Analyzing Stock Prices of Australia and New Zealand Banking Group

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Analytics 2
1. Australia and New Zealand (ANZ) Banking Group
Among various companies, Australia and New Zealand (ANZ) Banking group is one of the
biggest international banking and financial services group across the globe. Moreover, it is the largest
company in New Zealand following the acquisition of The National Bank of New Zealand in 2003.
Notably, ANZ was initiated in 1830 as the Bank of Australia to become Australia’s leading and fastest
developing bank. The company has its branches across the two countries; however, the headquarter is
located in Melbourne, Australia. The company has experienced tremendous growth in the past two
decades, which resulted in its listing in various stock exchange platforms, such as New Zealand, and
Australia. The company offers multiple services to its customers, which include banking, investment, and
insurance, among others. Therefore, the study seeks to explore the changes exhibited by the stock prices
of AZN; moreover, R statistical package will be used to predict the stock prices and compute factors
affecting the prices.
2. Data exploration and visualization
The primary concept in the data analysis and interpretation is exploration and visualization.
Therefore, the line chart below aid in showing the trend of stock prices of AZN recorded in a span of
three months (May, April, and March).

Analytics 3
3. Stochastic Modelling
There is no doubt one of the highly volatile variables in stock exchange markets is the stock
price. As a result, the variable possesses the unstable property caused by various factors, such as liquidity
on stock return, which result in the random and frequent changes or shifts in the prices (Adeosun, et al.,
2015, 353). As a result, various stakeholders, such as investors, co-operations, and researchers, among
others, tend to look for convenient techniques to estimate or predict the expected movement in the prices.
Among various methods used in the estimation of share prices, the stochastic modelling is the most
effective and suitable technique since the unstable property of the variable assumes a Markov process (a
primal component of stochastic modelling) (Antwi, 2017, 116). Consequently, Geometric Brownian
Motion the most applicable stochastic model used in the estimation of stock prices. The GBM model is
derived from the Brownian Motion (BM) developed by Robert Brown to explain the haphazard
movements of particles due to collision (Adeosun, et al., 2015, 353). Notably, unlike BM, the GBM only
takes values greater than zero (positive values); thus, it is an effective model (Imperial, 2018, 3). The
following function exhibits the GBM model;
S(t) = S0 exp W(t)
Whereby W(t) = μ + σ2/2
S0 is the initial stock price
S(t) is the current stock price (t)
μ represent the drift in a stochastic process
σ represent the volatility in a stochastic process
i. Volatility
As evident, stock prices are unstable thus uncertain, volatility exhibits the magnitude of the
uncertainty in the model. It is expressed by computing the standard deviation of the natural
logarithms of the price changes. The following functions shows volatility: σ = Sμ
√ τ
The τ represent the time in years.