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Discuss about the Introduction to Data Science, The stock market has become a vital part of the free market economy Several indicators are used to assess stock market performance. Millions of investors make decisions every day that impact on the stock market.

The stock market importance in the free market economy

The stock market has become a major source of great economic investment. The stock market has become a vital part of the free market economy [1]. Several indicators are used to assess stock market performance. Millions of investors make decisions every day that impact on the stock market.

Returns from such equity investments are subject to vary thanks to the movement of share costs, that rely on varied factors that might be internal or firm specific like earnings per share, dividends and value or external factors like rate, Gross Domestic Product (GDP), inflation, government rules and exchange Rate (FOREX).

The indicators of performance of a stock market include capitalization, liquidity and stock prices. Capitalization indicates the total market value of all shares that are registered as well as traded at the stock exchange. It is a product of the prevailing stock prices and number of shares issued by quoted companies. The capitalization therefore moves with changes in share prices. Liquidity refers to the extent to which the stock market allows trading of securities at stable prices whereas stock prices refer to the prevailing market prices for securities driven by the forces of supply and demand [2].  

Stock analysis is an important aspect for informing decisions on stock market investments. Stock analysis as defined by Roberts H.V. [3] refers to the evaluation of a particular trading instrument. Stock analysis attempts to determine the future trends of stock market instruments like share price. Investors depend on stock market analysis in order to make informed judgments on whether and/or what amounts of their income to invest in the stock market [4].

Transitions between rising and falling trends in stock markets are normally represented by price patterns [5]. It is important to understand price movements in the stock market. Stock market investments are determined by future price movements based on past and present price movements.

The study sought to establish the determinants of stock market performance and used stock prices as the indicator to be examined.

For cases of this research, we studied the trends of the State Bank of India (SBI) share price. Trends in the share price movements were observed and recorded for purposes of making future price forecasts.

The main aim of this research was to identify trends in stock share prices in order to provide informed advice to stock markets.

The performance of the securities market in any country could be a robust indicator of general economic performance and is an important part of the economy. With the introduction of free and open economic policies and advanced technologies, investors are obtaining easy accessibility to security markets round the world. The very fact that securities market indices became a sign of the wellbeing of the economy of a rustic indicates the importance of stock markets. This increasing significance of the securities market has actuated the formulation of the many theories to explain the operating of the stock markets.

For purposes of this research, we shall therefore aim to analyze the effect of past and current share prices on future stock share prices. Price analysis will help depict the overall stock market performance. By processing historical price data of stocks, it is easy to anticipate how that stock will be traded.

Indicators used in stock market performance assessment

Research questions

The following research questions shall be used to guide us through the research study;

  1. What is the relationship between stock prices and stock performance?
  2. What is the relationship between stock high prices and low prices?
  • What is the relationship between stock open prices at given intervals and the current trading prices at such intervals?

Hypotheses

The following hypotheses were formulated in order to answer the above research questions.

  1. H0: Stock prices are not indicators of stock performance.

H1: Stock prices are indicators of stock performance.

  1. H0: Stock high prices are not predictive of stock low prices.

H1: Stock high prices are predictive of stock low prices.

  • H0: Stock open prices are not predictive of stock current trading prices at given intervals.

H1: Stock open prices are predictive of stock current trading prices at given intervals.

The findings from this analysis can assist money establishments, corporations and individual investors in understanding the trends of stock prices and that they are higher advised on the way to gauge their investment choices whereas banks and different money establishments are able to give better financial recommendations and products to investors who look for funding to finance stock investments.

The results of this study would help stock markets and investors to make wise investment decisions. Insight into how prices affect stock performance will help investors derive proper valuations for their investments bearing in mind the price drivers.

Academicians and researchers can also benefit from the findings of this study because they will use the findings as reference for future researches on stock markets price analysis.

The findings will also contribute to the existing body of knowledge in fields of finance and economics.

This chapter examines the concepts and theories on stock price as an indicator of stock market performance. It also lays out literatures from past researchers and scholars on stock market performance.

Although common, the term stock market is being commonly confused with stock exchange. Stock markets describe the totality of all stocks held within a country whereas stock exchange is the entity of bringing together buyers and sellers to trade in stock [6].

In the past, buyers and sellers were individual investors but over time markets have become institutionalized with individual sellers and buyers being replaced by institutions such as banks. Shares of these institutions shall be traded in the stock exchange [7].

Existing literature has outlined that stock returns are partly predictable.  Predictability of these stock returns were shown to be attributed to past returns. Similarly, stock share prices can be predicted by examining past share prices [8].

Stock markets greatly depend on share prices. The value of stock shares determines the amount of investment that shall be made in the stocks [9]. A stock market achieves efficiency when stock investments reflect the market share prices.

Market potency theory suggests that a market is rational and provides correct rating. That is, these security prices square measure near to their elementary values owing to either the rational investors or the arbitragers obtain and sell action of under-priced or over-priced stocks. It's argued that in a potent economical market actual prices of individual securities already reflect the consequences of information based mostly each on events that have already occurred and on events that as of currently the market expects to occur in future. In different words, in an efficient economical market at any instance in time the particular value of a security are going to be a decent estimate of its inherent worth. On the contrary, determined market anomalies have a challenge for this argument.

