Finance - Stocks, Yields, and Portfolios - Essay Example

Prof Introduction: This is the share market report for three companies listed in the NASDAQ. The three entities are MicrosoftCorporation (MSFT), Mattson Technology Inc. (MTSN) and Advanced Management Strategies Group (AMSG). NASDAQ is majorly the stock market of choice for investors in the technology industry, and it enjoys a huge following among American citizenry. The data is available on various historical stock prices sites, including yahoo finance. Microsoft Corporation is the largest of the companies studied, with a noticeable presence in every level of computer software development. It majors in computer software development. Mattson Technology Inc. is in the field of designing, developing, and manufacturing equipment for the manufacture of semiconductors and other products. It is also a significant player in the NASDAQ daily operations, and has a big presence across America. Advanced Management Strategies Group majors in logistics, program management, business consulting, engineering support, product lifecycle management (PLM), PLM IT tools, and IT services management. That therefore implies that the stock analysis carried out comprises one software, one hardware, and one consultancy firm. The NASDAQ composite, an index of the NASDAQ, is studied alongside the three stocks. Summary of Performance: Nasdaq Composite MTSN MSFT AMSG Question 1. The Rates of Return: Discretely compounded return rate measures the rate of changes in the value of asset over a period assuming countable compounding periods while continuously compounded rate of return measures the rate of change in the asset value associated with a holding period under the assumption of continuous compounding. (Analyst Notes par 1). They are calculated as follows: Discretely compounded rate of return: Let s0 be the initial price of a stock and s1 be the current price of the same stock. The return rate R= (s1/ s0)-1 Continuously compounded rate of return: Let rt be the rate of return at a particular point in time. Let rt+1 denote a slight time increment. Then we can represent the change in the rate of return by rt, t+1. rt, t+1 = Natural logarithm of (st+1/st) = In (st+1/st) = In (1+Rt,t+1) where R= ((Return - Capital) / Capital) × 100% = Rate of Return. The arithmetic mean return is a computation of the average returns for a specified period of time. It involves summing up all the returns for the specific period, then dividing the total by the individual number of sub-periods. The geometric mean return calculates the average rate per period on an investment that is compounded over multiple periods (Finance Formulas par1). The following are the figures obtained from the various data when these these statistical features of the data were worked out. Below is a summary of the above described statistics for the three stocks and the Nasdaq Composite index. NASDAQ Composite: Continuous Arithmetic Discrete Arithmetic -0.193240383 -0.001932404 Geometric continuous Geometric Discrete 5.41441661 6.13452503 MSFT Continuous Arithmetic 0.202672219 Discrete arithmetic 0.001495521 Geometric continuous Geometric Discrete 5.877645622 6.138838848 AMSG Continuous Arithmetic -0.016078278 Discrete arithmetic -0.000148657 Geometric continuous Geometric Discrete 7.352796673 6.226747479 MTSN Continuous Arithmetic Discrete Arithmetic 0.224673203 -0.025098039 Geometric continuous Geometric Discrete 0.48196965 0.004987562 b) Calculating Covariance and Correlation between Stocks Covariance is a measure of the degree of association between two variables. For any two stocks, say ABC and XYZ, the covariance is measured thus: The various covariance values for the different stocks and the index were calculated as follows. Cov (MSFT, MTSN) = 0.002063645 Cov (MSFT, AMSG) = 0.000234394 Cov (MSFT, NASDAQ Composite) = -7.29412×10-5 Cov (MTSN, AMSG) = 0.00065737 Cov (MTSN, NASDAQ Composite) = -0.000416916 Cov (AMSG, NASDAQ COMPOSITE) = 3.41978×10-5 The formula for correlation is as follows. where Γ(x,y) = correlation coefficient which falls between -1 and +1. Below are the correlation coefficients as determined using Excel. Corr (MSFT, MTSN) = 0.41730442 Corr (MSFT, AMSG) = 0.255458402 Corr (MSFT, NASDAQ Composite) = -0.140514404 Corr (MTSN, AMSG) = 0.107124021 Corr (MTSN, NASDAQ Composite) = -0.120087966 Corr (AMSG, NASDAQ COMPOSITE) = 0.053089061 c) Positively correlated stocks point to a high likelihood of similar trend in movement over the determined length of time. The stocks may be having a common factor that makes them tend to behave this way, for example for companies producing closely related goods, or those producing complementary goods such as cars and petroleum companies. It is advisable that potential clients shun positively correlated stocks, because if they suffer a slump, it will result in a double loss to the investor. Among the stocks featured in this report, MSFT and MTSN have the highest positive correlation, at 0.41730442. They therefore rank as the riskiest to pair. MSFT and AMSG also have a positive correlation coefficient, at 0.255458402. However, this as does MTSN and AMSG at 0.107124021 has relatively low coefficients