Finance And Financial Management.

Main Body Word Count: 7402

Finance and Financial Management. Page 1
Main Body Word Count: 8900

TABLE OF CONTENTS

1 INTRODUCTION ........................................................................................................................................... 6
2 FIRST QUESTION ........................................................................................................................................ 7
3 SECOND QUESTION ................................................................................................................................. 11
4 THIRD QUESTION ...................................................................................................................................... 21
5 FOURTH QUESTION .................................................................................................................................. 30
6 CONCLUSION ............................................................................................................................................ 37
7 APPENDIX .................................................................................................................................................. 38
8 WORK CITED ............................................................................................................................................. 42
9 BIBLIOGRAPHY ......................................................................................................................................... 45


TABLE OF FIGURES

Figure 1: Profit and Loss Account (Group.1, 2012) ............................................................................................ 7

Figure 2: Cash Flow Statement (Group.1, 2012) ................................................................................................ 8

Figure 3: Price Variations (Group.1, 2012) ......................................................................................................... 9

Figure 4: Volume of Sales Variations (Group.1, 2012) ....................................................................................... 9

Figure 5: Determinants of Profitability (Group.1, 2012) .................................................................................... 10

Figure 6: Price, Volume, Direct Cost and Investment Variations (Group.1, 2012) ............................................ 10

Figure 7: Price and Earning ratio ...................................................................................................................... 11

Figure 8: P/E Ratio & Stock Price of Burberry (Morningstar, 2012) .................................................................. 12

Figure 9: P/E Ratio and Stock Price of Easy Jet (Morningstar, 2012) .............................................................. 13

Figure 10: P/E Ratio of Marks & Spencer (Left) and Debenams (Right) (Morningstar, 2012) .......................... 13

Figure 11: P/E Ratio of HSBC (Left) and Barclays (Right) (Morningstar, 2012) ............................................... 14

Figure 12: PEG (Historical Growth) 2011 (Yahoo UK & Ireland Finance, 2012) ............................................... 14

Figure 13: Beta Value per Company (Telegraph, 2012) ................................................................................... 15

Figure 14: Price per Share of the Companies (Telegraph, 2012) ..................................................................... 15

Figure 15: EPS Values of the Companies (Telegraph, 2012) ........................................................................... 16

Figure 16: Tesco Equity Evaluation Using PE Ratio. (Group.1, 2012)............................................................. 17

Figure 17: Tesco Equity Evaluation Using Dividend Discount Model Utilising 0% Growth (Group.1, 2012) ..... 18

Figure 18: Dividend Discount Model with 2% Growth (Group.1, 2012)............................................................. 19

Figure 19: Comparisons Equity Valuation (Group.1, 2012) .............................................................................. 20

Figure 20: Risk Vs Profitability Matrix (Group.1, 2012) ..................................................................................... 22

Figure 21: Portfolio Monthly Return Variation (Group.1, 2012) ......................................................................... 23

Figure 22: Diversification of Risk through Portfolio Creation (Group.1, 2012) .................................................. 23

Figure 23: Strong Positive Correlation (Group.1, 2012) .................................................................................... 25

Figure 24: Weak Positive Correlation (Group.1, 2012) ..................................................................................... 26

Figure 25: Negative Correlated Stock (Group.1, 2012) .................................................................................... 26

Figure 26: Aggreko Beta value vs. FTSE (Group.1, 2012) ............................................................................... 27

Figure 27: Relationship between the Variance of a Portfolio Return and the Number of Securities in the
Portfolio (Hillier et al., 2010) ............................................................................................................................. 29


Figure 28: Distribution of Equity Price at Expiration for both Security A and Security B. Options on the Two
Securities have the Same Exercise Price (Hillier et al, 2010) ........................................................................... 30

Figure 29: Increase in Call premium rate (Group.1, 2012) ............................................................................... 31

Figure 30: Straddle Strategy at Exercise Price 210 (Group.1, 2012) ................................................................ 32

Figure 31: Covered call strategy at exercise price of 205 (Group.1, 2012)....................................................... 34


TABLE OF ABBREVIATIONS

ABREVIATION DESCRIPTION

NPV Net Present Value

P&L Profits and Loss

S&P Standard & Poor

FTSE Financial Times Stock Exchange


1 INTRODUCTION
The following report considers various models used for evaluating companies by investors. The report starts
with an analysis of a company and the attractiveness of investing and future opportunities for the investment.
The analysis is completed with the use of Capital budgeting, net present value and the internal rate of return of
the investment.

The second part of the report analyses the PE ratios of five different companies registered in FTSE. The
research goes on to compare the companies within themselves, with competition and the industry average.
This section also considers different ways of valuation of the equity of a company, Tesco Plc and furthermore
compared with the market valuation.

The report goes on to analyse the returns of a given set of companies, over a period of sixty months as well as
monthly. The report determines the average monthly return for the portfolio and its standard deviation of the
selected companies. The co-variances or correlation coefficient is also derived for the selected securities.
Using this information and portfolio equations, the standard deviation of the portfolio is calculated. The
analysis ends with a discussion on naïve diversification and randomly selected securities in a portfolio.

The final section of the report completes a study on differing strategies employed for options including straddle
and covered call. The same is done with a given data of Marks and Spenser’s. Finally Corporate Governance
is considered with respect to Australia’s regulatory environment and the regulations impact on corporate
decision making.


2 FIRST QUESTION

a) Determine the investment’s net present value and the internal rate of return. All
key assumptions should be specified and explained.

The following assumptions were made during the analysis:

1) The investment of the company in a profit and loss account (P&L) report has been evaluated in order
to calculate the expected cash flows of tax payments. In the P&L the investment outlay of £9.00 million
is not included; however it is discounted in 6 periods of £1.50 million as capital allowances.

2) Regarding direct cost, the manufacturing cost of £12.00 per unit was taken; the company has
allocated an Overhead Cost of 10%. This is not included in the P&L analysis or in the Cash Flow
Statement, since is not directly attributable to the production of this new product.

3) As a fixed cost, there is a £90,000 per annum cost is directly attributable to this product and an annual
charge of £10,000 for the location. The product is charged £50,000 per annum for this space, but only
20% of this amount is results from the potential adoption of the investment.

4) The work already undertaken on the product of £1.3 million was considered as a sunk cost, since
historic costs are not relevant for decision taking; however further development work of £200,000 is
included as R&D cost, as well as a marketing campaign of £150,000.

5) In period 6, a capital gain of £2 million as a re-sale value of the investment is shown. The
aforementioned details are included in Figure 1.

