BUS5SBF Statistics for Business and Finance-Statistical Metrics

Between October 2009 and August 2010, the Google Price index experienced a decreasing trend from around 570 US dollars to approximately 420 USD dollar. This was a great drop in the investment which might have reduced the rate of investment for the stock. After August 2010, the stock price improved to around 600 USD in October 2010, which approximately remained in that level until February 2011. The price reduced to around 500 USD and it experienced seasonality in around June and July 2011. However, the seasonal effects persisted until June 2012, where the stock price increased significantly from June 2012 to February 2014, marking a maximum stock price of around 1200 US dollars between October 2009 and May 2014.

In comparison between the three stock prices, S & P seems to be have experienced minimum seasonal effects for the trend. In addition, its trend has been constantly increasing from October 2009 to May 2014, although it experienced some significant drop between April 2012 and October the same year. After this challenging period for S & P stock price index, it improved significantly from around 1100 US dollars to 1900 US dollars in May 2014. Google and Yahoo stock prices experienced constant and unchanging prices for longer periods, indicating that they experienced slowed growth in the market and investment.

1. Summary Statistics

a. Determining the stock that has more risk

 The table above shows the summary statistics of three stock prices, S & P, Google and Yahoo together with their adjacent returns. The returns can be used to determine the riskier stock and the best within the three. Yahoo stock price has the highest average returns of 1.48% followed by Google stock that has 1.25% and finally S & P stock price that has an average of 1.09%. Comparing the three stocks, Google has the highest variance of 60.15% against S & P stock that has 15% variation. Therefore, it can be concluded that Google stock price has the most investment risk followed by Yahoo and finally S & P Index.  S & P is the best stock to invest for individuals who does not wish to be involved in high-risk business, although stock with great risk has the highest returns on average. Comparing Google and Yahoo Index, the former is riskier than Yahoo because it has more variation.

b. Normality test

Testing normality for the three returns; S & P, Google and Yahoo, the test statistics will be obtained and the Q-Q plot will be plotted to determine whether the data is normally distributed.

Based on the table above, the three data for the stock price returns are normally distributed. This test is based on the following hypothesis.

Null hypothesis: The data is normally distributed

Since the observed p-values are greater than the significance level 0.05, we fail to reject the null hypothesis and conclude that the data is normally distributed. The argument can also be observed on the Q-Q plot plots shown below for the three variables.

The points are concentrated within the straight line indicating that they are normally distributed.After standardising the data, most of the points are concentrated in the straight line, which is a clear indication that the data is normally distributed which also applies to Yahoo stock returns data.

3. Testing whether Google and Yahoo have the same average returns

Null hypothesis: The average of Google and Yahoo are different

Alternative hypothesis: Google and Yahoo returns averages are the same

Based on the two-sample test shown above, the p-value is greater than the significance level, hence failing to reject the null hypothesis. Therefore, I would prefer to use Google stock as the investment stand because it has a greater chance of making at least 4% returns and a lower chance of making losses.

4. Calculating Excess returns

1. Estimating the CAPM linear regression

The intercept coefficient indicates that in cases where the excess market return is zero, the mean excess return on Google stock will be 0.5121%. Therefore, increasing the excess market return by 1% percent improves Google’s excess returns by 1.2343. Therefore, the market return more risky than Google returns because it contributes to the increment of excess returns for Google stock.

1. R²interpretation

The predictor variable (market return) was significant at 95% confidence level. Therefore, it contributes 38.06% of the total variation experienced on the Google’s excess returns. This can be observed in the table below, which the regression summary.

 Slope coefficient

The confidence interval for the slope is [0.8005, 1.668], which means that at 95% confidence level, the slope coefficient will always be contained in the interval provided that the data meets the same standards.

6. Determining whether Google stock was neutral 

The table above shows the lower and upper bounds of the confidence interval for testing whether Google stock returns are neutral. In this case, the test determines if the Google stock returns that are greater than 0 accounts for 50% of the data. The obtained bounds are [0.4497, 0.7140], indicating that at 95% confidence interval, the proportion of Google returns above 0 will always be with the interval.