of correlation, which indicates a positive but very weak correlation. Therefore we can conclude that all the stocks are risky to pair together according to the data available for the one year period under focus, and the implication is that none of these stocks should be paired by a potential investor. Negatively correlated stocks indicate the tendency not to adopt a similar trend in their movement over time. When one rates high in terms of returns, the other rates low. These stocks are affected by significantly different factors, therefore the tendency. Potential investors are advised to buy shares in such companies since it is highly unlikely that they will suffer a double loss, unlike positively correlated stocks. In this investigation the only negatively correlated values were obtained when two of the stocks were paired against their index, the Nasdaq composite. These were MSFT and MTSN. This fails to offer sufficient information as to whether the two stocks will fail to file high returns in the short term, since the coefficients of correlation are both too low, below the absolute 0.3 threshold. However their negative correlation with the index should be interpreted to mean the investors in the shares of the two companies will have tamed expectations as far as returns for the oncoming season are concerned, if the trend continues. It is notable that the two stocks, MSFT and MTSN also have the highest positive correlation. However AMSG stands out as the only stock with a positive linear correlation with the NASDAQ Composite index, indicating a projection to high returns in the near future. However this expectation is not rosy enough, since the correlation coefficient though positive, is very weak. Question 2. a) The following are the quarterly treasury bill yields for 2012 in the US. Fourth quarter: 10/01/2012 - 12/31/2012 2.5765% Third quarter: 07/01/2012 - 09/30/2012 2.5827% Second quarter: 03/31/2012 - 06/30/2012 2.8425% First quarter: 01/01/2012 - 03/31/2012 3.0032% The weekly yield rates are obtained by dividing the quarterly yields by 13, the number of weeks per every quarter. The results are as follows. Period Periodic rates Weekly rates First quarter 3.0032 0.2310 Second quarter 2.8425 0.2187 Third quarter 2.5827 0.1987 Fourth quarter 2.5765 0.1982 These weekly rates are used as an alternative for the risk free rate. b) The security characteristic line can be defined as the linear plot of a specified security plotted against the entire market portfolio at each point of time. The plot obeys the following model: Where: αi is the abnormal return βi(RM,t – Rf) is the non-distributable or systematic risk εi,t is the distributable risk. The plot shows the corresponding points in time for MSFT against Nasdaq. A line of best fit, the security characteristic line, is shown in red. Similar plots for AMSG and MTSN follow. From the above plot, the security characteristic line is almost stationary, though characterized by a very slow rise. The stock’s returns are experiencing an excessively strained positive return. The MTSN plot is characterized by a linear decline in relation to time. This is an indication of gradual decline in returns. The security characteristic line for the AMSG has a positive gradient, indicative of gradual improvement in the return. c) Entity Total risk MSFT 0.000756323 MTSN 0.033266588 AMSG 0.001161208 NASDAQ 0.000371 Beta Jensen’s Alpha Systematic risk Unsystematic risk MSFT 0.053 0.265 0.214 0.012 MTSN -0.137 -0.945 0.186 0.581 AMSG 0.205 0.422 0.229 0.497 c) Treynor ratio: It is a measure of excess returns, had the market been risk free, for every unit of market risk. It is based on the systematic risk and therefore uses the beta value to measure volatility. Sharpe ratio: It is the ratio of the difference between ratio of return for a quoted portfolio and the risk free rate to standard deviation of the portfolio returns. The formula for its determination is: Jensen’s measure: It is a representation of the mean return on an individual portfolio superior to the average prediction of the capital asset pricing model (CAPM), when the mean market return and portfolio beta are known. Appraisal ratio: It is the ratio of Jensen’s alpha to the unsystematic risk of the portfolio. Treynor ratio Sharpe ratio Jensen’s measure Appraisal ratio AMSG -1.04 -6.257 0.422 0.523 MTSN 1.5562 -1.169 -0.945 -0.225 MSFT -4.023 -7.752 0.265 0.358 Works Cited: Analyst Notes. (n.d.). CFA Exam Study Notes and Practice Questions. Discretely and Continuously Compounded Rates of Return. Web. Coate C. J., Frey K. J., Sakuvich S. N. (2009), Environmental Accounting and Reporting 101 Dunn, C., Cherrington, J. O, Hollander, A. (2005). Enterprise Information Systems. A Pattern Based Approach. Finance Formulas. (n.d.). Geometric Mean Return: Use of Geometric Mean Return Formula. Web. Keitel, Becerra et-al (2011). How to Calculate Environmental Costs, Case Company; Grafica Cienfuegos Treasury Direct. (2013). Interest Rates and Prices. Web. Accessed 20th January 2013. Whittaker, J. M. (2012). Congressional Research Service. The Unemployment Trust Fund (UTF): State Insolvency and Federal Loans to States. Web. 19th January 2013. Read More