Figure 1: Profit and Loss Account (Group.1, 2012)

For capital purposes, the total amount of investment outlay is £9.18 million, since there is some finishing
equipment that could be sold today for £180,000. Therefore the difference between investing or not, includes
an opportunity cost, which is added as well as the investment outlay in the Cash Flow Statement.


For working capital, 25% of expected sales is required on each period, therefore two outflows are considered,
one of £1.425 million in period 0 and another one of £475,000 in period 1. These two outflows are offset in
period 6 at the termination of the project.

To conclude, the Net Present Value (NPV) figure of £3,728,964 is proof that the project is financially viable to
invest in. “Furthermore, the IRR figure of 24.28% gives enough scope to secure an investment when a rate of
return of 14% is expected.

Figure 2: Cash Flow Statement (Group.1, 2012)


b) Undertake a sensitivity analysis for the assumed price and volume of expected
sales and interpret your results carefully. Provide a brief general discussion of
the potential risks associated with this investment.

The information derived from the sensitivity analysis concluded that this is a low risk investment. This was due
to the following reasons;

1) The price of the new valve can be reduced by 23.67% and sold at £29.01; this will still result in a
positive NPV as shown in Figure 3. This variance of 23% in price is sufficiently large enough to ensure
that the project remains profitable regardless of the volatility of the oil and gas industry. (Krauss, 2008)

Figure 3: Price Variations (Group.1, 2012)

2) In terms of volume, sales of the new item can be reduced by 35.61% and still record a positive NPV as
shown in Figure 3. As the product has a strong relationship with the oil industry, a drop on sales is
very unlikely since the industry has growth projections of 37% by 2030 over 2006 levels (Krauss,
2008). However, if the objectives are not reached, the company can still reduce prices in order to
increase demand as was previously suggested.

Figure 4: Volume of Sales Variations (Group.1, 2012)


3) As seen in Figure 5, direct cost and investment outlay have low impact in reasonable variations since
each one independently can still result in positive NPV when increased up to 70% for direct cost and
56% for the investment outlay.

Figure 5: Determinants of Profitability (Group.1, 2012)

4) If all the variables are evaluated together as shown in Figure 6, it can be identified that:

a. If it is necessary to reduce one of two factors, sales targets or price, the decision maker should
reduce the volume of units as this shows a higher NPV below 0%.

Whereas,

b. If it is necessary to increase the NPV, increases in price rather than in volume produce higher
returns.

Therefore, for price management purposes, the decision maker should understand that for each 1% of
price reduction, the correlation of sales volume should increase by 1.53%.Conversely, if sales volume
decreases by 1%, then a price increase of 0.67% will return the project to the same NPV.

Figure 6: Price, Volume, Direct Cost and Investment Variations (Group.1, 2012)

It can be concluded from the sensitivity analysis, that the range of variation from actual targets to the
breakeven point is proof of the low risk of this investment. The volatility of the oil and gas industry, which
probably has a direct impact on the demand of this new product, requires investments of high IRR such as this
one. Therefore it is strongly recommended to invest in the high pressure valve.


3 SECOND QUESTION

a) The price earnings ratios on September 9th 2011 for five companies traded on
the London Stock Exchange are listed below. Discuss the factors that might
explain the differences between these price earnings ratios. (You should make
as much use of the theory relating to the determination of price earnings ratios
as possible.)

COMPANY PRICE/EARNINGS RATIO
Burberry 20.50
EasyJet 8.90
Marks and Spencer 8.80
HSBC 7.50
Lomin 37.90

Table 1: Companies chosen by group 1 (Group.1, 2012)

The formula utilised to calculate the PE ratio is as follows:

PE Ratio = Market value per share / Earning per share (Atrill and McLaney, 2011)

PE ratio is one of major methods to judge the attractiveness of a particular stock of a company against
another. P/E ratio, or the price per earnings ratio gives an indication of how much investors are willing to pay
for a $1 of earnings in that particular company. This suggests that the higher the ratio, the more the investor is
willing to pay. Theoretically, a lower PE ratio means that the company gives a much higher ratio of returns on
its price of the share. In layman’s terms, a PE ratio of over 15 is considered as a risky venture because this
means that either the share price for the company is really high or the earning per share is really low. Whereas
any stock with a ratio below 15 is considered both safe and productive as the price would either be low or
earning per share will he higher

However, like any analysis of data there are multiple ways of looking at both the outcomes and the co-
relations. With any live market financial data, the similarity or variability of PE ratio needs to be judged after a
much deeper research through multiple ways as there are many impacting parameters’ for the same.

Figure 7: Price and Earnings ratio


In the set of P/E ratio’s the intuitive way is to compare the PE’s of the five companies and understand why
they vary from one another to this degree. Given this primary definition of PE ratio it is easy to bring out some
apparent information from the data. From the graphs is apparent that HSBC has the lowest PE ratio and thus
should have the highest rate of growth or earning. Whereas Lomin at 37.90 seems to be high both on relative
term as well as on the accepted parameter and signifies that an investor will have to pay $37.90 to earn $1
return.

PE ratio variation compared to the stocks

The examples below are two companies from the list, Burberry and EasyJet. Here there is a comparison with
the share price over the last few years and a chart of the PE ratio behaviour during the same period. These
companies have been chosen for the difference in the co-relation of the price and the PE ratio.

Burberry

The two charts below show the relation of share price and PE ratio. In the year 2009 the share prices were the
lowest of the five years range and this is complimented by the PE ratio also dropping significantly. In the same
year the profits declared were also the lowest for the time frame (Morningstar, 2012).

Figure 8: P/E Ratio & Stock Price of Burberry (Morningstar, 2012)

The comparison above shows clearly the share price to be the impacting factor in the PE ratio. As the price
dropped in year 2009, the PE ratio also dropped equally. This clearly shows that while the price (numerator)
was dropping in 2009, the earnings (denominator) remained the same.

Easy Jet


Figure 9: P/E Ratio and Stock Price of Easy Jet (Morningstar, 2012)

In contrast to the Burberry, the charts of Easy Jet shows an increase of PE ratio in the year 2009 despite of
the share price being the lowest in the same year. This shows that while the share price went down, the
denominator, which is the earnings, would also have dropped at a higher rate. It is important to mention that
there are other reasons for the PE to increase. For example, in 2003, Genentech DNA, a biotech firm had a
share price of $35.02 and the earning for the last four quarters were $0.12 per share, which resulted in an
extremely high P/E of 292. However, further research would have shown that the companies 2002 earning
was reduced by expenses incurred in litigation and redemption of its stock. If this has not happened
Genentech would have $0.92 a share in earnings for the year 2002, and giving it a P/E of 38. This while not
ideal, is not that different from 292.

