## Quantitative Methods

In this Assignment I choose to analyse the following three stocks: Johnson and Johnson DC (JNJ), Hewlett Packard CO (HPQ) and American Express INC (AXP). The data I use is based on the monthly average stock for 30 consecutive months from 31/12/2003 to 31/05/2006. Q1 This Assignment shall first begin with an individual statistical description of each series. Johnson and Johnson DC The graph below show the share price fluctuation during that period: From the graph above it demonstrates that Johnson and Johnson’s share price average highest on 29/04/2005, and lowest on 31/03/2004. After the share peak on 29/04/2005, the share started to drop and fluctuate a bit. However, it seems that the share price of Johnson and Johnson began to pick up on the 31/01/2006, and its share price 60.22 is higher than the beginning of the sample (51.66).

The table above is a descriptive statistic of the Johnson and Johnson’s stock during the period using Microsoft Excel. In here, because the mean (59.78333333) is very close to the median (59.66), the points on the distribution appear approximately symmetrical. We can assume that the distribution is very close to a normal distribution. The standard deviation describes how the share prices cluster around the mean. In here, the standard deviation is relatively small which indicates that the share price is stable during this period. Kurtosis is “a measure of whether the data are peaked or flat relative to a normal distribution”1 and “is based on the differences around the mean raised to the fourth power.”2 Because a normal distribution would have a kurtosis of zero, a negative kurtosis here indicates flatness of the distribution3.

The mean of the share prices is higher than its median, which indicates right-skewness. It means that most of the values are in the lower portion of the distribution. This distortion is caused by some extremely large values in the sample. The maximum of the sample is 32.9 and the minimum is 17.89 (see table above.) The positive skewness means that the distribution is right-skewed and that most values cluster around the lower portion with the exception of some large values.

These large values pull the mean upward so that the mean is greater than the median. The negative kurtosis means that the distribution is “flat.” The standard deviation is similar compared to Johnson and Johnson’s shares in this report, but Hewlett Packard’s share price has been fluctuated a little bit. General speaking, Hewlett Packard’s share price has been relatively stable during the period with a hint of future increases.

American Express

Compared to Hewlett Packard, American Express doesn’t fluctuate as much as Hewlett Packard. Again it fluctuates a little bit from the period 31/12/2003 until a quite low point 44.9666 on 31/03/2005. Then the share price begins to peak up and continuously grow until the highest mark 54.36 during the month of 31/05/2006.

The negative kurtosis again indicates flatness of the distribution, which means that no recurring values or clustering around the mean. The standard deviation is small compared to other shares in this report, which indicates that American Express share price has been relatively stable during the period. This can be enforced by the Range (12.142) which is the lowest compared to other shares.