Stock analysis and its role in stock market investments

Market efficiency is a desirable aspect in the stock market [10]. Most of past work on market efficiency relied on forecasting returns based on past returns. However, little research has been done on establishing market efficiency by forecasting share prices based on past share prices.

The issue of relation between major economic variables and share returns over the years has raised controversies among researchers owing to varying findings. On paper, major economic variables are believed to have an effect on returns on equities. However over the years, the determined pattern of the influence of macroeconomic variables (in signs and magnitude) on share returns varies from one study to a different in several stock markets.

In this research, we shall try to establish relationships between share prices and stock returns.

For purposes of this research we review the following key terms;

Interval refers to the time periods within which trades take place. Intervals can be intra-day, daily, weekly, monthly or annually. Interval helps investors know when is the optimal time to either buy or sell stock.

At each stock interval, stock will have four price types related to the interval; high price, low price, open price and close price.

High price is the highest value at which stock was traded at in a particular interval.

Low price refers to the lowest price at which certain stock was traded at in a particular interval.

This refers to the price at which stock trade took at in a particular interval.

This refers to the price at which stock was last traded at in a particular interval.

Trend refers to the general direction in which stock parameters change. At any instantaneous moment, stock can either have higher demand than supply or higher supply than demand. A stock that has higher demand than supply is said to be in Bullish trend while a stock that has higher supply than demand is said to be in Bearish trend.

Trend is important in depicting the general current and future performance of the stock market. Interpretation of trend shall help in informing judgment on whether or when to invest in the stock market.

At times trend could be positive while at other times trend could be negative, impacting differently on investors’ decisions.

Three types of trend do exist in the stock market;

Uptrends: This type of trend depicts a scenario whereby both the peaks and the troughs of a stock chart keep increasing successively. So, after given observational intervals, the stock prices get to a new high price and the low price becomes higher than the previous.

Downtrends: In this case, stock is constantly falling. After given observational intervals, the stock prices get to lower high and low prices compared to the previous highs and lows.

Sideways/horizontal trends: In this type of trend, stock does not notably fall or rise over an extended interval. Price highs and lows remain constant. It is difficult to decide whether and when to buy or sell stock when this type of trend is observed.

Determining stock market performance through price patterns

Peaks and troughs can be connected by a trend line. Trend lines that connect peaks will help in understanding the growth that a stock has displayed over an interval or period of time. Trend lines that connect troughs help in understanding the risks inherent in the stock over intervals or periods of time.

This research is qualitative research. The data used in this research is secondary data by taking samples from the State Bank of India (SBI). Sampling was done by purposive sampling technique. Price averages was performed using the simple moving average method.

Data collection

The data that was used in this study is secondary data that was collected based on the daily market statistics released by the State Bank of India (SBI) for the entire period of the study.

Indicator calculation

For purposes of this research, price was studied as an indicator of stock market performance. Calculation of the price indicators for purposes of this research was done using the following methods.

The simple moving average yields the mean of a data set for a given period.

A simple moving average (SMA) is the simplest style of moving average in security analysis. Simply, a simple moving average is calculated by adding up the last “X” period’s closing prices and then dividing that number by X.

Relative Strength Index is calculated based on SMA and close price of the stock for the given interval.

A gain results when the close price of a stock at a particular interval is greater than its open price. Stock gain shall be calculated by subtracting the price at which stock was bought from the price at which it was sold. A positive value shall indicate a gain. Average gain shall be found over all intervals over which stock was traded. A loss results when the close price of a stock at a particular interval is lower than its open price. A negative value resulting from the subtraction of the value at which stock was bought from the value at which it was sold shall result in a loss. Average loss shall be found by taking all losses over the intervals at which stock was traded divided by the total number of intervals over which such stock was traded.  RSI indicates the strength of the current trend. If a higher value of interval is chosen, more stable RSI values are obtained. A threshold value has to be determined. A state of sellers taking over buyers is reached when RSI falls below its threshold. A state of buyers taking over sellers is arrived at when RSI rises over its threshold. Consequently, stock prices will go high.

Rate of change is calculated based on current trading (tick) price and close price of the stock at a given. It measures the percent change in stock price from one interval or period to another. The formula for calculating rate of change is as shown below;

Current price refers to the price at which stock is currently being traded at a given interval whereas close price is the price at which stock was last traded at a particular interval.

The research objectives and questions

Rate of change could either be positive or negative. An increase in price at which stock is traded at a given interval relative to a past interval results in a positive rate of change while a decrease in the price at which stock is traded at a given interval relative to a past interval results to a negative rate of change.

Rate of change is directly proportional to the trend of the stock market. A positive rate of change shall imply a positive trend. Consequently, a negative rate of change shall imply a negative trend.

 A rate of change lesser than 20 implies that the market has higher supply than demand. A rate of change greater than 80 indicates that there is higher demand than supply of stock in the market.

Correlation coefficient shall be calculated to investigate the degree of association between high prices and low prices.

