Finance Portfolio Management - Report Example

Appendixes14

Appendix 1 Adjusted close price14

Appendix 2 Discrete rate of return15

Appendix 3 Arithmetic mean return and Geometric mean return16

Appendix 4 Variance and Standard deviation16

Appendix 5 Covariance matrix16

Appendix 6 Correlation matrix16

Appendix 7 Weekly rate of return of equally weighted portfolio16

Appendix 8 Risk free rate17

Appendix 9 Excess returns18

Appendix 10 Regression analysis19

Figure 1 Regression analysis for Square Inc19

Figure 2 Regression analysis for Tableau Software20

Figure 3 Regression analysis for Almaden Minerals21

Figure 4 Regression of Nasdaq22

Appendix 1123

Graph 1 Square Characteristic Line23

Graph 2 Tableau Characteristic Line23

Graph 3 Almaden Minerals24

Graph 4 Nasdaq Characteristic Line24

FINANCE PORTFOLIO MANAGEMENT

Introduction

The report will analyze three stocks listed on the NASDAQ namely square Inc. Tableau Software Inc. and Almaden minerals for the recent 28 weeks. The report will check on the rate of returns, variance, covariance correlation and associated risks. The report will also calculate beta and alpha of the stocks and draw the security characteristic lines.

Part 1:

1.1. Rate of return

The rate of return is the amount of dollars gained or lost in a particular investment period. The rate of return in the stock market entails the loss or gain at particular stock prices as they respond to market conditions, profitability, information and other factors. The rate of return is divided into the discrete rate of return and the continuously compounded rate of return.

1.1.1. Discrete rate of return

The discrete rate of return computes the rate of change in a stock in the market for a particular countable period (Arrow & Kruz 2013).

Discrete rate of return:

Whereby: P1 is the share price at the end of the period, P0 is share price at the beginning of the period, D is the dividend.

The weekly values in percentages for discrete rates of return the three stock namely Square Inc. Tableau Software Inc. Amalden minerals and NASDAQ are shown in appendix 2.

1.1.2. Arithmetic mean return and geometric mean return.

The arithmetic mean return is the summation of returns divided by the number of periods under consideration. However, the geometric mean return is the single return per-period which gives a similar cumulative performance as a sequence of actual returns.

Arithmetic mean return =

Geometric mean return =

For this report, the geometric mean is the best measure for the return, which shows the constant annual return in matching the total performance in the period being evaluated. In the table, the geometric mean is less than the arithmetic mean, which means the gap would be greater between geometric mean and arithmetic mean when the fluctuation gets larger (Qi et al, 2014). Arithmetic and geometric means for the stocks are shown in appendix 3.

1.2. Variance and covariance

Variance is the spread of data in a data set. Variance in a stock market measures how the returns are different from the industry or market average. Variance is accompanied with standard deviation. Together, they are used to calculate the level of risk in a particular investment portfolio (Pietersz, 2011). Risk is always reflected on the actual return on an investment

Variance =, Standard Deviation=

The variance of stocks Square Inc. Tableau Software Inc. Amalden minerals, and Nasdaq are shown in appendix 4.

Covariance is the relation of two variables. In the stock market, covariance is measured to show the degree at which two different securities are related. The securities are portrayed either positive asset return, or negatively asset return. A positive covariance means that asset returns move together while negative covariance show asset returns move inversely. The formula for calculation of covariance is as follows:

Covariance table is shown in appendix 5.

1.2.2. Correlation coefficient

The correlation coefficient is the degree to how two variables are linearly related (Pollet & Wilson, 2010). In the stock market analysis, competing firms use correlation coefficient to ascertain how the stocks are related in response to market conditions. Correlation coefficient numbers range from -1 to 1. The correlations are shown in appendix 6.

1.3. Performance results analysis

Stock is a viable investment. However, it carries a lot of risks that are always reflected in the rate of return. Volatility and standard deviations are used to calculate the levels of risk tied to an asset. In the discrete rate of return, Square Inc. fluctuated from – 3.7786% to 12.1547%. Tableau stocks moved from -7.8647% to 12.5931% while Almaden minerals stocks fluctuated from -12.7907% to 5.0847%. Therefore, out of the three stocks, most volatile stock is Square Inc. followed by Tableau. However, Almaden Stock is the most risky to invest into. Almaden stock has the largest difference between the arithmetic mean and the geometric mean confirming it is the riskiest asset in the portfolio followed by square Inc. then Tableau.

In the analysis of appendix 4, normally, investors are rational and they prefer stocks with the highest return and lowest risk per share. Square Inc. has the highest arithmetic mean of 2.6071% and the lowest risk at 4.0853%. Almaden posses the highest risk at 5.8539% while running into negative returns at -1.2509%. Thus, it is the most unfavorable investment. In correlation on appendix 5, the highest correlation is between Square Inc. and Nasdaq at 0.6850%, while the lowest correlation is between Almaden minerals and Tableau at -0.0208%

Part 2:

2.1 Variance of weighted Portfolio

The equally weighted portfolio is the weighting that gives the same weight and importance to each stock irrespective of the size of the company. The matrix algebra was used to calculate the weekly return and variance of the equally weighted portfolio. Applying the Theory with Matrix Algebra (2013), the return on the portfolio formula used is:

Assume it equals 33.33% and RA, RB and RC are the discrete averages of the three stocks respectively. Looking at appendix 7 the weekly rate of return equally weighted portfolio is 102.3%.