However, like any real life data it is important not to get carried away and to understand the parameters for this
difference and to analyze the reasons. The P/E ratio has some important drawbacks. A P/E ratio of 15 does
not intrinsically mean much, unless looked at in the context in which it is used. To understand the PE ratio it is
important to note the following;

1) While comparing P/E ratios from two companies, it is important to compare companies from the same
industry and same characteristics. For example; utilities companies typically have low multiples
because they are within a low growth and stable sector. Whereas, the technology industry is
characterized by high growth rates and constant variations. Comparing a tech company to a utility will
not give value to either. The comparison should only be of high-growth companies with others in the
same industry, or with the industry average.

2) The historical speed of the growth of the company and the expected trends of the growth in the future
should be considered. A company which has shown a growth of only 5% in the past but has a
disproportionate P/E means that the projected growth rates don't correlate to the P/E, and the stock
might be overpriced.

3) The PE ratio is only meaningful if taken in context. There can be periods when entire industries are
overvalued like in year 2000; Internet stocks with a P/E of 75 were looking cheap while the industry
was at an average P/E of 200. Retrospectively, neither the price of the particular stock nor the industry
benchmark gave the reality. This means that less expensive than industry average does not mean
something cheap, as the average itself may be greatly overpriced.

The theory above gives a deeper view on the companies selected and some more parameters for judging the
performance and the relevance of PE in the various contexts. While looking at any of the companies it is
important to ensure that we have a correct context for comparison. As mentioned earlier it is important to
compare the companies with companies of the same industry. In the two graphs below we have a comparison
of the two companies with their competitors in the industry.

Figure 10: P/E Ratio of Marks & Spencer (Left) and Debenams (Right) (Morningstar, 2012)


Here the PE ratio of Marks & Spencer’s is compared with Debenhams over a period of four years. The charts
show that M&S has over the last four years been showing a higher PE and has consistently remained above.
Debenhams, even at its peak has remained lower than the lowest PE shown by M&S.

Figure 11: P/E Ratio of HSBC (Left) and Barclays (Right) (Morningstar, 2012)

The stocks in the banking industry understandably would not have been the most lucrative from 2008 which is
reflected in the past three years PE ratios. However, when compared to the PE ratio of Barclays the figure
look high and gives the investor a reason to look at more criteria than just the PE.

Beyond PE for the selected companies

Given below are some of the other factors which are relevant in judging a stock along with the PE of the share.
The graphs below also show a comparison with the other factors.

PEG ratio

PEG is widely used to calculate potential value. Some favour it over the price/earnings ratio because it also
accounts for growth. Similar to the P/E, a lower PEG means that the stock is more undervalued. The PEG
Ratio uses the P/E Ratio of a stock, and compares it with the company’s annual growth rate (Yahoo UK &
Ireland Finance, 2012).

Figure 12: PEG (Historical Growth) 2011 (Yahoo UK & Ireland Finance, 2012)


Beta

One of the most popular indicators of risk is a statistical measure called beta. Beta conveys the measure of
volatility in the stock in relation to the market. The market as a norm has a Beta of 1, and individual stocks are
rated on the basis of how much they deviate from the market. A beta above 1.0 would mean that the stock is
swinging above the market movement. If a stock moves less than the market, the stock's beta will be less than
1.0. High-beta stocks are supposed to be riskier but provide a potential for higher returns; low-beta stocks
pose less risk but also lower returns. Stock analysts use this measure to get an understanding of a stocks' risk
profiles (Telegraph, 2012).

Figure 13: Beta Value per Company (Telegraph, 2012)

The beta analysis of HSBC shows a high ratio, this suggests that the share value of HSBC is more volatile
than the market. However, the volatility the PE ratio is one of the lowest. This confirms what has been stated
earlier that low price earnings ratios do not necessarily mean that the share is of good value or safer to buy.
Another reason could also be that investors are avoiding the stock as its expected future earnings may be
poor. Lomin on the other hand has a high PE ratio and a very high beta factor which indicates that it is both
over priced and has a higher market risk.

Figure 14: Price per Share of the Companies (Telegraph, 2012)


EPS

Figure 15: EPS Values of the Companies (Telegraph, 2012)

The formula utilised to calculate the earnings per share is as follows:

Earnings per share = Earnings available to ordinary shareholders / Number of ordinary shares in
issues (Atrill and McLaney, 2011)

The earnings per share in the chart above show that the net income per share can be equal even while the PE
ratio for the companies may differ. For example Burberry and HSBC have similar earnings per share, but their
PE ratios are vastly different. The inference from the data is that the PE ratio does not reveal the volume of the
shares being traded or the net income and hence difficult to conclude on the earnings per share.

b) Choose a company from the FTSE 100 and carry out a full valuation of the firm’s
equity. Use financial websites and your chosen company’s financial reports to
full use when collecting the data for your analysis. You should use several
estimates for each input into your valuation models. How do your estimates
compare to the company’s market equity valuation? How do you interpret the
difference?

The following study shows the full equity evaluation of Tesco based on the current market standing of the
shares. There are multiple ways to complete the valuation based on multiple parameters. The analysis below
has been completed with five methodologies which arrive at different conclusions on the valuation.

 Equity evaluation using PE ratio

The evaluation using PE ratio is completed based on the ratio of Tesco’s PE as against the retail. As
discussed in this report earlier, the P/E ratio of a company is calculated using the following formula,

P/E ratio = Price per share / Earnings per Share

Utilising the above formula (Hillier et al, 2010) the current P/E ratio of Tesco is 9.53 whereas the P/E ratio of
retail sector in UK is 9.85. To understand the same in the context of the overall market it is also important to
know the PR ratio of the overall UK market, which is at 11.46.


The EPS of Tesco is 33.10pence so the following formula could be used for deriving the price per share of
Tesco; Price per share = P/E ratio * EPS (Morningstar, 2012)

Since the PE ratio of Tesco is lower and has been behaving that way for the last few years it was important to
look at the valuation of the company in comparison with the market. Taking retail sector P/E ratio into
consideration the price per share of Tesco would be; 9.85 * 0.33 = 3.25 (Morningstar, 2012)

The number of shares in issue for Tesco is 8014.47 million as declared in the financials of the company
(Yahoo UK & Ireland Finance, 2012). The equity value of the company can be arrived at by multiplying the
number of shares and price per share. This gives a valuation of 8014.47*3.25 = 26,051.03 million or 26.05
Billion.