The correlation coefficient value shall be calculated using the following formula;

Correlation analysis was used to examine relationship between stock high prices and low prices over given intervals.

Linear regression is used to model the relationship between two variables by fitting a linear equation to observed data.

The linear equation is in the form of   

Linear regression tool was used to model the relationship between current trading stock price at given intervals and the open prices at the given intervals.

Data was represented in boxplots, histograms, bar graphs, line graphs and scatter plots.

Data was entered into MS excel and analyzed using the R software.

Findings confirm that SBI exhibits presence of univariate stylized facts as described below:

Excess volatility: Several empirical studies imply that it is hard to justify the discovered level of variability in asset returns by variations in “fundamental” economic variables. Specifically, the incidence of huge (negative or positive) returns is not at all times predictable by the arrival of latest information on the market.

Heavy tails: the distribution of returns displays a heavy tail with positive excess kurtosis. Returns are not normally distributed. This feature can be exhibited as shown in the histogram below. The plot is skewed to the right implying non-normality.

Absence of autocorrelations in returns: autocorrelations of asset returns are often not significant, aside from very small intraday time scales wherever microstructure effects acquire play.

Volatility clustering: large changes of one sign(positive or negative) are likely to be followed by huge changes, and small changes are likely to be followed by small changes of the same sign.

Volume/volatility correlation: trading volume is positively associated with market volatility. Moreover, trading volume and volatility show a similar sort of “long memory”.

It can be observed that the share prices of a company are very sensitive and may change very rapidly (upward or downward).

Simple moving average was used to find the overall mean of the stock price and the means of the high and low prices within given intervals. The mean was found to be 273.5466. The mean of the high prices was found to be 277.8240 and that of the low prices was found to be 269.8490.

The hypotheses formulated for the research

Therefore, when the price is above 273.5466 the stock is considered to be in a general upward trend whereas prices below 273.5466 shall be considered to lead the stock to a general downtrend.  

The correlation coefficient between the high prices and low prices at given intervals was found to be 0.9860132 indicating a strong positive association between the high prices and low prices and we therefore reject the null hypothesis that there is no relationship between stock high prices and low prices at given intervals in favour of the alternative hypothesis that there exists a relationship between stock high prices and low prices at given intervals. The strong positive correlation coefficient implies a general upward trend.

A linear regression model was fitted to observe relationship between open price and the tick price at given intervals and a regression plot plotted. 

The regression plot depicts an upward positive trend therefore we reject the null hypothesis stock open prices at given intervals are not predictive of current trading prices at such intervals in favor of the alternative hypothesis that stock open prices are predictive of stock current trading prices at given intervals. An increase in the open price leads to a corresponding increase in the tick price.

The higher the open price, the higher the tick price at any given interval.

In the approaches discussed it is assumed that a scenario of a willing buyer and a willing seller is met at any instantaneous time. However, this is not always the case.

We have considered data only from SBI stock market. The behavior of these models not be the same across other stock markets in India and out of India since motivations vary across stock investors.

We have assumed that in the stock market prices are static. However, in reality this is not the case. Stock prices do change almost every millisecond.

We have relied on price data from January 2018 to 17th October 2018 for the stocks which we analyzed. When new data is fed in to the model its accuracy may vary.

Conclusion

It can be concluded that there is a strong positive relationship between the stock high prices and low prices over given intervals. Therefore, as high prices increase, so do low prices. As high prices decrease, so do low prices consequently decrease.

It is also concluded that current trading price of stock at a given interval of time is directly proportion to the open price of the stock at that given interval as there exists a positive linear relationship between the two variables.

References

X. Z. Paresh Kumar Narayan, "Market liquidity risk factor and financial market anomalies," Evidence from the Chinese stock market, p. 12, 2010.

R. H.V., "Stock-Market ''Patterns'' and Financial Analysis: Methodological Suggestions," p. 11, 1959.

S. L. HU YANJING, "The Factual Test Of Weak Form Efficiency On Chinese Stock Market And Comparing With International Markets

," p. 8, 2006.

C. K. R. V. (. S. R. Vishwanath (auth.), "Investment Management," A Modern Guide to Security Analysis and Stock Selection, p. 634, 2009.

R. G. Deborah Owen, "Mapping the Markets," A Guide to Stock Market Analysis, p. 145, 2006.

M. K. G. D. M. Gopal K. Basak, "Equilibrium and stability of a stock market game with big traders," p. 17, 2009.

J. J. Murphy, "Intermarket Technical Analysis," Trading Strategies for the Global Stock, Bond, Commodity, and Currency Markets, p. 146, 1991.

E. D. F. L. B. M. RUI ALBUQUERQUE, "Marketwide Private Information in Stocks," Forecasting Currency Returns, p. 47, 2008.

F. L. A. M. Morten Balling, "Financial Markets in Central and Eastern Europe," Stability and Efficiency, p. 401, 2004.

D. E. PROKHOROVA J.V., "Analysis To Activity Of The Banks On Stock Market Of The Ukraine," p. 3, 2010.

M. Q. Michael Magill, "Normative properties of stock market equilibrium with moral hazard," p. 22, 2008.

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