Investments Concepts and Applications - Assignment Example

Running Head: Share Calculation [Writer’s Name] [Instructor] [Date] Table of contents Introduction 3 Background Theory 4 Methodology 7 Portfolio Analysis 9 Comments on all portfolios 14 Result Discussion 15 Limitations 19 Recommendations 20 References 21 Appendix 22 Introduction When people invest in stocks, it is usually in a number of different stocks. People typically invest their wealth in a portfolio of assets. The portfolio approach to investment is linked to an investment and risk strategy. By owning multiple assets, certain types of risk can be reduced. Constructing a portfolio requires a thorough selection process involving deciding which types of assets and the quantity these assets to purchase, and more importantly at what time to purchase. This selection process is based on performance measurement techniques analyzing an asset or portfolio’s financial variables and statistics (i.e. return, std-dev, beta etc). The optimum portfolio chosen will ultimately depend on individual investor choice. Nevertheless it is assumed that most investors are rational and risk-averse to differing degrees. Background Theory Risk Risk it the probability of earning less than expected return which can be identified by the variability of return to the asset which can measured by the standard deviation. Research has shown that most of the benefits of diversification, in term of risk reduction, can be gained by forming portfolio containing 15 to 20 randomly added assets. Types or risk Unsystematic risk or diversifiable risk: this risk is firm specific risk and can be eliminated by adding more securities in a portfolio to diversify away the risk in the portfolio. Systematic risk or non-diversifiable risk: the associated risk relate to those factors influence the whole market such as war, inflation, exchange rate. The fact that it is non-diversifiable it is considered the only relevant risk for an investor. Std. Deviation (Total Risk) Unsystematic Risk (Unique Systematic Risk (Market) No. of Securities The risk in a portfolio consisting of one asset can be measured by variance which measures how much is the dispersion of return from the mean. However, correlation is what is important in a portfolio which is made up of multiple assets. The optimum portfolio is in the end based on the risk tolerance of that investor. Covariance and Correlation Covariance describes the relationship between two variables statistically. A positive covariance means that asset returns move together. Negative covariance suggests that the returns move inversely. The correlation coefficient is a measure that determines the degree to which two variable's movements are associated. The correlation is equal to the covariance divided by the product of the asset’s standard deviations. All of Our ten stocks have positive covariance. This means when market index (all ordinaries) increase by 1, those share will also increase by the ‘covariance amount’. Beta Beta measures the volatility of the security, relative to the asset class. The CAPM equation Er = Rf + b(Rm – Rf) is implies that investors require higher levels of expected return to compensate them for higher levels of expected risk. Beta indicates the linear regression of the return of portfolio and the return of the market. The Beta of the market is 1 which is the slope in the regression line indicating the sensitivity of a security to the market. It takes both negative and positive values and zero meaning no correlation between the return on the market compared to the return of the portfolio. A positive value of beta means the increase in the return on the market will reflect an increase on the return of the portfolio, the return of the portfolio of negative value will perform better in recession like state. Portfolio Return Portfolio return is the weighted average of the returns on the securities comprising the portfolio. The risk of a portfolio depends solely on the correlation between the returns on the assets in a portfolio containing 10 or more assets, if the asset number is small then the risk of the portfolio will depend on the risk of the individual assets and the portfolio may take the risk of the riskiest assets in this case. When the correlation coefficient is less than one it generally means reduced portfolio risk. If the correlation coefficient is negative, risk is reduced even more, but this is not a necessary prerequisite for diversification gains. According to ‘expected utility’ investors are risk-averse. Despite these facts, we should note