Whereas the market capitalization of Tesco given in the financial websites comes to 25,706.40 million or 25.70
billion (Morningstar, 2012), there is a difference of circa £350 million in our estimation.

Data displayed in Billions

27
EQUITY VALUE

26

26.05
25.70 *

25
MARKET VALUE PE EVALUATION

Figure 16: Tesco Equity Evaluation Using PE Ratio. (Group.1, 2012)

While Tesco has outperformed its competitors in the past there has been a reduction in the PE ratio of Tesco
recently due to the profit warning sounded in the third quarter. Since in this evaluation calculation of the share
price is based on the EPS* PE ratio, the price per share has come out lower, which would explain the variation
of 350 million between both the valuations of Tesco.

 Using dividend discount model

The valuation of a company can also be done based on its dividend. The value of a firm’s equity for the
investor would be equal to the present value of all the expected future dividends. The equity of Tesco can also
be evaluated by the dividend discount model. The dividend discount model could be used in two methods.

The value of equity with constant dividend is given by the formula:

1) Zero growth :P0 = Div/R

When the dividends grow at rate g the equity is valued by the following formula;

2) P0 =Div/(R-g) where P0 is the present value of share.

The R in the formula can be calculated using the Capital asset pricing model (CAPM). Capital asset pricing
model is used to find the discount rate. This would mean expected return on the stock would be equal to risk
free interest rate plus the multiplication of beta with market premium. This could be described in the following
formula;


R=Rf +beta (Rm - Rf), where beta being the beta of the security, Rf is the risk free rate and Rm is the
expected market return.

The 10 year UK government bond (Rf) yield is 3.75; the current beta of Tesco security is 0.58 (Morningstar,
2012)

The last 5 year declared dividend of Tesco is 9.64, 10.90, 11.96, 13.05 and 14.46 pence, which gives an
average dividend of 12 pence for the period.

 Zero growth : P0 = Div/R

If the analysis is completed at various levels of sensitivity of rate of market return (Rm) there are different
valuations for the company. Given below are three different valuations arrived at with three separate market
return rates.

a) Market return – 7%

With the same formula R=Rf +beta (Rm - Rf) would give R=3.75+.58(7-3.75)=5.635

Using the dividend growth mode P=Div/r we could get the present value of share as 214.28.

P=12/.056=214.28.

Therefore Equity value=8014.47 *214.28=17,150 million or 17.15 billion.

b) Market return=5%

R=3.75+.58(5-3.75) therefore R=4.47

P=12/.044=272.22

Therefore Equity value=8014.47 *272.22=21799.35 million or 21.79 billion.

c) Market return=9%

R=3.75+.58(9-3.75) = 6.79

P=12/.067=179.10

Therefore Equity value=8014.47 *179.10=14,353.91million or 14.35 billion.

Data in Billions

25
EQUITY VALUE

20

15
21.79
10 17.15
14.35
5

0
4.47 5.63 6.79

RATE OF DISCOUNT WITH 0% GROWTH

Figure 17: Tesco Equity Evaluation Using Dividend Discount Model Utilising 0% Growth (Group.1,
2012)


The chart above gives a picture of the different valuations generated through varying rate of discount. This
goes on to show that the valuation can change by nearly 52% or 7.44 billion with a change of 2.32% in the rate
of discount.

The formula utilised to derive dividends with growth is as follows:

Dividends with growth: P0 =Div/(R-g) where P0 is the present value of share with g being the dividend growth
rate.

For the calculation of the formula there has to be a future growth projection. For this method of valuation to
work the g has to be less than R, so as an assumption the g is taken as 2%. Given below are the three
different valuations when the three different rates of discounts (R) are used (calculated using CAPM model);

a) Rate of discount= 6.79% and g = 2%

12/(0.067-.02) = 12/.047 =255.31 Pence per share

Therefore at a share price of 255.31 pence and an issued share of 8014.47 million the total valuation for
Tesco will be 20436.89 million or 20.45 billion.

b) Rate of discount = 4.47% and g =2%

12/(0.047-.02) = 12/.027 =444.44 Pence per share and thus giving a valuation of 35584.24 million or 35.55
billion.

c) Rate of discount = 5.63% and g = 2%

12/(0.056-.02)=12/.036 =333.3 Pence per share and thus giving a valuation of 26688.18 million or 26.69
billion.


40
35
EQUITY VALUE

30
25
20 35.55
15 26.69
20.45
10
5
0
4.47 5.63 6.79
RATE OF DISCOUNT WITH 2% GROWTH

Figure 18: Dividend Discount Model with 2% Growth (Group.1, 2012)

As the chart shows a change of 2.32% in the rate of discount can make a change of 15.1 billion or 73.8%. The
graph when compared with Figure 17 of zero growth also gives out the stark change in the valuation when a
growth of even 2% is added on to the rate of discount. The variance of valuation between the highest and
lowest among the two graphs is 21.2 billion.


 Final Comparison


26.05

35.55 25.71

26.69
21.79 20.45
17.15
14.35

4.47 5.63 6.79

RATE OF DISCOUNT RATE OF DISCOUNT WITH 2% GROWTH MARKET PE EVALUATION

Figure 19: Comparisons Equity Valuation (Group.1, 2012)

The green line shows the current market. Of the seven different valuations the chart shows valuation by PE
ratio (industry) seems to be the nearest of the actual valuation. The reason is that the PE ratio of Tesco is not
too different from the PE ratio of the industry. The rate of discount without growth is giving the lowest valuation
at all sensitivities. The graph illustrates and explains how the same company’s valuation can differ so much
through different approaches.


4 THIRD QUESTION

a) Determine the average returns over the 60 month period for each of the five
securities and their respective standard deviations using Excel. Determine the
returns for the five share portfolio for each month in the period. On this basis
determine the average monthly return for the portfolio and its standard
deviation. Discuss briefly the standard deviation of the portfolio returns in
relation to the standard deviations of the securities making up the portfolio.

An equally weighted portfolio is a group of shares in which the same amount of money has been invested in
each stock (Berk, DeMarzo and Harford, 2009), this is also known as naïve diversification whereby no analysis
has been completed in the stock selection.

The drawing below shows the five companies which were selected at random to create a equally weighted
portfolio. The companies selected are as follows; Aggreko, Barclays, Johnson Matthey, Pearson, Vodafone
group.

The average return over the 60 month period was calculated for each of the 5 companies and the portfolio as
shown below.

