Forecasting and Quantitative Analysis of ANZ Stock Returns

This report involves statistical analysis to determine the future returns of ANZ stock by holding the stock in alignment with the past or lagged returns derived through the stock. The report includes presentation of data graphically, calculation & presentation of descriptive statistics, regression analysis to test the predictive power of past returns on future returns, summarizing the results, providing conclusions and making recommendations.

FORECASTING AND
QUANTITATIVE
ANALYSIS

Table of Contents
INTRODUCTION...........................................................................................................................3
MAIN BODY..................................................................................................................................4
Presentation of data graphically and discussion of results..........................................................4
Calculation & presentation of descriptive statistics for the stock returns of ANZ......................5
Regression analysis to test the predictive power of past returns on future returns......................6
Summarizing the results, providing conclusions and making recommendations........................7
REFERENCES................................................................................................................................9
Books and Journals......................................................................................................................9

INTRODUCTION
Forecasting and quantitative analysis with regards to stocks involve statistical analysis to
determine the future returns by holding the stock in alignment with the past or lagged returns
derived through the stock. This report would be based on the forecasting & quantitative analysis
of one such Australian listed stock that is, ANZ which is one of the stock forming part of ASX
200 index. ANZ or the Australia & New Zealand Banking Group limited is a multinational
financial services & banking company of Australia headquartered in Melbourne, Victoria. This
bank has obtained second largest & fourth largest place in Australia on the basis of assets held
and market capitalization. The current corporate entity of the bank was set up in 1970 on 1st
October with the merger between ANZ and ES&A bank which was considered as the largest
merger of the Australian history (Ghosal and et. al. 2020).
ANZ is a public limited bank and accordingly traded as ASX: ANZ and NZX: ANZ along with
being one of the component of ASX 200 Index. It served the population across the globe through
range of financial & banking services such as consumer banking, corporate banking, private
banking, investment management & banking, credit cards, private equity, mortgages and global
wealth management (Gunst and Mason, 2018). With 51000 employee base, this bank is serving
approximately 9 million customers across the globe where six million are belonging from
Australia itself who are served through 570 or more branches of the bank.
In this report, the weekly stock returns of ANZ would be calculated and presented
graphically. Further, the calculation, presentation and discussion will be done of description
results obtained for the weekly stock returns of ANZ for past two years. Next, the regression
model will be used to determine the predictive power of past returns on future returns along with
explaining correlation, slope and p value of the series. At last the summary will be presented for
the results and accordingly, recommendations will be made for the improvement in analysis.
The time interval chosen for the forecasting & quantitative analysis performed here is weekly
data where the opening stock prices of ANZ will be taken into account to indicate how returns
have changed every week during the last two years. Daily data if taken for six months would
give a short picture of ANZ stock performance while the monthly data of ANZ stock prices for 5
or more years makes the analysis time consuming (Valaskova, Kliestik and Kovacova, 2018).

Accordingly, weekly stock price data will be taken to capture the market volatility in a better
way. Further, the time period of 2 years will be taken beginning from 1st October 2020 to 1st
October 2022 which is considered to be not so short as well as long period for the purpose of
analysis & forecasting and thus, makes the process simple.
MAIN BODY
Presentation of data graphically and discussion of results
0 2 4 6 8 10 12
0
2
4
6
8
10
12
Weekly returns of ANZ from 2020 - 2022
The above graph shows the weekly returns derived from holding the stock of ANZ from 2020 to
2022 and accordingly, it can be seen that the returns are showing randomness in its movement
where the returns are not following any kind of trend or pattern. This is because of the returns
calculated on the opening price of ANZ stock having taken the random values and accordingly
moving upward or downward randomly without following any trend.
Accordingly, there is no requirement of transforming or decomposing the data pertaining
to weekly stock returns of ANZ for making it well-organized and predictable. It is needed for
build a model as well as making predictions. Decomposed data are free from any kind of
seasonality or trend where the seasonality factor and trend factor are eliminated from the time
series data (Farzaneh and et. al. 2020). As the data of weekly stock returns have already taken
random values and no trend or seasonality is present here, there is no need for further
transformation or decomposition or adjustment to be done in the company’s stock returns data.
Overall, decomposition of time series data is done only when the factor of trend or seasonality is

