Woolworths Limited & DUET Group PDF

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Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813

FINC5001 Capital Market and Corporate Finance Major Assignment Lecture: Stream 11 Group: Unicorn Two Stocks: WOW and DUE

Group Members

SID

Can Zhou

312030592

Qin Jiang

420027638

Cheng Li

420046949

Xiao Zhang

420063131

QuQing Ling

311040813

Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813 EXECUTIVE SUMMARY The primary objective of this analysis is to recommend a portfolio, combined with two stocks listed on the Australian Securities Exchange (ASX) from different industries: Woolworths Limited (WOW) and DUET Group (DUE), that rational investors may construct to minimize the risks of their investments. Therefore, the risk and return profiles of various portfolio combinations of these two securities are to be examined from two different perspectives respectively—Mean-Variance (MV) and Capital Asset Pricing Model (CAPM.) approach. More precisely, the main part of our study would start with the justification of the appropriate data collection, which is followed by the detailed calculation processes under two different models. Finally, based on the rationale and underlying assumptions, along with the critical analysis of the two methods, the corresponding investment recommendations would be made for our targeted investors.

Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813 Contents 1. Background of WOW and DUE ........................................................................................ 1 2. Justification of Data Selection ........................................................................................... 1 2.1 The length of estimation period .......................................................................................................... 1 2.2 The frequency of sample data ............................................................................................................. 2 2.3 The share price and dividend.............................................................................................................. 2 2.4 The market index ................................................................................................................................. 2 2.5 The risk-free asset and return ............................................................................................................. 3

3. Mean-variance approach .................................................................................................. 3 3.1 Calculation of expected return and standard deviation of WOW and DUE ....................................... 3 3.2 Calculation of portfolio combination expected returns and standard deviation ................................ 5 3.3 Graph of the portfolio combination .................................................................................................... 6

4. CAPM approach ............................................................................................................... 6 4.1 Introduction of CAPM approach ........................................................................................................ 6 4.2 Calculation of beta of WOW and DUE ............................................................................................... 7 4.3 Calculation of expected return of WOW and DUE ............................................................................. 8 4.4 Calculation of expected returns and beta of portfolio combination ................................................... 8 4.5 Graph of portfolio combinations ........................................................................................................ 9

5. Analysis ............................................................................................................................. 9 6. Conclusion and recommendation .................................................................................... 11 6.1 Recommendation for MV approach .................................................................................................. 12 6.2 Recommendation for CAPM approach ............................................................................................. 12 6.3 Further discussion ............................................................................................................................12

References: ......................................................................................................................... 13 Data Sources: ...................................................................................................................... 16 APPENDICES .................................................................................................................... 18

Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813

1. Background of WOW and DUE

WOW is short for Woolworths Limited, which is perceived as Australia’s top retailer accounting for almost 37 per cent grocery market share, suggested in Woolworths market continuing to grow: CEO (2012). Its main operations stretch across grocery supermarkets, liquor, petrol and consumer electronics (Woolworths Limited, 2011). Furthermore, according to Woolworths wins market share in NZ supermarket battle (2012), Woolworths has recently gained a bigger slice (around 40%) of New Zealand supermarket pie. DUE is the abbreviation of DUET Group, which is an Australian energy investment funding group and principally invests in Australian and New Zealand’s energy utility assets (DUET Group, 2012). With a total asset of 8.64 billion (Market Watch, 2012), DUET tends to provide stable and predictable dividends to security holders, as reported in DUET Group (2011). Moreover, according to DUET Group website (2012), it will seek to invest in energy utility assets in OECD countries, aiming at strengthening its strategic position. 2. Justification of Data Selection