NAME OF THE COMPANY AVERAGE STANDARD DEVIATION
AGGREKO 3.62% 10.83%
BARCLAYS 0.42% 17.38%
JOHNSON MATTHEY 1.30% 8.37%
PEARSON 1.07% 5.27%
VODAFONE GROUP 0.63% 6.34%

Table 2: Portfolio Average Return (Group.1, 2012)

The standard deviation of the returns of the individual security measures how risky the security would be if
held in isolation (Hillier et al., 2010)

In the context of this diagram it can be seen that the organisations which have been chosen have been
positioned into the four quadrants. Barclays is shown to be high risk, low profitability which may seem counter
intuitive, however that within this matrix the risk/profitability of the company is relative to the other companies
which have been chosen.


Figure 20: Risk Vs Profitability Matrix (Group.1, 2012)

The month on month average returns from 5 companies in the equally weighted portfolio are shown below in
the table.

MONTH 2005 2006 2007 2008 2009
Jan -1.49% 0.61% 3.37% -4.10% -11.41%
Feb 0.84% 1.41% -0.75% 1.27% -4.83%
Mar 1.57% 6.11% 5.08% 1.46% 21.53%
Apr -1.42% 2.03% 3.96% -0.34% 25.84%
May 3.26% -8.38% 3.39% -1.93% -1.50%
Jun 2.47% 1.30% 1.32% -4.17% -3.98%
Jul 5.20% -0.61% -3.74% 0.07% 10.76%
Aug 1.67% 2.23% -3.64% 3.44% 13.14%
Sep 3.14% 6.99% 4.20% -14.69% 1.96%
Oct -0.87% 5.61% 5.94% -19.61% 0.19%
Nov 2.48% 0.23% -7.53% 0.37% -0.72%
Dec 5.14% 5.82% 1.05% 6.21% 7.41%

Table 3: Portfolio Monthly Average Returns

For clarity these figures have been plotted on a graph, as can seen the returns were fairly steady if
unspectacular, however, from September 2008 September 2009 the market became volatile and there have
been large fluctuations between gains and losses.


Figure 21: Portfolio Monthly Return Variation (Group.1, 2012)

The average monthly portfolio returns are summarised as below. Please refer to the appendices for more
detail.

PORTOFOLIO STATISTICS PERCENTAGE
Average 3.99%
Standard Deviation 12.20%
Variance 1.49%

Table 4: Summary of Portfolio Statistics

Figure 22: Diversification of Risk through Portfolio Creation (Group.1, 2012)


From the analysis within the graphic above, the standard deviation 6.78% of the portfolio is less than the sum
of weighted average of the standard deviations of the individual securities 9.64% (Hillier et al., 2010). It can be
concluded from this analysis that by diversifying the amount of stocks in a portfolio the exposure to risk is
reduced.

b) i. Using Excel derive the co-variances or correlation coefficient for each pair of
securities. On the basis of this information and using portfolio equations, based
on the average covariance and average variances calculate the standard
deviation of the portfolio. Compare your results to those obtained in (a). Explain
the basis of the derivation of the standard deviation of portfolio returns.

The co-variances and the correlation coefficient for each pair of securities are given below.

AB AC AD AE BC BD BE CD CE DE Average
Covariance 0.010 0.004 0.002 0.001 0.006 0.002 0.001 0.001 0.002 0.001 0.003

Correlation 0.517 0.417 0.429 0.218 0.428 0.257 0.061 0.329 0.303 0.265 0.322

Table 5: Covariance & Correlation Among Companies

The company key is as follows:

CODE COMAPNY
A AGGREKO
B BARCLAYS
C JOHNSON MATTHEY
D PEARSON
E VODAFONE GROUP

Table 6: Code of Companies

The formula utilised to derive the variance of the portfolio is as follows;

Variance (Return of portfolio) = 1/n [average variance of the individual stocks]+[1-
1/n)[average covariance between the stocks]] (Berk, DeMarzo and Harford, 2009)

The data for the equation above have been extrapolated from the raw data given and are shown in the table
below; if any further reference is required it may be made within the appendices.

TITLE VALUE
Number of Stocks (N) 5
Average variance of individual stocks 0.0110
Average cov between stocks 0.0030
1/n (Average variance of individual stocks) 0.0022
[1-1/n)[Avge covariance between the stocks]] 0.0024

Table 7: Portfolio Variance Calculation


Thus:

Variance (Return of portfolio) = 0.0022+0.0024 = 0.0046

From the aforementioned, we find that the variance of the portfolio derived through the co-variances is the
same as that found by calculating the returns directly which were determined in Question 3, part a. This is as
shown below;

Variance 0.46%

Table 8: Portfolio Statistics Summary

The basis of this derivation is as follows:

var(Return of portfolio) = 1/n [avge variance of the individual stocks]+[(1-1/n)[avge covariance between
the stocks]] (Berk, DeMarzo and Harford, 2009)

The following assumptions are made in order to calculate the variance of the portfolio using the above
equation.

1) The variance of all securities in the portfolio is considered to be equal and for this purpose the value
has been taken as the average variance of 0.0109 (Hillier et al., 2010).

2) The covariance between any two stocks in the portfolio is considered to be equal and for this purpose
the value has been taken as the average covariance of 0.0030 (Hillier et al., 2010)

3) The given portfolio is equally weighted. Because there are 5 securities, the weight of each stock is 1/5
= 0.20 (Hiller et al., 2010)

For deeper analysis the pairs of stocks were plotted graphically and the highest and lowest positively
correlated pairs are shown below.

Figure 23: Strong Positive Correlation (Group.1, 2012)


Highest positively correlated pairs.

50%

40%
30%
20%
10%

0%
-10%
-20%
-30%

-40%
-50%
01/01/2005
01/03/2005
01/05/2005
01/07/2005
01/09/2005
01/11/2005
01/01/2006
01/03/2006
01/05/2006
01/07/2006
01/09/2006
01/11/2006
01/01/2007
01/03/2007
01/05/2007
01/07/2007
01/09/2007
01/11/2007
01/01/2008
01/03/2008
01/05/2008
01/07/2008
01/09/2008
01/11/2008
01/01/2009
01/03/2009
01/05/2009
01/07/2009
01/09/2009
01/11/2009
B E

Figure 24: Weak Positive Correlation (Group.1, 2012)

For analytical purposes stock B (Barclays) above was replaced with the National Grid stock values to
determine what effect this would have on the portfolio. National grid was chosen as it was felt that it would be
polar opposite to Aggreko which is a temporary generator solution company. The results are as shown below.

