Part B Part B of this TMA relates to your own research project. The project plan that you submit for this TMA should be the initial plan about the topic that you want to research for your...

A STATISTICAL REPORT ON NASDAQ (1971-2010)
Introduction:
The NASDAQ Stock Market, also known as the NASDAQ, is an American stock exchange. "NASDAQ"
originally stood for "National Association of Securities Dealers Automated Quotations".

It is the largest
electronic screen-based equity securities trading market in the United States and second-largest by market
capitalization in the world.

As of January 13, 2011, there are 2,872 listings.

It has more trading volume
than any other electronic stock exchange in the world.
For years traders and investors have looked for patterns in stock prices that they could use for better
eturns. The overall finding is that it is difficult to earn above average profits by trading on publicly
available information because it is already available in the securities prices. So here we will look to find
any profitable opportunities or anomalies that go against the concept of efficient market. This empirical
data analysis study is intended to find any significant pattern in NASDAQ or any specific significant
month effect on the stock market.
Research Methodology:
Our data consists of the percentage changes in the monthly closing values of the NASDAQ ("National
Association of Securities Dealers Automated Quotations") from March 1971 to December 2010.We
analyze the entire data to
ing various key features of the data and important movement of the market in
different months.
In addition to analyzing for the entire period (March 1971-December 2010) we have divided the entire
period into the following sub periods to have a better understanding of the market conditions since the
existence of NASDAQ:
(1) 1971-1991(which includes the first oil crisis in 1973,recession in the year 1981 and 1991)
(2) 1992-2001(which includes recession in the year 2001)
(3) 2002-2010 (recession in the year 2008)
We wish to show that the month effect is sensitive to the time period under study.
We present the distribution of monthly percentage changes and test for normality using Jarques-bera
Statistic which essentially is (n/6)(S
2
+(K-3)
2
4) where n= sample size, S= Skewness, K= Kurtosis. Under
normality conditions, for large n, this follows chi-square distribution with two degrees of freedom.
We will study the month effect in the monthly percentage changes in three different ways:
1. If the mean of monthly changes is different from zero, we will subject the mean percentage
change for a given month to the following hypothesis:
H0: μi=0 vs H1: μi≠0
2. If mean of monthly change is different from other months, we will subject the mean percentage
change for a given month to the following hypothesis:
H0: μi=μj vs H1: μi≠μj
3. If the variability of the percentage changes for a given month is different from the remaining
months , I will subject the mean percentage change to the following hypothesis:
H0: σi=σj vs H1: σi≠σj where j={1,2,…,i-1,i+1,…,12}
In addition to standard t-test which assumes normality we will use Kruskal-Wallis non-parametric test
which tests for difference in several population medians. We also use Mood’s Median Test which is
highly robust against outliers and e
or in the data.
The Data and Descriptive Statistic:
The data consists of 479 end of month NASDAQ values and hence 478 values of monthly percentage
changes.
Over the year the value has increased from 101.34 (at the beginning of Fe
uary 1971) to 2,652.87 (at the
eginning of January 2011) – a 2517,79% increase with an average percentage change of 0.89 per month.
The mean monthly percentage change in the NASDAQ value over the entire period is highly significant
(level of significance 2%). The standard deviation of monthly percentage changes was 6.39 . The
Summary Statistics of the monthly percentage changes are given in Table 1:
Table 1: Monthly Percentage Change in 1971-2010
Observations 478
Mean 0.892257
Median 1.257466
S.D. 6.393727
Max 21.97586
Min -27.2339
Skewness -0.49666
Kurtosis 1.792662

As we can see in the histogram below the distribution is slightly skewed to the left as the mean is smaller
than the median. The Jarque-Bera Statistic equals to 83.6564 for a p-value less than 0.01. As the p-value
is 0.05 the normality assumption is violated. So, we will have to lay importance on the histogram.
From the histogram, the distribution is sufficiently normally shaped. Assuming normality, the
probability that NASDAQ will increase in any month is 55.62% and that it would decrease is
44.38%.


From the above normal P-P plot also sufficiently validates normality assumption as the P-P plot
almost follows the straight line.
Table 2 shows the frequency of monthly increases more than 10% and Table 3 shows the
frequency of monthly decreases more than 10% in the entire period over each sub period:
Table 2:
Monthly Increases greater than 10% : 1971-2010
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total
1971-1991 5 1 2 1 9
1992-2001 2 1 1 1 1 1 1 1 1 3 2 15
2002-2010 1 1 1 1 1 5
Total 8 1 0 2 2 1 1 2 1 4 4 3 29
Table 3:
Monthly Decreases greater than 10% : 1971-2010
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total
1971-1991 1 2 1 2 1 7
1992-2001 2 1 1 1 2 2 1 10
2002-2010 1 1 1 1 1 5
Total 0 2 2 1 1 1 0 4 4 3 3 1 22

There were a total of 51 such incidents (in39 years), 25 occu
ed in 1992-2001 (in 10 years). Over the
entire period January experienced a maximum of 8 increases, followed by October and November with 4
increases. August and September suffered a maximum of 4 decreases more than 10% in the entire period.
In the entire period December of 1999 saw the highest increase ever and the biggest decline was in
October of 1987 (the month that included “Black Monday”).
Analysis of Results:
The months with significant mean percentage increases were January with 3.76 followed by May with
0.76. None of the months suffered overall significant decrease in the entire period. Overall there was
significant increase in mean percentage in the entire period with 0.89.
Table 4: Monthly Percentage Change in 1971-2010
1971-2010 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC ALL
Observations 39 39 40 40 40 40 40 40 40 40 40 40 478
Mean
3.75 -0.13 0.04 1.48 1.51 1.01 -0.49 0.37 -0.73 0.69 1.72 1.46
0.89
Median 3.24 -0.40 0.80 1.67 2.77 1.50 -0.79 0.99 0.24 1.94 2.29 1.40 1.26
S.D. 6.26 7.08 5.39 5.89 5.34 5.16 5.31 6.59 6.04 8.37 7.54 6.49 6.39
Max 16.75 19.19 7.58 15.00 11.07 16.62 10.52 11.66 12.98 17.17 14.22 21.98 21.98
Min -8.58 -22.39
-
17.10
-
15.57 -11.91 -11.06 -9.22
-
19.93
-
16.98
-
27.23 -22.90
-
18.76 -27.23
Skewness 0.33 -0.33 -1.23 -0.33 -0.32 0.22 0.16 -0.92 -0.63 -0.90 -1.30 0.16 -0.50
Kurtosis -0.45 2.28 2.28 2.15 1.03 -0.32 1.39 -0.82 1.22 0.67 2.31 2.65 1.79
t-test Sig(2-tailed) 0.00 0.91 0.97 0.12 0.08 0.22 0.56 0.73 0.45 0.60 0.16 0.16 0.00
LCB 1.76 -2.43 -1.69 -0.40 -0.20 -0.64 -2.19 -1.74 -2.66 -1.98 -0.69...