Prior to the estimation and comparison of the risks and returns of various portfolios combined by WOW and DUE under both Mean-variance and CAPM method, a series of historical raw data should be first selected. Also, as the evaluation in this study would be rather restricted in terms of the appropriate data that we can collect and the underlying rationale and assumptions attached to the two approaches, a benchmark of the statistics to be applied in the calculation for risks and returns is indispensable (Greg, Jonathan and Andrew, 2011). Moreover, identical data should be gathered to facilitate comparative analysis possible. Accordingly, the appropriate data selected in our study should be justified in the following aspects. 2.1 The length of estimation period In order to determine an appropriate length of estimation period, two perspectives should be taken into account. First, as our analysis is inclined to give investment recommendations to 1

Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813 individual investors, who are rather concerned with short-term investment horizons, the threeyear period is of great interest to them (Ng and Wu, 2006). Whereas, Ng and Wu (2006) asserts that investments with a five-year horizon are better choice for those investors that prefer intermediate returns. Also, it is crucial to eliminate the extreme impact of global financial crisis in the year 2008 on the short-term investments, as it is suggested by Schmeling (2009) that the effect of economic cycle in the short run is insignificant to affect the stock market. Therefore, in our study, a three-year period from March 2009 to March 2012 is used to collect the relevant data for estimation. 2.2 The frequency of sample data In terms of the sampling frequency, three categories of data including daily, weekly and monthly are available for different research purposes. In our analysis, the monthly data is appropriately selected for the evaluation of the three-year period risks and returns. As asserted by Howe and Xing (2003), the weekly and monthly data are more widely applied by researches for risks and returns analysis compared with daily data, which tends to be more appropriate in the estimation of high volatility. As a result, in order to come up with more accurate calculations, the monthly data is used in our analysis. 2.3 The share price and dividend First of all, according to Kim, Kim and Shin (2012), the closing price serves as the best indicator of the changes in stock market, as well as what the share price is. Also, dividends should be accounted for in the calculation in great part because fluctuations in share prices are influenced by dividends. Precisely, the announcement of dividends on ex-dividend day would result in the adjustment of share price. Besides, the dividend policy tends to shape the purchasing behavior of the individual investors (Dong, Robinson and Veld, 2005). Therefore, closing prices of last trading day of each month and dividends on ex-dividend date are used in our calculation. 2.4 The market index Academics and practitioners tend to use S&P/ASX 200 Accumulation Index as the closest proxy for the performance of the Australian stock market. As reported by Deutsche Bank Group (2011), S&P/ASX 200 Accumulation Index, as a reference index, is made up of the top 200 listed Australian entities in terms of the market capitalization. Also, unlike S&P/ASX 200 as a 2

Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813 price index, it is an accumulation index with dividends re-invested accounted for over time (Deutsche Bank Group, 2010). For research and practical purposes, Clements and Drew (2004) suggest that S&P/ASX 200 Accumulation Index tends to serve as a better proxy for Australian equity market. Moreover, according to Forbes and Basu (2011), this index is deemed as the most widely used benchmark to measure the performance of local share market, which was further confirmed by Independent Investment Research Pty Limited (2011). Accordingly, S&P/ASX 200 Accumulation Index can provide effective estimations as market proxy, also considering that dividends are calculated for our individual stocks. 2.5 The risk-free asset and return According to Damodaran (2008), basically, risk-free rate is perceived as the expected return on risk-free assets, which mainly include the bonds issued by top-rated governments such as the US, the UK and Germany (Bollen, 2011). Also, Hughes (2012) asserts that the risk-free rate, that is, the yield on Treasury securities provides a benchmark against which the expected returns on other risky investments can be estimated. Similarly, as supported by Hsieh, Huang, Yan, Wu and Lai (2011), government bonds rate should be used as risk-free rate of return. Still, the question remains on the trade-off between short-term Treasury bills and long-term Treasury bonds. Without taking the inflation and market risk into consideration, Mukherji (2011) proposed that the 10-year Treasury bonds are the most commonly represented as risk-free securities, which was held by Damodaran (2008) as well. It is, therefore, concluded that the 10-year government bonds will be employed in the calculations of CAPM approach. 3. Mean-variance approach