Figure 25: Negative Correlated Stock (Group.1, 2012)

Variance 0.21%

Table 9: Re-Calculated Portfolio Statistics

The conclusion from this diagram and table is that by using one negatively correlated stock, instead of a 0.5
correlated stock (Barclays), the standard deviation of the portfolio has further reduced from 6.78% to 4.5%,
thus reducing the portfolio risk.


b) ii. Provide an estimate of the beta for one of the securities and discuss the
meaning and reliability of the estimate you have derived. Comment on the
possible differences between your estimate and those provided by commercial
concerns on the internet.

The Beta value of a stock is the sensitivity of a specified stock return in relation to the fluctuation of the market
index. For example a stock with a beta value of 1 means that the stock rise and falls at the equivalent rate to
the index.

The Beta value of Aggreko has been considered and its returns have been compared against the FTSE
returns provided. The beta value of Aggreko is greater than 1 and thus can be considered to be an aggressive
stock.

From the given data set the Beta value of Aggreko has been determined as 1.32 (refer to the appendices for
the method of deriving this figure). This means that if the market performance improves by 1%, the stock value
increases by 1.32%. The same is true for a drop in stock performance relative to market performance as
shown in the diagram below.

PERCENTAGE GROWTH
2.64%

2.00%

FTSE 100 Aggreko

FTSE 100 Aggreko

-1.00%
-1.32%

Decrease Increase

Figure 26: Aggreko Beta value vs. FTSE (Group.1, 2012)

The reliability of Beta values may be questioned due to;

 Beta values are for historical data and not a representation of future performance (Little, n.d.).

 If the organisation is going through changes, for example new product lines or new market penetration
the Beta value will not represent these changes (Little, n.d.).

 The index which Beta values are derived from may affect the reliability, if companies are out with the
index utilised, for example the FTSE may not the best index to derive data for non UK markets
(McNulty, 2009).

 The time period of given Beta values may be unknown, thus long term investors have a different risk
profile to those traders who have a short term risk perspective thus leading to difficulties for those
investors who use Beta to gauge their respective portfolio risk (McNulty, 2009).

The Beta value from the internet is 1.19 (Reuters, 2012). The beta displayed on Reuters.com is calculated
based on trailing 5-year prices, on a monthly basis, relative to the S&P 500 (Reuters, 2012). Hence the Beta
value changes with every new month recorded as the moving average changes.


The differences between the Beta figures are attributable to the following reasons;

1) The data set provided for the assignment is for the period between 31/01/2005 and 31/12/2009. The
Beta value taken from Reuters.com is calculated from the periods of the past 5 years.

2) Furthermore, the Beta value calculated is against FTSE values whereas those listed are relative to
S&P 500 values.

The returns of Aggreko are taken for the past 5 years from yahoo finance and Beta values are calculated
against the FTSE index. The results are summarised in the below table, as can be seen the indexes, periods
and betas are all different.

It can be concluded that regardless of the data utilised in deriving the Beta values of Aggreko, the stock
remains aggressive.

SOURCE YAHOO FINANCE CALCULATION REUTERS
Period 2008-2012 2005-2009 2008-2012
Index FTSE FTSE S&P
Beta 1.312 1.32 1.19
Conclusion Aggressive Aggressive Aggressive

Table 10: Variation of the Beta Values (Group.1, 2012)

c) Explain what is meant by naive diversification and explain the consequences of
increasing the number of randomly chosen securities in a portfolio.

Naive Diversification is a strategy whereby an investor simply invests in a number of different assets in the
hope that the variance of the expected return on the portfolio is lowered. The investment portfolio is built
through a random or naive selection of assets regardless of any mathematical formula. (Harvey, 2011)

Although computerized models can look impressive, the benefits of advanced mathematical modelling are
unclear. Investigations into optimization theory have argued against the effectiveness of sophisticated models.
"Optimal Versus Naive Diversification: How Efficient is the 1/N Portfolio Strategy," conducted by Dr. DeMiguel
is a good example of them. The difference between them and the naive approach is not statistically significant;
they point out that basic models perform well, thus complexity does not always help. (Bloch, 2011)

In relation to investments there are systematic and unsystematic risks. The systematic risk arises with a single
security only, whereas the unsystematic risk is diversified away in a large portfolio. Though both the risks
cannot be eliminated completely, studies show that for an infinite population of stocks, a portfolio size of 20 is
required to eliminate 95% of the diversifiable risk on average. (Hiller et al., 2010)

By increasing the number of randomly chosen securities in a portfolio will result in the variance being more
dependent on covariance between individual securities than on the variances of the individual securities. Thus,
if the number of securities included in a portfolio were to approach the numbers of securities in the market,
one would expect the variation of the portfolio return to approach the level of systematic variation-that is, the
variation of the market return, suggesting a relationship which behaves as a decreasing asymptotic function as
can be seen in Figure 1. (Evans and Archer, 1968)


Figure 27: Relationship between the Variance of a Portfolio Return and the Number of Securities in the
Portfolio (Hillier et al., 2010)

An addition of 80 stocks is required to eliminate an extra 4% (i.e., 99% total) of diversifiable risk on average.
This result does not depend on the sampling periods, the investment horizons or the markets involved. For a
finite population of stocks, the corresponding portfolio size required will be smaller (Tang, 2004).

However, recent researches conclude that forty to fifty stocks is all that is needed to achieve diversification.
Previous studies took into account the time series variability of returns but ignored the cross sectional
variability and the possibility of alternative weighting schemes. Benjelloun resolves this matter by addressing
all these issues simultaneously. (Benjelloun, 2010)


5 FOURTH QUESTION
Prices of Calls and Puts Options the shares of Marks & Spencer

SHARE EXERCISE CALLS PUTS
PRICE PRICE Sep Oct Nov Sep Oct Nov
205 12.0 24.0 27.0 6.0 17.5 19.5
2010
210 9.5 21.5 24.5 8.5 20.0 22.0

a) Explain carefully why the November calls are trading at higher prices than the
September calls.

The following are the possible reasons for the November call options trading at higher premium than the
September call option.

Assumption: The option type is American call.

Expiration date: The longer period the call has until it expires, the longer the period for the option holder to
exercise the option. The longer which this expiration is the greater the call option price.

Volatility: The volatility of the underlying share price is an important determinant of an option's underlying
value. The greater the variability of rate and magnitude of the underlying asset, the more valuable the call
option will be. Buyers of the call option expect that the probability that share value will remain higher than the
exercise price is higher during November than during September.

