.11(7-3.25)= 7.4125
The Rio Tinto company expected rate of return is
3.25+0.95(7-3.25)= 6.8125
6.
security market line is the method in which the risk will be represented in respect of the
stock with reference to the whole market for the particular time (Soner, Touzi and Zhang, 2012).
By this the securities which are risky will be determined with the help of this. In this the market
return and risk free rate will be used and by that the rate will be identified.
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7.
The return that will be earned by the portfolio will be determined on the basis of the
earnings which are made by all the securities which will be involved in that portfolio. The ratio
in which they will have to be maintained will be decided and then the decision will be made in
respect of it. It has been provided that CBA shall occupy 60percent of the share and rest of the
portion will be held by RIO. So according to this portfolio return will be calculated and that has
been provided below:
Portfolio return = return of CBA * 0.6 + return of RIO * .40
= 0.70 *0.6 + 3.07 * 0.40
= 1.648 %
so the return that will be earned by this portfolio is 1.648 percent.
In this beta od portfolio will also be calculated that will be done with the help of beta of
individual stock (Stojanovic, 2012). The calculation will be made for this and by that the risk
which will be involved in the portfolio will be determined as beta is the factor which represntd
the amount of risk involved in any portfolio.
Beta of portfolio = 1.11 * 0.6 + 0.95 * 0.4
= 1.046
8.
From the above calculations which are made it can be seen that among all the securities
which include CBA, RIO and the portfolio the returns which are earned are 0.7 , 3.07 and
1.648 percent and beta is 1.11, 0.95 and 1.046 respectively.so the investment will be
made in RIO as it is having the lowest risk and also the return earned by it is highest so
this will be chosen above all the others.
Conclusion
From the above mentioned report it has been concluded that there are many such aspects
which are involved in the financial management and for that different calculations are
done in the report. It has been determined that the rate at which earnings will be made
shall be identified so that proper evaluation will be made and that will be helpful in
further achievement of growth. The manner in which the amount to be deposited for the
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payment that will have to be made in future is identified with the technique called annuity
approach. The installments are made and calculation in respect of it has been shown
above.
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