that in terms of stocks you will see a trend of low positive correlation between most of them due the companies being reliant on something similar, e.g. materials such as copper and so on. Methodology This study involves the examination of historical share price data of ten companies listed on the ASX for a period of five years of daily data. We critically analysed the data to achieve a summaries of risk and return for each of the 10 constructed portfolios by calculating the standard deviation, return, variance and betas. The ten companies selected: ASX Code Company Name Sector TLS Telstra Corporation Limited Technology WOW Woolworths Limited Retail QAN Qantas Airways Limited Services BLD Boral Limited Materials WDC Westfield Group Shopping Centre Markets CBA Commonwealth Bank of Australia Financial CSR CSR Limited Materials QBE QBE Insurance Group Limited Financial DJS David Jones Limited Retail BHP BHP Billiton Limited Resources We use equally weighted method to construct our portfolios implying an identical amount is invested in all assets, despite stock price or market capitalization. In theory an equal-weighted portfolios incur large transaction costs and also considered more diversified than a value-weighted index. Moreover, small companies generally have greater growth patterns than larger companies thus investments based on an equally weighted index may face higher returns. The following formulas are used in the calculation. Mean Return= Variance= Standard deviation= Covariance= Correlation= Equal-weighted portfolio return= Portfolio Analysis Portfolio’s 1 – 5 based on Standard Deviation in ascending order. Portfolio One Consisting of 1 Stock: TLS Portfolio Results   1 Portfolio Mean 0.00005 Portfolio Variance 0.00012 Portfolio Std Deviation 0.01078 Portfolio Beta 0.01797 Since there is only one asset in the portfolio, the return, standard deviation, beta and variance will be consistent with the individual stock (TLS). This portfolio has the lowest standard deviation and beta (risk). Portfolio Two Consisting of 2 Stocks: TLS and WOW Portfolio Results   2 Portfolio Mean 0.00045 Portfolio Variance 0.00007 Portfolio Std Deviation 0.0000337 Portfolio Beta 0.02104 Portfolio 2 has a positive and higher return. Portfolio 1 has higher risk. Thus a rational/risk-averse investor will prefer portfolio 2. Portfolio 2 is also considered diversified since more then one asset is included in the portfolio. Portfolio Three Consisting of 3 Stocks: TLS, WOW and QAN Portfolio Results   3 Portfolio Mean 0.00039 Portfolio Variance 0.00007 Portfolio Std Deviation 0.0000334 Portfolio Beta 0.00791 The addition of the QAN stock increased the risk of the portfolio and also gave a negative return. However this portfolio is still far more diversified then portfolio 1, nevertheless portfolio 2 remains the optimum portfolio as this point. Portfolio Four Consisting of 4 Stocks: TLS, WOW, QAN and BLD Portfolio Results   4 Portfolio Mean 0.00036 Portfolio Variance 0.00007 Portfolio Std Deviation 0.0000331 Portfolio Beta 0.01926 In portfolio 4 we notice a slight increase in risk and a poorer return then portfolio 3. Theoretically, a portfolio with a small amount of assets will endure the risk of the most risky assets in that portfolio. Portfolio Five Consisting of 5 Stocks: TLS, WOW, QAN, BLD and WDC Portfolio Results   5 Portfolio Mean 0.00037 Portfolio Variance 0.00006 Portfolio Std Deviation 0.0000298 Portfolio Beta 0.01815 The trend continues with lower returns yet std-dev improved faintly from portfolio 4. I would like to note that the difference between portfolio 4 and portfolio 5 proves the golden rule of finance: higher risk equates to higher returns. Portfolio Six Consisting of 6 Stocks: TLS, WOW, QAN, BLD, WDC and CBA Correlation between CBA and the 5th portfolio: 0.181784 Portfolio Results   6 Portfolio Mean 0.00041 Portfolio Variance 0.00007 Portfolio Std Deviation 0.0000360 Portfolio Beta 0.02158 Portfolio 6’s return and risk simultaneously climbed relatively significantly. Portfolio 2 remains the optimum portfolio. Portfolio Seven Consisting of 7 Stocks: TLS, WOW, QAN, BLD, WDC, CBA and CSR Correlation between CSR and the 6th portfolio: 0.262466 Portfolio Results   7 Portfolio Mean 0.00016 Portfolio Variance 0.00009 Portfolio Std Deviation 0.0000456 Portfolio Beta 0.01654 Since portfolio 6 returns have increased slightly and risk has also dropped recognising the fact that as more assets are added into the portfolio is should gradually become more diversified. Portfolio Eight Consisting of 8 Stocks: TLS, WOW, QAN, BLD, WDC, CBA, CSR