A
PROBABILITY

B

Exercise Price

PRICE OF EQUITY AT EXPIRATION

Figure 28: Distribution of Equity Price at Expiration for both Security A and Security B. Options on the
Two Securities have the Same Exercise Price (Hillier et al, 2010)


As can be seen from the above diagram option B is more valuable than A as there is a higher probability that
the share price of B will fluctuate outside of Curve A.

Change in implied volatility

Apart from changes in the price of the actual underlying commodity or security, the price of an option is most
affected by changes in implied volatility. Implied volatility measures the aspect that option traders expect the
historical volatility will be in the future. The actual option price will determine implied volatility. The volatility is
implicit in the price of the option.

For example:

High implied volatility means that sentiment is extremely bullish or bearish and that option traders believe
there is a greater likelihood of higher or lower prices being reached in the future (Katiforis, n.d.).

If sentiment in the commodity textile and trading market becomes bullish, the prices of Marks and Spenser’s
call options will rise even before the actual price of crude oil does.

Option buyers will be prepared to pay more for the option as there is the perception of the market making a
large move in their favour.

Increase in Share Price: The increase in the call price for a given change in the share price is greater when
the share price is high than when the share price is low. It is expected that the share price for November will
higher than that of September and hence making the call option more profitable. The higher the share price,
the more valuable the option. Hence the call option buyers are expecting the share price to rise over the
period and the difference between the share price and exercise price to increase. Moreover, the buyers expect
a sharp rise in share price between September and October which is in fact higher than the premium paid and
hence profitable to the buyer.

Interest rate: Call prices are a function of the interest rates. The ability to delay payment is more valuable
when the interest rates are high and less valuable when the interest rate is low. A higher interest rate of the
November call options than the September call options could be a reason for the higher premium.

It is observed that there is a spike in the premium between September and October. This indicates that there
is an expected rise in the share price during that period which will make these calls to be profitable. A spike in
the share price over a short period could be due to many reasons, some of which are as below.

Figure 29: Increase in Call premium rate (Group.1, 2012)

1) Imminent declaration of favourable results, Marks and Spencer declare their half yearly results in
November (Marks and Spencer, 2011), so traders are willing to pay a higher premium for this months


option. Research undertaken by Amin and Lee state that “option traders initiate a greater proportion of
positions before earnings news”

2) Imminent acquisitions/takeovers

3) New projects in near future

4) Impending profits due to Christmas sales

b) Draw a diagram illustrating a straddle, using calls and puts expiring in
November and an exercise price of 210. Explain the circumstances in which an
investor might consider it worthwhile to invest in a straddle.

Used mainly as a market neutral strategy, the straddle is employed by investors where the market is expected
to become volatile in the future. The strategy is primarily dependent on four parameters – strike price, volatility,
premium and time.

The idea is to buy a call option and a put option at the same strike price. The most important aspect of the
price is the volatility in the market, not the rise or fall of the share price. The timing of the option purchase is
also important as an option bought for a stock which is already in a state of volatility may be as profitable as
the premium to buy the option will already be high. The final profit is calculated after deducting both the
premiums paid, thus the premium price has a direct impact on the strategy. Time decay is also a threat to the
strategy as there is a finite shelf life to the options. This means that there is a real time threat to the straddle
becoming worthless as the time limit approaches.

The diagram below gives a projection of the straddle strategy where the exercise price (strike price) of 210
and a premium of 24.5 and 22 for call and put, respectively.

Figure 30: Straddle Strategy at Exercise Price 210 (Group.1, 2012)

As previously mentioned, the net profit from the strategy is calculated after deducting the premiums from the
gross profit. For an exercise price of 210 and with zero premiums, the call option would be profitable if the
share price rises above 210 for a call option, the put option will be profitable if the share price falls below 210.
However, in this case there are two varied premiums payable for the call and put options. A straddle is
profitable if the option exercised (put/call) brings about a return greater than the sum of premium prices paid
for buying the put and call options.


Here the premium paid for put and call option = 22.0 + 24.5= 46.5.

From the diagram above, we can identify that the straddle achieves breakeven in the following scenarios;

1. Share price falls below 210-46.5 = 163.5

2. Share price rises above 210+46.5=256.5

While the potential maximum profits remain infinite, the share price volatility must be high in order for the
straddle to be profitable as a strategy. If the share price remains within a price range of 163.5 and 256.5 the
option will be worthless and would result in a loss of 46.5. This also means that each passing day towards
November without movement of the stock would erode the value of the option.

The share price volatility must be high in order for the straddle positioning to be profitable.

c) Develop a covered call using the data provided and discuss the nature of the
payoffs produced and the potential uses of the strategy

A covered call is one in which 100 shares are purchased at the current price (210) and the call is sold on the
same stocks for a premium and an exercise price is set.

For example:

The expenditure would be cost of 100 shares = 210*100=21000

The premium for each of the call options is taken from the table given. Hence for 100 stocks, the premiums
charged would be;

EXERCISE PRICE SEPTEMBER OCTOBER NOVEMBER

205 1200 2400 2700
210 950 2150 2450

Table 11: Revenue due to option premiums (Group.1, 2012)

The returns would be what we get if the stock price remains the same.

If the stock price increases;

If the price of the stock increases beyond the exercise price, the call would be exercised and the cost of the
stocks would be;

205 20500 20500 20500

210 21000 21000 21000

Table 12: Selling price of stocks at exercise price (Group.1, 2012)


Hence the profit for each of the cases would be (premium price + cost of goods sold - expenditure to buy the
stocks).

205 700 1900 2200

210 950 2150 1950

Table 13: Profits during stock price increase (Group.1, 2012)

If stock price decreases;

The following are the minimum values that the stock price must go down to in order for a loss to occur. In other
words, the below are the break even points of share price for the various covered call options.


205 198 186 183

210 200.5 188.5 185.5

Table 14: Break even prices for covered calls (Group.1, 2012)

The owner of the shares should sell before the share price drops to these prices, as otherwise the covered call
will not be profitable.

Eg: Consider the September option at excise price of 205.

Profit = 205*100 + 12*100 – 210*100=700
PROFIT

198 205
Break Even Point Exercise Price

SHARE PRICE

Figure 31: Covered call strategy at exercise price of 205 (Group.1, 2012)


The covered call strategy gives a cushion against a predetermined fall in share price in exchange for the
profits gained in case of market price difference to buying price.