3.1 Calculation of expected return and standard deviation of WOW and DUE Prior to the estimation of the expected return for individual stock, the monthly returns should be calculated. In our study, first of all, the closing share prices on the last trading day of each month and dividends on ex-dividend date are taken into account. Also, as the period of the collected data stretches from 31 March 2009 to 30 March 2012, 37 corresponding monthly returns should be obtained by the formula (1):

3

Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813

Where: Pt = closing share price at month t

Pt-1 = closing share price at month t-1

dt = the monthly dividend over the holding period

𝑟𝑡 =montly returns

Subsequently, the monthly expected return of WOW and DUE can be measured as the mean of the above monthly returns using the formula (2):

Where: Cr = monthly expected return

𝑟𝑡 = monthly return

n = the number of periods (in our case n=37 months) Regarding the standard deviation of returns, Frino, Hill and Chen (2009) suggests that it can be estimated from a historical time series of returns, provided that the random process that generated returns in the past gives a prediction of the similar process that will generate returns in the future, and also that an observed set of historical returns represents a random draw from an underlying distribution of returns are assumed. Accordingly, based on these assumptions, the standard deviation can be calculated as follows by the formula (3):

Where: Cr = monthly expected return

𝑟𝑡 = monthly return

n = the number of periods (in our case n=37 months) According to the above three formulas, the expected return and standard deviation of WOW and DUE can be summarized in Table 1 (Calculation details are referred to Appendix 2.1): Table 1 Monthly ER and SD of WOW and DUE Shares

Monthly Expected Return 4

Standard Deviation

Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813 WOW

0.46%

4.00%

DUE

1.51%

4.58%

3.2 Calculation of portfolio combination expected returns and standard deviation In terms of the expected return of a portfolio combination, it can be calculated with the proportions that WOW and DUE shares contribute to the portfolio, as well as their individual expected return as follows:

Where: 𝑟𝑝 = expected return of portfolio combination 𝑥1 , 𝑥2 = proportion of the portfolio invested in WOW and DUE 𝑟1 = expected return of WOW

𝑟2 = expected return of DUE

Then, the standard deviation of a two-security portfolio can be derived from the formula (5):

Where: V𝟏, V𝟐 = the standard deviation of WOW and DUE Also, the covariance of WOW and DUE can be calculated as follows:

Where: V𝟏𝟐 = the covariance of returns on DUE and WOW In summary, the expected returns and standard deviations are shown in Appendix 2.2 and the covariance of WOW and DUE is 0.0013, indicated in Appendix 2.1.

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Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813 3.3 Graph of the portfolio combination Based on the results calculated in Appendix 2.2, the corresponding graph can be obtained showing the monthly expected returns (y-axis) and standard deviations (x-axis) of portfolio combinations as follows:

Mean-Variance Approach Portfolio Monthly Expected Return

0.01600 0.01400 0.01200 0.01000 0.00800 0.00600 0.00400 0.00200 0.00000 0.03800

0.04000

0.04200

0.04400

0.04600

0.04800

Portfolio Standard Deviation

Figure 1 Monthly ER and SD of portfolio combinations

4. CAPM approach

4.1 Introduction of CAPM approach The Capital Asset Pricing Model (CAPM) is normally constructed for pricing on an individual security or a portfolio via the determination of its risk premium. Also, as both the risk-free asset and the market portfolio lie on the Capital Market Line (CML), the liner relationship between the expected return and standard deviation of any portfolio chosen by a rational investor should be presented by the formula (7):

6

Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813 In equilibrium, through substituting the standard deviation of returns with the beta, the formula (7) can be rewritten as follows, in order to calculate the expected return on the portfolio 𝐸𝑟 𝑝  and individual security 𝐸(𝑟𝑖 ) respectively.

