Research Report

Introduction

Australian Securities Exchange (ASX) is the largest financial market in Australia. ASX is located in Sydney and currently has a capitalization of $1.4 trillion which places it among top-10 exchange markets in the world (Australian Securities Exchange, 2013). The main market indexes that are traded on ASX are All Ordinaries (includes all ordinary stocks on the market) and S&P/ASX 200 (includes top-200 stocks).

BHP Billiton is an Australian-based multinational corporation that operates in natural resources industry. The company has operations in 41 countries and at the end of 2012 was ranked as fourth largest company in the world by market capitalization (Financial Times, 2013). Stock of BHP Billiton is traded on ASX and it is one of the major components of All Ordinaries index. This report will employ statistical techniques to analyze weekly stock price fluctuations and returns of BHP Billiton and to test whether the relationship exists between the returns of BHP Billiton and returns of All Ordinaries index.

Statistical Analysis of BHP Billiton Stock Prices

Figure 1 depicts the timeline changes of BHP Billiton stock price between January 11, 1999 and December 31, 2012. In can readily be observed that there was no constant trend present over such a long period. Instead we can distinguish a period of stable price (from 1999 till mid-2003), a period of rapid growth (from mid-2004 till mid-2007), a period of high price fluctuations (from mid-2007 till end of 2008), a period of growth (from 2008 till 2010) and last period when the stock price was falling (2010-2012). Thus, we can conclude that statistical characteristics of the stock prices will probably include high variance and mean value somewhere close to $20. 

Table 1 gives the summary statistics of BHP weekly stock prices. We note that there are 730 data points in our sample which is a large dataset. The mean value is approximately $23 as was predicted. The median is close to the mean which means that the data points are distributed almost evenly around the mean. This assertion is supported by the skewness value of only 0.2 which is close to 0 if symmetric distribution. The measures of dispersion are indeed high as was predicted from graphical analysis. The variance is 177 and standard deviation is 13.3 which combined with the kurtosis of -1.53 means that the distribution is characterized by fat tails.

Analysis of Distribution of Returns

Figure 2 gives visual representation of the returns of BHP Billiton stock and All Ordinaries index during 2011-2012. We can readily note that both time series fluctuate around zero (probable mean and median) and that the fluctuations of stock returns are larger than those of index returns. This implies that the volatility and standard deviation for BHP Billiton returns will probably be larger.

The descriptive statistics for the BHP Billiton and All Ordinaries returns (for full sample 199-2012) is given in the Table 2. We can indeed observe the mean returns are close to zero in both cases. The medians are however closer to 0.5% (in particular, 0.30% for All Ordinaries and 0.58% for BHP) which is probably a consequence of the overall total growth of the economy and stock prices during the discussed time period. The standard deviations are indeed high for both BHP Billiton and All Ordinaries (4.35% and 2.14% respectively). Moreover, as it was predicted from graphical analysis, the fluctuations of stock returns are indeed higher than fluctuations of index because two measures of dispersion (standard deviation and range) are two times larger for the stock. The skewness and kurtosis figures are quite far from zero for both All Ordinaries and BHP which implies that the distribution of the returns is not normal. In fact, empirical research implies that the actual distribution should be log-normal (Knight & Satchell, 2001) which is probably the case.

Analysis of Relationship between BHP Billiton and All Ordinaries Returns

Although All Ordinaries index includes all ordinary stocks that are traded on ASX, the weights of the stocks in the index differ. Each stock is assigned a weight that corresponds to the share of its market capitalization in the total capitalization of the ASX. Since BHP Billiton is one of the largest companies on ASX (by market capitalization) its stock would have one of the largest weights in the index which implies that index returns should be somehow related to the stock returns.

Such relationship is readily apparent from the Figure 2. The two time series demonstrate noticeable co-movement. Table 3 reports statistical parameters that reflect the relationship between BHP stock returns and All Ordinaries index returns. We observe the correlation coefficient of 0.66 which implies quite strong positive linear correlation and supports our assumption of co-movement.

The relationship between the two returns is also assessed through estimation of beta coefficient (Elton, 2010). This coefficient is a slope coefficient from the simple linear regression between market index return (as independent variable) and stock return (as dependent variable). In our case it is equal to 1.35 which means that the movements of stock have positive linear relation to the movements of index and that the magnitude of stock movements is larger than the magnitude of index movements (as coefficient is larger than 1). These findings fully support our previous implications about the relationship between All Ordinaries and BHP Billiton returns.

Conclusion

The analysis of the BHP Billiton stock prices has shown that they have demonstrated significant fluctuations during the period 1999-2012. The returns of this stock were also fluctuating around zero. The same is concluded about the returns of All Ordinaries index, for which the magnitude of fluctuations was lower. The moderate relationship between the two returns was revealed which leads to the conclusion that in the majority of cases stock of BHP Billiton moves along with the market but demonstrates higher magnitude of changes.