Assets allocation is the most import and technical step for investors when they want to invest in the financial market. This report will give an example of how to use Portfolio Theory and the Efficient Frontier to distribute weight among the selected 20 stocks to make an optimal portfolio. Lastly, it will compare the six constructed models and find the best one. There are some terms that will be used in this report. Efficient frontier is be used by rational investor to choose the best combination of risk and return among all possible combinations (Essential Investment,2003).Optimal market portfolio is regarded by Doeswijk, Lam and Swinkels (2012) as the best choose or benchmark choose of portfolio for any ordinary investor because it includes all assets’ value among the market.Minimum variance portfolio (MVP) focuses on the goal of reaching the lowest risk through determining appropriate weight of each asset. “MVPs illustrated returns similar to their benchmark capitalization weighted indices but with 25-30% lower standard deviation.”(Haugen and Baker (1991), Clarke, Silva, and Thorley (2006), and Poullaouec (2008) cited in Bausys)
The No Short-selling Portfolios
1.1 Briefing the Selected Shares In order to estimate the efficient frontier and figure out the “market portfolio” in the S&P/ASX 200 Australia market, 20 reliable stocks were selected. Moreover, monthly price and market capital from October 2002 to September 2012 were collected from Bloomberg. To be specific, there is an important assumption of the classical portfolio theory that returns are normally distributed (Alexander, 2008). As shown in the chart 1, the stocks are collected by different capitalization magnitudes. The red bars represent the historic average market capitalizations, while the blue bars tell the current market capitalizations.
Group 22: S&P/ASX 200 Australia Chart 1 Market Capitalizations of 20 Stocks 200000.0 150000.0 100000.0 50000.0 0.0 CURRENT_ MKT_CAP HISTORIC_ MKT_CAP
In addition, these stocks are from various GICS Sectors. Indeed, as shown in the Chart 2 and Appendix A, there are 10 sectors which the stocks belong to. And the number of stocks from a GICS sector is generally decided by the sector’s market capitalization. Chart 2 Sector Breakdown (Soucre: S&P Dow Jones Indices)
1.2 The Risk Free Rate There are several international and domestic instruments that could be regarded as the risk free asset in Australia market. Here, Australia 90 Day Bank Accepted Bills, AUTB1Y, AUTB3M and LIBOR have been chosen as the proxy of the risk free rate. The chart below shows the differences between these rates. The trends of them are generally the same, though there are some tiny numerical differences. In general, the best proxy could be the 3 month Australia government bond. Unfortunately, the historic data of it before June 2009 is unavailable. And comparing to the Australia 90 day bank accepted bills, 1 year Australia government bond suffers more inflation risk. Libor could not reflect the market situation as well as Australia90 day bank accepted bills do. According to Reserve Bank of Australia (RBA, 2012), 90 day bank accepted 2
Group 22: S&P/ASX 200 Australia
bills is the benchmark indicator for short term interest rates in Australia market. Obviously, it is reasonable to select Australia 90 day bank accepted bill as the risk free rate. Chart 3 Sector Breakdown (Soucre: S&P Dow Jones Indices)
9 8 7 6 5 4 3 2 1 0 10/2002 02/2003 06/2003 10/2003 02/2004 06/2004 10/2004 02/2005 06/2005 10/2005 02/2006 06/2006 10/2006 02/2007 06/2007 10/2007 02/2008 06/2008 10/2008 02/2009 06/2009 10/2009 02/2010 06/2010 10/2010 02/2011 06/2011 10/2011 02/2012 06/2012 AUTB3M(%) LIBOR(%) 90 Day Bank Accepted Bills(%) AUTB1Y(%)
1.3 The Efficient Frontier and the Market Portfolio In order to estimate the efficient frontier, some key data should be solved in advance: the...