present in the data which makes it necessary to adjust the data for trends or seasonality in order
to make qualitative predictions.
White noise in time series data like the weekly data of stock returns of ANZ involves the
variable taking place independently along with its distribution being identical giving the value of
mean equivalent to zero (Requioma, et. al. 2020). Therefore, as in the given case, it has been
already discussed that weekly stock returns are randomly distributed throughout the two - year
time period in the past along with the mean value being equivalent to zero, this time series of
weekly stock returns looks like white noise.
Calculation & presentation of descriptive statistics for the stock returns of ANZ
RET
Mean 0.003410821
Median 0.001820867
Mode 0
Standard
Deviation
0.033347885
Kurtosis 0.943158835
Skewness 0.361939973
Range 0.188870933
Minimum -0.0775899
Maximum 0.111281033
Sum 0.358136166
Count 105
Through the above descriptive analysis, it has been identified that the total number of weeks
taken for the stock return analysis and forecasting for the last two years are 105 weeks. Also, the
total returns generated from the stock of ANZ during the period 2020 to 2022 amounted to
35.81% as seen through the sum figure in the descriptive statistics table above. The mean value
of the returns series has been identified as 0 along with the median value being 0 which indicates
that the weekly returns of ANZ stock have randomness in its nature because of which the returns
have taken random values (Kemp, Hort and Hollowood, 2018). The mean value which shows the
average of the total data which can be considered to be the acceptable return currently by such
stocks. In the above descriptive statistics, 0.00 signifies that the return of the stocks of ANZ
given literally no return as shown by the value of 0. Also, the above table shows the value of

median which shows the middle value from the list of the total data being analyzed and studied
for such descriptive statistics under consideration. It shall be noted that such list of data needs to
be in ascending order in order to be able to calculate median from such data (Mishra and et.al.,
2019). The value of median of such data of stock returns of ANZ is 0.00 which again signifies no
relevant significance as the mean was also 0.00 and the middle value is also 0.00. although the
mean and median is 0.00 but it is clear that maximum value of such returns is 0.11 and minimum
value is -0.077 which shows that the return ranges from -0.077 to 0.11 thus, rendering the range
of 0.1888 of the returns generated form the stock of ANZ during the period of 2020 to 2022.
The standard deviation in any descriptive statistics is the measure of dispersion of the data from
the mean of such a data. Lower standard deviation denotes that the current data is clustered
around the mean of such data and higher standard deviation shows that the data is more spread
from such mean. Therefore, in the given data set of returns generated form the stock of ANZ
during the period of 2020 to 2022, the value of standard deviation comes to 0.033 i.e., 3.33%.
Such a value of standard deviation shows that there is lower level of standard deviation. This
means that the data related to the returns of the stock of ANZ from 2020 to 2022 is not spread
and is clustered around the mean value which is 0.003 (Kaur, Stoltzfus and Yellapu, 2018).
Theoretically, this shows that the data values are not very far differentiated from the mean of the
data set and the mean value is a reliable source of information regarding the returns of the stock
of ANZ. This data set includes total of 105 individual returns of ANZ relating to the different
time periods which are being assessed for its movement and direction of movement through the
analysis of descriptive statistics.
Regression analysis to test the predictive power of past returns on future returns
Null hypothesis: There is no statistical relationship between the past returns and future returns
and thus the predictability of past returns is very less.
Alternative hypothesis: There is a statistical relationship between the past returns and future
returns and thus the predictability of past returns is much more.
By testing the above hypothesis at 95% confidence level through regression model the following
results have been obtained.
Regression Statistics

Multiple R 0.00455187
8
R Square 2.07196E-
05
Adjusted R
Square
-0.009783
Standard Error 0.03367117
9
Observations 104
ANOVA
df SS MS F Significance
F
Regression 1 2.4E-06 2.4E-06 0.002113 0.963422
Residual 102 0.115642 0.001134
Total 103 0.115645
Coefficie
nts
Standard
Error
t Stat P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Interce
pt
0.003428
56
0.003318 1.0333
42
0.3038
88
-0.00315 0.01001 -0.00315 0.01001
Retlag 0.004553
998
0.09906 0.0459
72
0.9634
22
-0.19193 0.20103
9
-0.19193 0.201039
Regression equation obtained on the basis of above analysis is as follows:
Y = a + bx
Y = future returns or the weekly returns of ANZ stocks
a = intercept of the regression line where the x axis and y axis intersect each other = 0.003
b = slope of the regression line = 0.0046
x = value of RETLAG (returns of the last week)
Accordingly, the regression equation for the stock returns of ANZ would be as follows:
Ret = 0.003 + 0.0046(Retlag)
Number of observation 105
Adjusted r square -0.009783