This strategy is considered to be conservative as it offers limited exposure to the decline of the underlying
stock price and the decreases the risk of stock ownership. The counterpoint to this is that there is limited
payoff potential due to the “cover” of the stock price. Income is forthcoming from the premium gained from
writing the call. Furthermore, the benefits from owning the stock such as dividends and voting rights are
gained by the investor.

d) Focus on one country (not the UK) and review the main corporate governance
regulations in place (www.ecgi.org). The regulatory environment can have a
massive impact on the way in which corporations do their business, how they
are financed, and the popularity of banks and the financial markets. Review the
main regulatory features (investor protection, etc.) for your chosen country and
their overall impact on corporate decision-making.

Australia, like other countries has suffered corporate failures through the preceding decades, the highest
profile cases have been one.tel and HIH, the latter losing Aus $5.3 billion. From these failures a robust
Corporate Governance standard was formulated in 2004 named Corporate Law Economic Reform Program
Act 2004, commonly called CLERP9. The CLERP act proposed three bodies to ensure that the principles of
Corporate Governance could be monitored and adhered to; the Financial Reporting Council to oversee
standard setting for audit and accounting, the Australian Securities Exchange’s (ASX) Corporate Governance
council to ensure the development of best practice for listed companies and the Shareholders and Investors
Advisory Council to ensure retail investors had a forum to air issues. Shareholder rights are not set out in
these guidelines; these items are contained in the Commonwealth Corporation Act 2001.

There are six main principles of Corporate Governance; these are discussed below from an Australian
perspective.

1) Ensuring the basis for an effective corporate governance framework.

As discussed in the introduction the basis for an effective corporate governance framework is to ensure that
there is sufficient and clear legislation which guides organisations to best practice. The formation of the ASX
Corporate Governance council in 2002 laid the foundations of a robust, practical and transparent system.
More than two thousand organizations participate in the reporting process laid out in the guidelines.
Furthermore, the ASX guidelines require companies to follow the “if not, why not” principle, this requires listed
companies to state that if they are not adhering to the recommendations laid out, it is necessary for the
organization to disclose the reasons for non-compliance in their annual report.

The impact which these regulations have on corporate decision making is that any listed company has clear
and comparatively strict regulations, without the prescriptive requirements laid out, for example, under the
Sabanes-Oxely act of the USA. The premise of “if not, why not” is, in the authors opinion a method of giving
some latitude as organisations merely have to state reasons for noncompliance with the recommendations but
doesn’t implicitly improve governance. However, the fact that any noncompliance has to be disclosed in the
annual report gives transparency and allows shareholders to question the board/management on these
subjects.

2) Rights of shareholders and key ownership functions and 3) The equitable treatment of
shareholders.

Principle 6 of the ASX Corporate Governance Principles is entitled “Respect the rights of shareholders”
however the main thrust of this article is to ensure that the shareholders are communicated with effectively
and that the latest technology is used.

However there is further legislation entitled the “Corporations act 2001.” The types of shares which are
mentioned are ordinary shares and voting shares. There is nothing stipulated as to specifics of the voting
shares By not defining the criteria of these shares leaves the rules of ownership open to the organisations
interpretation. From a corporate decision making perspective this flexibility should be advantageous to the
company as it will give latitude of how to distribute the shares. However, from a governance view this could be


construed as not entirely ethical. These rights would have to be written into the organisations constitution to
ensure that any potential shareholder were cognizant of their rights.

4) Disclosure and Transparency

Principles 4 “Safeguarding integrity in financial reporting” and 5 “Make timely and balanced disclosure” of the
ASX principles set out the requirements for disclosure and transparency.

The main thrust of principle 4 is in regards to the audit committee, its composition and reporting procedures. In
essence the reporting committee should be sufficiently large enough with the appropriate technical expertise
to be able to understand the matters raised.

Principle 5 states the guidelines for reporting and disclosure of all items pertinent to the company. It breaks
down the requirements of what and how the information should be reported.

From a corporate decision making perspective the challenge will be to find suitably qualified and independent
directors who are able to understand the requirements of a modern day organisation.

5) The responsibilities of the board.

Principle 2 covers the structure of the board and their responsibilities. This article is very detailed, however the
key points are as follows:

“Companies should have a board of effective composition, size and commitment to adequately discharge is
responsibilities and duties.”

The detail of this principle splits into six points detailing the specifics, for example what is an independent
director, the selection process of directors. The other points cover the various required committees and their
composition.

The principle of “if not, why not” comes into the fore with the various reporting requirements. Due to the level
of the detail specified if a company was to follow the letter of the principles then there would be some difficulty
in finding the appropriate people with the right qualifications. Furthermore the level of paperwork that would be
generated will require a robust administration team.

6) The role of stakeholders in Corporate governance.

Under the terms of Principle 3 “Promote ethical and responsible decision making” stakeholders are identified.
The term used is “organisations should comply with their legal obligations and also consider the reasonable
expectations of their stakeholders”. This is a subjective phrase and allows a certain degree of latitude for
organisations to work in.

The challenge for an organisation is to understand who their stakeholders are. The stakeholder is dependent
upon context and timing. The easily identifiable stakeholders are staff and shareholders, however as was seen
in the recent BP Gulf of Mexico disaster the stakeholders who became involved were the US President,
senate and congress.


6 CONCLUSION
As mentioned in the start of the report, the different sections of the report look at various methods of analysis
for judging a company or security on its appeal for investors. The analysis also delves on some of the tools
used by newer investors like straddle and covered call options. While there have been some of the commonly
used and popular methods of analysis have been focussed on in the study, it is important to point out that
these are neither comprehensive nor exhaustive.


7 APPENDIX

a) Variance Calculation


b) Covariance Calculation

Covariance
A B C D E
A 0.012 0.010 0.004 0.002 0.001
B 0.010 0.030 0.006 0.002 0.001
C 0.004 0.006 0.007 0.001 0.002
D 0.002 0.002 0.001 0.003 0.001
E 0.001 0.001 0.002 0.001 0.004

Correlation coeff
A B C D E
A 1 0.51654 0.41674 0.42879 0.21799
B 0.51654 1 0.42816 0.25706 0.06066
C 0.41674 0.42816 1 0.32894 0.30299
D 0.42879 0.25706 0.32894 1 0.26527
E 0.21799 0.06066 0.30299 0.26527 1

AB AC AD AE BC BD BE CD CE DE Average
Covariance 0.010 0.004 0.002 0.001 0.006 0.002 0.001 0.001 0.002 0.001 0.003
Correlation 0.517 0.417 0.429 0.218 0.428 0.257 0.061 0.329 0.303 0.265 0.322


c) Beta Value Calculation


d) Using Negative Correlated Stock


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