and QBE Correlation between QBE and the 7th portfolio: 0.280316 Portfolio Results   8 Portfolio Mean 0.00008 Portfolio Variance 0.00011 Portfolio Std Deviation 0.0000531 Portfolio Beta 0.01832 Our 8th portfolio seems to be the best thus far since portfolio 2. The trend of lower risk and improved returns continues. Portfolio Nine Consisting of 9 Stocks: TLS, WOW, QAN, BLD, WDC, CBA, CSR, QBE and DJS Portfolio Results   9 Portfolio Mean 0.00019 Portfolio Variance 0.00009 Portfolio Std Deviation 0.0000471 Portfolio Beta 0.01917 The addition of the 9th stock (DJS) made little difference to portfolio 8, however returns decreased and std-dev increased. Portfolio Ten Consisting of 10 Stocks: TLS, WOW, QAN, BLD, WDC, CBA, CSR, QBE, DJS and BHP Portfolio Results   10 Portfolio Mean 0.00028 Portfolio Variance 0.00009 Portfolio Std Deviation 0.0000452 Portfolio Beta 0.01389 Our 10th Portfolio conveys considerable difference in returns jumping from a 0.00019 to a positive return of 0.00028. Portfolio 10’s risk is also lower then portfolio 9. Comments on all portfolios Portfolio 10 conveys the greatest systematic risk (beta), yet it demonstrates the specifications that a risk-averse investor would prefer relative to the other 9 portfolios. Although portfolio 10 shows greater risk compared to the previously optimum portfolio 2, it achieves a higher return and more importantly is far more diversified due to the addition of 10 rather than 2 stocks. Naturally via the adding of 10 stocks negative returns were finally avoided. (However there are explanations for these negative returns, see limitations below) Result Discussion From the graph we notice the volatility in variance in portfolios 1 to 7 followed by a steady decrease in variance from portfolios 8 to 10. This graph certainly supports the idea that if we have 10 to 15 assets in a portfolio it will be well diversified thus reducing unsystematic risk. If we look at the total risk, we see a dramatic decrease by just adding one more stock to the portfolio. This is interesting because the first stock in portfolio 1 has the smallest std deviation of 0.01078 and just by adding another stock to the portfolio (of similar risk) we see a drastic reduction in std deviation The addition of stocks to our portfolios had the result of eliminating non-systematic risk (beta approaching 1). By portfolio 10 beta is almost in line with market risk and thus our portfolio is now beginning to be faced only with systematic risk. Systematic risk should now be the investor’s key priority. Our findings here are favorable; from portfolio 6 to 10 we witnessed a gradual simultaneous decrease in risk and a relatively sharp climb in returns. Limitations Concentrating on only 10 stocks in our portfolio analysis, we were not able to entirely demonstrate our aim. Limited number of stocks in a portfolio restricts our examination of exactly how many assets should be added in a portfolio for it to be well diversified. As mentioned previously the investor’s final result will be based on whether he/she is risk-averse, risk neutral or risk seeking. More importantly, the addition of only one type of asset (stocks in our case) to fully diversify a portfolio is unusual. An analysis with the addition of bonds or property to the portfolios for instance could have yielded superior results. Adding only stocks to a portfolio could yield biased or subjective results. For example, our returns where mostly negative till we constructed our 10th portfolio, this is not due to poorly chosen stocks but might have been due to the occurrences of late last year and the financial crises. Thus the addition of other assets to our portfolios may have caused a significant difference in risk and returns in this case. Recommendations In our opinion, stock investment contains a relatively high risk in contrast with buying bonds and properties. It is necessary to determine the weight that should be invested in each asset while investing in risky assets. During this time period we recommend risk seeking investors to invest in the stock market. On the contrary risk neutral or risk-averse investors are recommended to hold the money and observe the potential risk in the market. References AspectHuntley, 2009, [online], Available at URL:http://www.aspecthuntley.com.au [Accessed 1 Aug. 2009]. ASX, 2009, [online], Available at URL: http://www.asx.com.au/. Brailsford T., Heaney R. and Bilson C., Investments Concepts and applications, 3rd ed, Thomson, 2007, Melbourne Yahoo Finance, 2009, [online], Available at URL: http://au.finance.yahoo.com. Appendix Read More