The analysis was conducted so as to study the behavior of two stocks i.e Commonwealth Bank of Australia and ABM resources. We began our analysis using various financial and government websites. For Instance, the risk free rate was derived from RBA, Australia using 30 Day Bank Accepted Bill as a proxy. On the other hand, all the stock related and market index(S&P 500-APX 200)information was derived from Yahoo Finance. We concluded the report by conducting a regression analysis between the excess return of each stock over risk free rate and excess return of market index over risk free rate
As we can infer from the above data that ABM resources has higher risk in the form of higher standard deviation in comparison to Common Wealth Bank of Australia, but still the former stock offers lower return than the latter. Thus, ABU is inefficiently priced stock.
Data and Risk Free Asset:
The data for the report has been sourced from yahoo finance and RBA website. The period of our analysis is from January 2011 to January 2014.
While we only got the monthly adjusted closing prices for each stock and market index, we converted the prices into monthly returns using excel formula, which is clearly accessible in the attached spreadsheet. In general, we just calculated the excess return for each month in comparison to the previous year using the following formula:
As for the proxy of market index, we used S&P/ASx-200 Index. The monthly adjusted prices for the index were also derived from Yahoo Finance and the monthly returns were derived using the same formula as specified above. We have used the S&P/ASX-200 index as a proxy for the market index as it is primarily designed to reflect the Australian Equity Market.
Similarly, The yield on a 30 day Bank Accepted Bills (BAB) is used as the risk free interest to calculate the excess returns for both the market and individual stocks. The data on the bank bills was sourced from Reserve Bank of Australia Statistical Tables F1. Important to note that for the purpose of conducting of the regression analysis, we converted the annual return into monthly return by dividing it with 1200.
The yield on BAB was considered as a risk free interest because BABs can only be sold by prime banks. Such banks must have a rating of at least AA- on the long term securities and A1+ on the short term securities. This means there is virtually no risk of default since a short term security rating of A1+ is of highest credit quality.
The prices are adjusted after stock splits and dividend payments. This is achieved by use of multipliers. If for example two shares are issued for each share (2 for 1 split) the preceding prices are multiplied by 0.5. The dividend multiplier is computed by subtracting the dividend paid as a proportion of the closing price of the previous day from 1. For example if a dividend of $0.05 is paid in Sep 17th and the closing price for Sep 16th was $25, then the multiplier is (1-0.05/25) = 0.998. Just like in the case of split multiplier, the preceding prices are adjusted by multiplying them with dividend multiplier. An Example is as in the following table
Single Index Model
The single index model (SIM) divides the excess returns of a stock into three components as follows
Where αiis the firm specific expected return,ri is the return on the stock,rf is the risk free interest, βi is the firm’s beta, rm is the market return and ei is the return due to unexpected firm-specific factors.
The Single Index Model(SIM) was estimated by regressing the excess returns of both the stocks against the excess returns of the market index. The extensive results have been duly attached in the spreadsheet.
Below given are the summarized results of our regression analysis:
As we can see from the above table that the beta for stocks varies from the market sensitivity. However, CAN has beta closer to the market while ABM has higher sensitivity to the market risk with the beta of 1.44. Thus, ABM can be classified as an aggressive stock.
Based on the measure of goodness of fit (R-Square), both the companies have different level of systematic risk as compared to the non-systematic risk. For Instance, while R square multiple of CBA is 57.6%, for ABU it is only 2.8%13.62%. Thus, ABU have the capacity to diversify major portion of its total risk.
The betas computed in this analysis might be different from those of other providers for the following reasons
- Several providers of the beta use the Market Model for their estimation. This model makes use of raw returns instead of the excess returns.
- Some firms estimate their beta value by forecasting it as a function of past betas.
- Some providers use models containing additional factors such as growth, firm size and leverage.
- In some cases, the estimate is based on different length of time or different frequency e.g. using weekly returns instead of the monthly returns.
- Some sources provide the adjusted Beta instead of the raw beta.
As for the trading idea, ABU has the lowest alpha of -0.009. Thus, a risk free (zero-beta) portfolio can be formed by buying an S&P/ASX- 200 index ETF and selling ABU stock. The proportions forming the portfolio are calculated as follows
(Portforlio beta)βp=wABUβABU+wEFTβEFT=0⇒where wABU+wEFT=1
Proportion for ABU
Proportion for S&P/ASX-200 index ETF
Where, βABU and βETF are the beta for ABU and S&P/ASX-200 index ETF respectively. There are several risks associated with arbitrage trading.
- The values of beta and alpha are computed based on historical prices. The market is very volatile and the future might not behave in a similar manner.
- If very many people execute a similar strategy at the same time, the prices of the two stocks might be highly affected. Such a scenario would lead to huge losses.
- Mispricing of securities in the market doesn’t last for long and therefore it is difficult to find an arbitrage opportunity. As a result of the advanced technology in use today, mispricing of securities is usually eliminated very fast.