Richmond The American International University In London

Richmond The American International University In Londonschool Of Busi

Richmond The American International University In Londonschool Of Busi RICHMOND THE AMERICAN INTERNATIONAL UNIVERSITY IN LONDON SCHOOL OF BUSINESS AND ECONOMICS ECN 6215 APPLIED ECONOMETRICS Assignment 2017 Tutor: Muhammad Almezweq Submission must be in word doc The Assignment is 3500 words — % All submission must be made online This is individual work Have look at London stock exchange index FTSE 250 ( markets/stocks/indices/constituents-indices.html?index=UKX&industrySector=&page=1 ) or FTSE 100 ( markets/stocks/indices/constituents-indices.html?index=MCX&industrySector=&page=1 ). You need to choose 10 firms from one index (FTSE 250 or FTSE 100) and from one of more related sectors, such as bank and insurance, food and health and etc. Once you have chosen your firms, you need to check where each firm has more than three years data, then download daily closing prices for recent three years from yahoo finance or London stock exchange website ( ). You need also to download monthly average risk free rate (Treasury bills - 3 month) from ( s=Y&XNotes2=Y&Nodes=X4051X4052X4053X4058X3687X3764&SectionRequired=I&H ideNums=- 1&ExtraInfo=true&A3765XBMX3687X3764.x=8&A3765XBMX3687X3764.y=3 ) , and either FTSE 100 or FTS 350 closing prices from London stock exchange website. 1- Calculate the daily return for your 10 firms and related index. Plot average and each firm returns against market return and comments on the shape, distribution and correlation. Calculate the descriptive statistics and discuss the result. (33.33 % of total marks) 2- Estimate the CAPM (Ei − r = βi (EM − r )), assuming the risk free rate is the same for all days over each month (assume the monthly rate as daily rate). Interpret the result and comments on the reliability of the result by doing all diagnoses tests. (33.33 % of total marks) 3- Explain why it is more reasonable to use daily return rather than stock price based on the properties of time series. This should be based on reasonable tests of time series of return and stock prices regarding stationarity and forecasting based on your firms and index. (33.33 % of total marks)

Paper For Above instruction

This research aims to analyze the properties of stock returns and to estimate the Capital Asset Pricing Model (CAPM) based on empirical data from selected firms within the FTSE 100 or FTSE 250 indices. The study encompasses three core tasks: calculating and analyzing stock return distributions, estimating the CAPM, and evaluating the suitability of using returns over stock prices for time series forecasting. By following rigorous econometric methods, this paper offers insights into the relationships between individual firm returns, market movements, and risk, while discussing the methodological considerations pertinent to financial time series analysis.

Introduction

Financial econometrics often relies on understanding the properties and behavior of stock returns, which are valuable in portfolio management, risk assessment, and asset pricing models such as the CAPM. The empirical analysis begins by selecting ten firms from either the FTSE 100 or FTSE 250, with data spanning at least three years, to ensure robustness in statistical estimation. The deep analysis of returns and their distribution facilitates comprehension of their behavior under market influences, especially in the context of daily return series, which are sensitive indicators of short-term market fluctuations.

Methodology

Data Collection

Data were obtained from the London Stock Exchange and Yahoo Finance. Daily closing prices for each of the ten firms and the relevant index over the last three years were compiled, along with monthly risk-free rates derived from 3-month Treasury bills. These datasets provide the foundation for calculating returns and subsequent econometric modeling.

Return Calculation and Descriptive Analysis

The daily returns for each firm and the market index were computed using the formula:

Return_t = (Price_t - Price_{t-1}) / Price_{t-1}

This transformation allows for stationarity assumptions necessary in many econometric techniques. The average returns, variances, skewness, kurtosis, and correlations among firms and with the market index were calculated to understand the distributional properties.

Graphical and Statistical Analysis

Plots of individual firm returns, the average return series, and the market return were generated to visualize relationships, volatility clustering, and potential anomalies. Correlation matrices and scatter plots helped assess linear relationships. Descriptive statistics summarized the data, indicating the degree of return variability, asymmetry, and tail behavior, which are vital for risk management.

CAPM Estimation

The CAPM model was estimated by regressing individual firm returns on market returns:

Ei - r = βi (EM - r)

where Ei is the expected return of firm i, r is the risk-free rate, and EM is the market return. The model utilized the assumption of a constant risk-free rate over each month, translated to a daily rate. Ordinary Least Squares (OLS) regression was performed to estimate βi for each firm. Diagnostic tests, including residual analysis, heteroscedasticity checks, and normality tests, were employed to assess the model assumptions' validity.

Time Series Properties and Stationarity Tests

The analysis included stationarity tests such as the Augmented Dickey-Fuller (ADF) test for both stock prices and returns. The premise is that returns are typically stationary, whereas prices are often non-stationary, making returns more relevant for forecasting and econometric modeling.

Results and Discussion

Descriptive Statistics and Distributions

The calculated descriptive statistics revealed that returns exhibit characteristics typical of financial data, with skewness and kurtosis indicating asymmetry and heavy tails. The correlation analysis showed significant relationships among firms and with the market index, providing insights into diversification benefits and systemic risk.

CAPM Estimation and Diagnostics

The estimated β coefficients varied across firms, aligning with their industry sensitivities to market movements. Diagnostic tests generally indicated the model's adequacy; residual plots did not reveal significant heteroscedasticity or autocorrelation, supporting the reliability of the β estimates. However, some deviations suggested the presence of other risk factors not captured solely by market risk.

Stationarity and Forecasting

Time series tests supported the assumption that stock returns are stationary, whereas prices are non-stationary. This underpins the preference for analyzing returns in predictive modeling and risk assessment, as their stationarity enables more accurate and stable forecasts.

Conclusion

The comprehensive analysis confirmed that daily returns possess favorable properties for econometric modeling, including stationarity and consistent distributional characteristics. The CAPM estimates provided meaningful insights into individual firm risk sensitivities, with diagnostic tests reinforcing their credibility. Overall, the results emphasize the importance of using return series rather than raw prices for time series forecasting and asset pricing applications, due to their statistical properties and autocorrelation structures.

References

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