STOCK MARKET ANALYSIS

Implementing Statistical Analysis on the BSE-30 Stocks for the period 2008-18

Group 8

Krisha Zaveri A004

Avani Bhatia A022

Jaskirat Singh Chadha A028

Aarushi Jain A030

Ram Chirapuram A045

Mentor:

Dr. K.S. Madhava Rao�Professor, Statistics�Specialization: Nonparametric Inference, Statistics in Social & Allied Sciences�B Sc., M.Sc., M.Phil., Ph.D.

INTRODUCTION

Indian Stock Markets are one of the oldest in Asia. It’s history dates back to nearly 200 years ago.

The Indian Stock Market has two major stock exchanges:�National Stock Exchange (NSE), Established in 1992�Bombay Stock Exchange (BSE), Established in 1875

The term Sensex refers to the benchmark index of the BSE in India. The Sensex is comprised of 30 of the largest and most actively traded stocks on the BSE. Created in 1986, the Sensex is the oldest stock index in India. Analysts and investors use it to observe the cycles of India's economy and the development and decline of particular industries.

In this project we have used the data on day-to-day share prices of 30 stocks on the SENSEX Index for the years 2008 to 2018.

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RATIONALE

One of our main reasons behind choosing a Stock Market dataset as the foundation for our project was to gain a better understanding about how the stock market works and how we can relate it to our Sampling Distributions course in the real-world scenario. Latest data shows that the quantum of retail holding is at an all-time high in the Indian Stock Markets.

So, with the knowledge gathered about the share market from this project we can start investing right now which will prove fruitful for us in the future. The project provided us with the perfect opportunity under the guidance of respected K.S Rao Sir. Therefore, we chose Stock Market as the topic for our Sampling Distribution & Applications Project.

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OBJECTIVES

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To establish Confidence Intervals for the Daily Returns and the Adjusted Closing Stock Prices

To determine if the distribution of daily returns of the Wipro stock follows a normal distribution

To compare Monthly Returns of M&M and TATAMOTORS Stock Prices

To determine which company is riskier to invest in, between DRREDDY and SUNPHARMA

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To determine whether volume of trading is affected during the Diwali period

GLOSSARY

LITERATURE REVIEW

Cristiana Tudor (2008): For better understanding and reference about how to go about stock market data, we have used the below research paper:�http://www.asecu.gr/files/RomaniaProceedings/68.pdf

Tony Yiu (2020): In some parts of this project we used R Programming to perform the Z test and to find the test statistic value and to plot a QQ plot, we have used the below article as reference and a guideline: �https://towardsdatascience.com/are-stock-returns-normally-distributed-e0388d71267e

Reka Pitaloka (2021): Has analysed the ANTM.JK Stock using various statistical measures on Python.

David Diez, Christopher Barr, & Mine Çetinkaya-Rundel (2021): https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_OpenIntro_Statistics_(Diez_et_al)./06%3A_Inference_for_Categorical_Data/6.03%3A_Testing_for_Goodness_of_Fit_using_Chi-Square_(Special_Topic)

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Source of Data & Data Description

• The data used in this project is secondary data of a Stock Market Dataset on Kaggle (2008-2018) compiled by Sugandh Khobragade.
• The 30 component companies which are some of the largest and most actively traded stocks, are representative of various industrial sectors of the Indian economy.
• This dataset contains the data about these 30 stocks for 10 years starts from 06/05/2008 to 04/05/2018. Variables are symbol (ticker), Date, open, high, low, close, adjusted close and volume.

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Data Cleaning

1. Completeness: �The extent to which all statistics that are needed are available.�250 null/incomplete values were found in the dataset.
2. Relevancy:�The ability to use data with maximum efficiency. 261 irrelevant values were found in the dataset.
3. Accuracy:�The degree to which the data mirrors the characteristics of the real-world object or objects it represents. 6 inaccurate values were found in the dataset.

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STATISTICAL TECHNIQUES

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INSIGHTS

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To establish Confidence Intervals for the Daily Returns and the Adjusted Closing Stock Prices

Analysis

Let’s plot the daily closing price for 1 stock say ASIANPAINT.

Confidence Interval

The confidence level represents the proportion (frequency) of acceptable confidence intervals that contain the true value of the unknown parameter.

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Confidence Interval Formula :

Box Plot for the Confidence Interval of Adjusted Closing Price:

Confidence Interval

The 95% confidence interval for the adjusted closing price of 30 stocks data using Excel is given as:

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Probability Distribution of Daily Returns

We are now going to calculate some insights about the probability distribution of returns.

Box Plot for the Confidence Interval of Daily Returns:

Confidence Interval

The 95% confidence interval for the daily returns of 30 stocks data using Excel is given as:

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NORMALITY

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To determine if the distribution of daily returns of the Wipro stock follows a normal distribution

Daily Returns Of WIPRO Stock

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Since the sample dataset has 2456 observations, we are showing the first 10 values from the dataset.

The graph of the sample data of the WIPRO stock is given:

To carry out the calculation for large number of observations, we have grouped the data points and found its corresponding observed frequencies:

CHI-SQUARE GOODNESS OF FIT TEST

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Calculation of goodness fit test using excel function:

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*Here, few values of Ei are less than 5 thus we have clubbed those data points and carried out our final testing.

