- Introduction
The report describes the process of the analysis of two stocks which has been done using the Single Index Model. It includes collecting and sorting the data, analysis this data using the SIM and regression analysis and the explanation and the evaluation of the results. The findings are useful for decision making in the financial planning.
- Stocks Analyzed
The table above contains the information about two analyzed stocks: the company name, stock code, relevant sector, the average return and the standard deviation of the return. Last two points have been computed using the monthly price data spanning January 2012 to January 2014.
The average return and the standard deviation of Myer Holdings LTD are higher than the average return and the standard deviation of BHP Billiton LTD. It means the stock of BHP Billiton LTD is more inefficiently priced and limits the possibility of large returns for investors while the Myer Holding stock enables the large variation of the price.
The Myer Holding stock has been selected for the analysis because this stock had taken the ninth place in the ASIC’s most shorted stocks. This stock has been so heavily shorted as it has the large standard deviation of the returns. At the same time this company operates in the sector of the human services, so the company is more flexible than the industrial companies and has the more fluctuating price of the stock.
- Data and the risk-free Asset
The sources of the data which has been used in the analysis are different. The list of the ASIC’s shorted stocks was found on the official site of the Australian Securities & Investments Commission (http://www.asic.gov.au/) and the data was sorted from the most shorted to the less shorted stocks.
The monthly adjusted close data of the stocks and the S$P/ASX-200 Index was retrieved from the Yahoo Finance (http://www.finance.yahoo.com/). All data span is from January 2012 to January 2014. The monthly returns were computing with the adjusted close prices using following formula:
where Ptacis the adjusted close price of the during month, Pt-1acis the adjusted close price of the previous month. The monthly returns of the S$P/ASX-200 Index was used in the SIM as the market return rates
All adjusted close price is adjusted for dividends and stock splits. There are the dividend and split multipliers which are used for adjustment of the prices. The split multiplier is calculated as split ratio. For example, in a 4 to 1 split, the pre-split data is multiplied by 0,25. The dividend multiplier is computed using the following formula: 1-DPex, where D is a dividend and Pex is the pre-dividend close price, so the pre-dividend data is multiplied by the that dividend multiplier.
The 30 day bank-accepted bill was used as a proxy of risk-free asset. This information was retrieved from the site of the Reserve Bank of Australia (http://www.rba.gov.au/). This data were presented as percentage per annum, so it was necessary to divide this data by 1200 in order to receive the monthly risk-free rate.
There are two assets which can be considered as risk-free asset. The first is the bank accepted bill and the second one is the Australian Treasury notes. Both assets are short-term assets. But there is difference between these assets. The BAB can be emerged and sold only by prime banks; the Australian Treasury notes are emerged and sold only by government. The rate of return of the BAB is higher than the Australian Treasury notes. Both assets are strongly secured, but the security of the BAB can decrease during the bank crises, therefore the Australian Treasury notes are more trustworthy. The BAB was used in this analysis because there are gaps in the data of the Australian Treasury notes. But the bank-accepted bill is also suitable as a proxy of the risk-free asset.
- The Single Index Model
The Single Index Model is the financial model which is used to compute the return of the asset taking into account the different risks, risk-free rate and market rate of return. The SIM is presented the following formula:
ri-rf=αi+βirm-rf+εi,
where ri is the rate of return of the stock during the period,
rf is the risk-free rate,
rm is the market rate of return during the period,
αi is the alpha of the stock (abnormal return),
βi is the beta of the stock (responsiveness to the market return),
εi is the residuals return,
(ri-rf) is the excess return on the stock,
(rm-rf) is the excess return on the market.
- Regression Results
The table above contains the results of the regression analysis of two stocks. The table includes the following sections: stock name, alpha, beta, standard error and R2. Each indicator has own significance.
Alpha reflects the abnormal risk of the stocks. The risk doesn’t have the explanation. Both stocks have the relatively low alpha. But the Myer Holding LTD has the positive alpha while the BHP Billiton LTD has the positive alpha.
The beta reflects the sensitiveness of the stocks to the changes of the market returns. The beta is higher the sensitiveness is higher too. Hence the beta of the Myer Holding LTD is high and very sensitive to changes of the market return. This stock is aggressive. The beta of the BHP Billiton LTD is less, but it isn’t low. This stock has the average sensitiveness to changes of the market return.
The standard error and R2 reflect the non-systematic and systematic risks respectively. The non-systematic risk of the Myer Holding LTD stock is higher than this risk of the BHP Billiton LTD stock. The systematic risks of both stocks are approximately equal and significantly higher than the non-systematic risks. Almost all risks of two stocks can be diversified.
The beta which was computed in this analysis can differ from other betas in other analyses, because other analyses can use more one factor models, the beta can be computed using other data spans or using a function of the past beta.
- Trade Idea
The table above contains the alphas and betas of two stocks. The SPDR S&P/ASX 200 was used as an S&P/ASX 200 index ETS. The beta of portfolio must be equal zero to get the risk-free portfolio: W1βm+W2βs=0, where W1+W2=1.
W1βm-W1βs+βs=0→ W1=-βsβm-βs→W1=-0,9507281,981323-0,950728=-0,9225
βm-W2βm+W2βs=0→W2=-βmβs-βm→W2=-1,9813230,950728-1,981323=1,9225
Therefore, it is necessary to trade the Myer Holdings LTD on the short positions and the SPND S&P/ASX 200 Fund on the long positions. This portfolio has very low risk.
The portfolio return can be presented in such way:
rp+rf=W1αm+W2α2;
rp+rf=-0,9225*0,00556+1,9225*0,00366=0,0652.
But our values were based on the historical prices, so the prices can unexpectedly vary in the future. If other investors choose our trade idea, we can also get the unexpected result.
References:
Australian Securities & Investments Comissions. (n.d.). Retrieved from http://www.asic.gov.au/;
Australian Securities & Investments Comissions. (n.d.). Short position reports. Retrieved from http://www.asic.gov.au/asic/asic.nsf/byheadline/Short-selling-reporting?openDocument;
Reserve Bank of Australia. (n.d.). Retrieved from http://www.rba.gov.au/;
Reserve Bank of Australia. (2014). Interest Rates and Yields – money Market – Monthly F1. Retrieved from http://www.rba.gov.au/statistics/tables/index.html#interest_rates;
Yahoo Finance. (n.d.). Retrieved from https://au.finance.yahoo.com/;
Yahoo Finance. (n.d.). About historical prices. Retrieved from https://help.yahoo.com/kb/finance/SLN2311.html?impressions=true.