Value of the slope 0.0046
P value of the slope 0.963422
Through the above regression analysis results, it can be seen that the predictive power of
lagged returns is very poor because the p value obtained through the regression model is 0.963
which is greater than the significance value of 0.05 and thus the null hypothesis must be accepted
which states that the predictive power of lagged returns on future returns from ANZ stock is less
because of no statistical relationship existing between the predictor variable and response
variable which include Retlag and Ret respectively. Further, the value of slope has come out as
0.0046 which indicates that a one unit change in predictor variable that is, Retlag or past returns
would result in 0.0046 change in the response variable that is, Ret or future weekly returns from
ANZ stocks. This shows that the predictability of the independent variable or x variable which is
Retlag showing the past returns of the ANZ stock is very less in determining the current or future
weekly returns that would be obtained through holding the stocks of ANZ (Bhatnagar, and et. al.
2021). Also, the value of adjusted r square has obtained which indicates the changes that is
taking place in dependent variable with the changes taking place in independent variable. This
value comes as -0.0097 where the value is negative and this means the Retlag are not capable of
determining or forecasting the future returns of Ret. At last the number of observations with
reference to the weekly stock returns of ANZ includes 105 weeks which are relevant to the past
two years that is, from October 2020 to October 2022.
Summarizing the results, providing conclusions and making recommendations
Through the above report, it has been determined that the weekly returns of ANZ stock is
showing decreasing patterns however, no constant trend or seasonality found in the time series
data. As the prices of stock of ANZ is taking random value, the mean value of the weekly returns
comes as 0 and thus, the data can be said to be looking like white noise (Brook and Arnold,
2018). Further, the lagged or past returns of the stock are found to be less powerful in predicting
the future stock returns of ANZ because of the acceptance of null hypothesis, negative adjusted r
value and the value of slope found to be very low or equivalent to zero. The following
recommendations could be made for the improvement of the analysis:

 The Retlag must be replace with some variables like the market risk (beta), market size
(market capitalization), profitability of the company or the book value of stock. This is
because these factors are better representative as well as highly affecting the stock prices
of the company. Thus, making predictions for future stock returns much simpler & easy.
 The analysis could be improved by taking the data for greater term like five years which
can be both weekly or monthly to indicate how ANZ stock is providing returns on year
on year basis (Desboulets, 2018).
 It is also recommended to include the time series data for the ASX index 200 of which
ANZ is one of the component in order to make predictions for future weekly returns from
the stock. ASX 200 being a market index would be best for determining the statistical
relationship between the movement of ANZ stock prices and movement of market index.
The market index is the best indicator of future movement in the price of stock forming
it.
The variables that has been used in this report for the purpose of quantitative analysis &
forecasting are two which includes retlag (past returns of the stock) and the returns of the current
week for determining how much the past returns are powerful in predicting the future stock
returns of ANZ (Desboulets, 2018). The methods used for the analysis are graphical
representation to determine the trend in the weekly stock returns of ANZ, descriptive statistics
for determining the average returns provided by the ANZ stocks on weekly basis. At last,
regression analysis has been used for the purpose of testing the hypothesis in order to determine
whether the Retlag is powerful in predicting the future returns of the stock on weekly basis.

REFERENCES
Books and Journals
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Desboulets, L. D. D., 2018. A review on variable selection in regression
analysis. Econometrics, 6(4), p.45.
Brook, R. J. and Arnold, G. C., 2018. Applied regression analysis and experimental design. CRC
Press.
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field for the minimum phase of solar cycle 23. In AIP Conference Proceedings (Vol.
2286, No. 1, p. 030006). AIP Publishing LLC.
Farzaneh, S., and et. al. 2020. Assessment of noise in time series analysis for Buoy tide
observations. International Journal of Maritime Technology, 13, pp.41-49.
Valaskova, K., Kliestik, T. and Kovacova, M., 2018. Management of financial risks in Slovak
enterprises using regression analysis. Oeconomia copernicana, 9(1), pp.105-121.
Gunst, R. F. and Mason, R. L., 2018. Regression analysis and its application: a data-oriented
approach. CRC Press.
Ghosal, S., and et. al. 2020. Linear Regression Analysis to predict the number of deaths in India
due to SARS-CoV-2 at 6 weeks from day 0 (100 cases-March 14th 2020). Diabetes &
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Mishra, P. and et.al., 2019. Descriptive statistics and normality tests for statistical data. Annals of
cardiac anaesthesia. 22(1). p.67.
Kaur, P., Stoltzfus, J. and Yellapu, V., 2018. Descriptive statistics. International Journal of
Academic Medicine. 4(1). p.60.