The variance of the portfolio using matrix formula is:

2.2 Compare the returns and variances

The equally weighted portfolio return in part 2.1 is 102.3% and therefore it is higher than the arithmetic mean of Square Inc. at 2.607% and Tableau at 1.713%. Almaden minerals stock is further behind at -1.2509% while it is also higher than the Nasdaq market at 0.4984%. comparing the equally weighted portfolio return to the variance, Square Inc. stock is at 16.68% while having a risk level of 4.085%. Tableau has 17.38% variance with the riskiness of 4.169%. However, Almaden stock possesses the great variance and risk in the portfolio at 34.27% and 5.854% respectively.

Part 3: 3.1. Risk-free rate

The risk-free rate is the theoretical rate of return on an investment assumed to have zero risks for example treasury bills. The risk-free rate is a representation of the interest an investor expects from investment in a risk-free asset for a period of time. This part used an extract from the USA Federal Reserve yields of the 26-week treasury bills shown in appendix

Weekly return= annualized rate/52

3.2 Security Characteristic Line and Regression analysis

The security characteristic line is part of Regression models. In definition, regression analysis is the discussion concerning the relationship between the dependent and independent variable explaining the phenomenon. The regression models assist in forecasting the prices of particular stocks on the stock exchange market. The characteristic line is formed using the regression line. It is also known as the security market line that is the line of best fit in a scatter diagram. It uses the regression equation;

Ri = αi + βiRM + ei

The excess return on the security and is the dependent variable in the regression analysis. αi is the intercept of this equation and expresses a security’s expected excess return when the market excess return is zero. βi is the slope coefficient beta which is the typical response of a particular share’s excess return with regards to the changes in the market index’s excess return. While ei represents other risk factors. The Security Characteristic Line is to show a possible scatter diagram for a stock’s excess return. The market model proposes that the return on a security depends on the return on the market portfolio and the security responsiveness is measured in beta.

The characteristic line is used to compute the asset pricing model and modern portfolio formation techniques.

3.3 Systematic risk and unsystematic risk

The security risk of every stock is partitioned according to systematic risk and unsystematic risk. Systematic risk is the inherent risk affecting the entire market, also known as market risk. Systematic risk is the day to day fluctuations in the stock prices. The unsystematic risk is the specific risk that is diversifiable. Unsystematic risk affects the company stock that one invests in.

Total risk = Systematic risk + unsystematic risk

σi2 = βi2σm2 +σ2 (ei)

Where: σi2 is total variance, σm2 is market variance, σ2 (ei) is firm-specific risk.

The total risk is calculated as the variance of returns for that stock. The part of systematic risk (βi2σm2) depends on the β and σm. Therefore, the market variance (σm) and the beta of security will influence the magnitude of systematic risk. In addition, the systematic risk will affect all firms, therefore, systematic risk will remain. The part of unsystematic risk depends on the σ2 (ei). Generally, the unsystematic risk will even out, and can be eliminated by diversification. The said risk is independent and therefore unrelated across stocks. The total risk of each stock and the portfolio are shown in appendix 16, and the systematic risk and unsystematic risk for each stock and portfolio are also represented respectively.

Part 4 4.1 Evaluation

The method of using variances is widespread in stock analysis mainly because it offers key fluctuation rates of specific stocks and investors can clearly make reasoned judgments on the riskiness of the asset accompanied with standard deviation computation. Covariance and correlations help to ascertain the right portfolio of investment depending on how they are able to move together. For example from the three stocks, square and tableau are positively correlated and can be picked into one investment, however, Almaden minerals do not correlate with the other two. Regression analysis is efficient in analyzing stocks with the overall market index.

4.2 Limitations

Despite the widespread positivity, this analysis method contains some limitations. In the first instance, variance only offers the riskiness of the portfolio, however, it does not offer any mitigation measures against the risks. The method is only limited to the three stocks and therefore cannot show the trend of the whole market. Also, it does not offer accurate predictions on the volatility of stocks. A small error in the regression will distort the whole information and gives wrong analysis (Chatterjee & Hadi, 2015).

4.3 Further Analysis

There is a need for further analysis on how to analyze the poor performing stocks and encourage investors to invest in them. Always, investors have been driven to well-performing stocks leaving the bad stocks depreciating further. This can be done by encouraging an analysis that will make the investor combine a good stock and poor stocks for hedging purposes. Also, further analysis should consider the exact type of risk tied to an asset and how they are reflected in the overall return.

Conclusion

In conclusion, the report analyzed three stocks, Square, Tableau and Almaden minerals using rate of return, variances and correlation. The analysis also employed regression analysis and use of security characteristic line to make decisions about the portfolio. Limitations and propositions for further analysis were also discussed.