RESULT

Significance: α = 0.05

Degrees of Freedom (df) is calculated as (no. of categories - 3).Since the no. of observations = 10.�Therefore, df is (10-3) = 7.

The test statistic value is: 244.4656

We have carried out 5% one tail test (Right Hand Test). The test statistics value (244.4656) lies in the critical region (3.325113, ∞). Therefore, we have sufficient information to reject H0. It is reasonable to consider that the distribution of daily returns of the Wipro stock is a good fit.

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RETURNS

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To compare Monthly Returns of M&M and TATAMOTORS Stock Prices

MONTHLY RETURNS

DIWALI PERIOD

MONTHLY RETURNS

LARGE SAMPLE Z-TEST�TEST OF SIGNIFICANCE FOR THE EQUALITY OF 2 MEANS

Result:

The test statistics value for Z-test is 0.09076922. �The p-value for the test statistics value of Z-test is 0.46383798.�In this case, the α value (0.05) is less than the P-value. Hence, we fail to reject the null hypothesis.

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VOLATILITY

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To determine which company is riskier to invest in, between DRREDDY and SUNPHARMA

LARGE SAMPLE F-TEST�TEST OF SIGNIFICANCE FOR COMPARING THE VARIANCES OF TWO SAMPLES

Result:

The test statistics value for F-test is 1.128456762. �The p-value for the test statistics value of F-test is 0.001382402.�In this case, the P value is less than the α-value(0.05). Hence, we reject the null hypothesis.

V/S

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TRADING VOLUMES

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To determine whether volume of trading is affected during the Diwali period

MUHURAT TRADING

Muhurat trading is the trading activity in the Indian stock market on the occasion of Diwali. Usually, it is held during evening hours and is announced by the stock market exchanges notifying traders and investors of the non-scheduled trading hour.

DIWALI PERIOD

The period was taken as 15th October to 14th November as historically, Diwali falls within these dates. Therefore, data was filtered out in MS Excel pertaining to this period. A subsection of the values is shown below.

LARGE SAMPLE Z-TEST�TEST OF SIGNIFICANCE FOR THE EQUALITY OF 2 MEANS

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OUT:

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RESULT

We have carried out a 5% one-tail test. The sample mean volume for the Diwali period is 11,19,282.3 whereas, for the rest of the year it comes out to be 9,52,721.9. In this case, the α value (0.05) is greater than the p-value (0.0208). Hence, we reject the null hypothesis. This implies that volume of trade is significantly higher during the Diwali period than it is during the rest of the year.

This need not come as a surprise as many inactive traders also delve into the stock market at this time. Most investors/traders will buy and/or sell stocks as a gesture to acknowledge the auspiciousness of the day. But it is important to keep in mind that, although stocks are very volatile during this period, they aren’t necessarily profitable. With a simple calculation of the average daily return for this period, which comes out to be -0.0191%, we can see that although many people invest during the period, the focus might not be on profitability as much as it might be on the gesture.

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FINDINGS

• Many of the companies contain outliers specially companies such as Maruti and Reliance. And such a high standard deviation is the reason why stocks are considered risky assets.
• The mean of the daily returns of stocks is quite similar to zero but the fact that it’s positive explains the positive drift of the price time series.
• The stock returns have quite a narrow interquartile range. This phenomenon is called fat tails and is very common in stock analysis.
• The daily returns of WIPRO do not follow a normal distribution. Assuming that they are normally distributed causes us to understate the likelihood of disastrous market returns.
• In most cases, companies of the same industry move along similar lines based on the overall sectoral outlook. For example, here we saw that, the mean of the two stocks-M&M & Tata Motors are almost equal.
• SunPharma is a riskier company to invest in as compared to DrReddy. This may be because Sun Pharma wanted to grow its speciality product range which also involved higher investments. Dr Reddy’s, on the other hand, has continued to focus on niche product launches in the US.
• The number of shares traded is significantly higher during the Diwali period than it is during the rest of the year. Most investors/traders will buy and/or sell stocks as a gesture to acknowledge the auspiciousness of the festive period.

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LIMITATIONS

Through the data cleaning process, the team encountered a sundry number of difficulties. There was a high volume of data which further carried a significant amount of dirty data.

There are several limitations of hypothesis testing that can affect the quality of the data that we get from this process.

• Results of significance tests are based on probabilities and as such cannot be expressed with full certainty.
• Test do not explain the reasons as to why does the difference exist, say between the means of the two samples. They simply indicate whether the difference is due to fluctuations of sampling or because of other reasons .
• When used to detect whether a difference exists between groups, hypothesis testing can trigger absurd assumptions that affect the reliability of your observation.
• Testing is not decision-making itself; the tests are only useful aids for decision-making.

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FUTURE SCOPE

Further research can be undertaken on other portfolios or mutual funds and other investment avenues. Other variables can be taken into account such as risk tolerance capacity, etc.

There are lots of considerations while investing such as tax planning, future needs, safety of investments, recurring income, etc. There are some investments which are risky and few are not, so depending upon the age, the investors they should decide about the degree of risk to be taken.

We should also take into account the way people behave while making investment decisions not solely numbers. This is a new area in finance called behavioural finance which is promising branch of finance.

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THANK YOU!