Where: V𝒑 , V𝒎 = standard deviation of market and portfolio 𝐸𝑟𝑝  𝐸(𝑟𝑖 ) = the expected return on portfolio and security i

𝑟𝑓 = the excess market return

𝑟𝑓 = the risk-free rate

𝐸𝑟𝑚 −

E𝑝E𝑖= the beta of portfolio and security i

4.2 Calculation of beta of WOW and DUE As the beta should be estimated through the historical data, the above equations should be rearranged as:

Where: 𝑟𝑖,𝑡 𝑟𝑓,𝑡 𝑟𝑚,𝑡 = return on share i, risk-free asset and market over period t 𝑟𝑖,𝑡 =

(𝑃𝑡 −𝑃𝑡−1 )+𝑑 𝑡

𝑟𝑚,𝑡 =

𝑃𝑡−1 (𝐼𝑡 −𝐼𝑡−1 ) 𝐼𝑡−1

(𝑃𝑡 , 𝑃𝑡−1 = the closing share price at month t, t-1)

(𝐼𝑡 , 𝐼𝑡−1 = the market index at month t, t-1)

Also, as CAPM implies that the coefficient a is equal to 0, and coefficient b, which measures the beta of share i is a regression coefficient that can be calculated from historical data (Frino, Hill and Chen 2009). Accordingly, E is given below:

As indicated in Appendix 3.1, the beta for WOW and DUE are 0.353103, and 0.249191 respectively.

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Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813 4.3 Calculation of expected return of WOW and DUE

As indicated by formula (9) above, under CAPM approach the return on security consists of two components: the risk-free rate of return and risk premium.

Justification of risk free return 𝒓𝒇 and market risk premium As discussed above, a 10-year government bond is used as risk-free rate of return in our calculation. Also, according to Bornholt (2007, p. 75), the failure of accurate estimation on market risk premium would lead to severe results under CAPM approach. Therefore, as Fama and French (2006, p. 2169) suggest that the market risk premium can be better estimated on the basis of the long-term average returns on equities in excess of bond rates. Based on all these analysis, it is concluded that the expected market risk premium can be represented by the average market risk premium from March 2009 to March 2012; and the monthly expected returns for WOW and DUE are 0.6131% and 0.5565% respectively (Refer to Appendix 3.2 for calculation details).

4.4 Calculation of expected returns and beta of portfolio combination The beta 𝛽𝑝 and expected return 𝐸𝑟𝑝  of portfolio can be calculated by the following formula:

Where: 𝐸𝑟𝑝  = the expected return of portfolio 𝛽𝑝 = beta of portfolio 𝐸(𝑟1 ) 𝐸(𝑟2 ) = the expected return of WOW and DUE 8

Group Name: Unicorn SID: 312030592, 420027638, 420046949, 420063131,311040813 𝑥1 𝑥2 = proportion of the portfolio invested in WOW and DUE 𝛽1 𝛽2 = beta of WOW and DUE 4.5 Graph of portfolio combinations Based on the results calculated in Appendix 3.3, the corresponding graph can be obtained showing the monthly expected returns (y-axis) and beta (x-axis) of portfolio combinations as

Portfolio Mothly Expected Return

follows:

CAPM Approach

0.006200 0.006100 0.006000 0.005900 0.005800 0.005700 0.005600 0.005500 0.000000

0.100000

0.200000

Portfolio Beta

0.300000

0.400000

Figure 2 Monthly ER and Beta of portfolio combinations 5. Analysis

In order to give a rational and proper examination of the risk and return profiles of various portfolio combinations of the two shares, Grauer and Janmaat (2004) support that Mean-variance and CAPM models are the most popular estimation approaches. However, due to the underlying assumptions attaching to those model application theories, their rationales may turn out to be practically infeasible in reality. Accordingly, in this section, the rationales and underlying assumptions under the two approaches will be identified and critically analyzed. The rationale and assumption of MV When making investment decisions in capital markets, rational invest...