Testing of Randomness of Stock Price of Prime Commercial Bank Ltd.

The random walk theory is the occurrence of an event determined by a series of random movements - in other words, events that cannot be predicted.Applying the random walk theory to finance and stocks suggests that stock prices change randomly, making it impossible to predict stock prices. The random walk theory corresponds to the belief that markets are efficient, and that it is not possible to beat or predict the market because stock prices reflect all available information and the occurrence of new information is seemingly random as well. 

The random walk theory is in direct opposition to technical analysis, which contends that a stock's future price can be forecasted based on historical information through observing chart patterns and technical indicators. 

To test the random walk theory, the stock price of Prime Commercial Bank Limited is taken. The stock price from 18^st March 2013 to 29^th July 2013 is taken as a sample data. The 90 days trading data is analyzed to check the randomness of stock price of Prime Commercial Bank Ltd. The result are summarized below:

Runs Test
	Price_PCBL
Test Valuea	323.7444
Cases < Test Value	37
Cases >= Test Value	53
Total Cases	90
Number of Runs	20
Z	-5.383
Asymp. Sig. (2-tailed)	.000
a. Mean

The runs test can be used to decide if a data set is from a random process.A run is defined as a series of increasing values or a series of decreasing values. The number of increasing, or decreasing, values is the length of the run. In a random data set, the probability that the (I+1)th value is larger or smaller than the Ith value follows a binomial distribution, which forms the basis of the runs test.Run represents the no of times the stock price was changed from the mean value. 

The observation shows that, the mean stock value over the period of 90 trading days is Rs. 323.74 The stock value remains below the mean price for 37 days, and remaining 53 days, it is above the mean price. So, during the course of price change, the price changes 20 times around the mean value, which is called number of runs. From the table, the significance value is 0.00 hence the stock price of Prime Commercial Bank does not follow random pattern.

Autocorrelation is a mathematical representation of the degree of similarity between a given time series and a lagged version of itself over successive time intervals. It is the same as calculating the correlation between two different time series, except that the same time series is used twice - once in its original form and once lagged one or more time periods.The term can also be referred to as "lagged correlation" or "serial correlation". From the data, the autocorrelation in stock price can be shown in following table.

Autocorrelations
Series:Price_PCBL
Lag	Autocorrelation	Std. Errora	Box-Ljung Statistic
			Value	df	Sig.b
1	.739	.104	50.836	1	.000
2	.561	.103	80.443	2	.000
3	.405	.103	96.080	3	.000
4	.273	.102	103.250	4	.000
5	.175	.101	106.232	5	.000
6	.130	.101	107.892	6	.000
7	.075	.100	108.451	7	.000
8	-.020	.100	108.492	8	.000
9	-.119	.099	109.929	9	.000
10	-.181	.098	113.306	10	.000
11	-.239	.098	119.269	11	.000
12	-.255	.097	126.178	12	.000
13	-.263	.096	133.629	13	.000
14	-.228	.096	139.274	14	.000
15	-.235	.095	145.367	15	.000
16	-.224	.095	150.969	16	.000
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.

Autocorrelation Test

H_o = there is no autocorrelation i.e. the stock price are in random order.

H₁ = there exist autocorrelation and price does not follow random order.

From the autocorrelation table, p-value of (1-16) lag is 0.00 therefore null hypothesis is rejected. Hence the stock price of Prime Commercial Bank Ltd. doesn’t follow random pattern. So, the stock price of Prime Commercial Bank Ltd. can be predicted using past data.

Submitted By: Mr. Laxman Aryal

Apex College, Mnikkya