Fn285 Financial Modelling And Dealing Assignment

Fn285 Financial Modelling And Dealingassignment On Modelling Financia

This assignment requires an individual to develop a linear financial model based on the Arbitrage Pricing Theory (APT), incorporating three variables: stock prices, S&P 500 index, Treasury bill yields (3 months), and the USA consumer price index (CPI). The goal is to collect relevant monthly data, transform it appropriately, analyze the variables through descriptive statistics, estimate the model using econometric techniques, and interpret the results, ensuring the classical assumptions of OLS are satisfied or corrected if necessary. The assignment emphasizes demonstrating proficiency with EViews, data handling skills, statistical analysis, model testing, and professional reporting.

Paper For Above instruction

The purpose of this paper is to demonstrate the application of the Arbitrage Pricing Theory (APT) to model a financial relationship involving multiple economic variables. APT, developed by Stephen Ross in 1976, posits that the returns of a financial asset can be explained by multiple macroeconomic factors or systematic risk factors, each with associated sensitivities or loadings. Unlike the Capital Asset Pricing Model (CAPM), which considers only market risk, APT allows for a multifactor approach, providing a more flexible and comprehensive framework for understanding asset returns (Ross, 1976). The model assumes that asset returns are linearly related to a set of factors, and returns can be expressed as:

Y_t = α + β₁X_1t + β₂X_2t + β₃X_3t + u_t

where Y_t is the dependent variable (stock price), X_1t to X_3t are independent macroeconomic variables, and u_t is the error term assumed to be normally distributed with mean zero and constant variance. The three variables selected for this model include the stock price, S&P 500 index, 3-month Treasury bill yield, and the USA CPI, as these are critical indicators influencing stock returns and reflect macroeconomic risk factors.

Data Source and Transformation

The data for this analysis are sourced from reputable financial and economic databases. Stock prices and S&P 500 index data are obtained from Yahoo Finance, providing monthly closing prices necessary for modeling stock returns. Treasury bill yields are collected from the Federal Reserve Economic Data (FRED) database, which offers reliable monthly interest rate data for 3-month T-bills. The USA CPI data are also retrieved from FRED, reflecting monthly inflation rates that impact real returns. Data extraction involves downloading raw data series, ensuring consistent timeframes, and transforming raw prices into returns where applicable. For instance, stock and index prices are converted into monthly returns via the natural logarithmic difference: R_t = ln(P_t) - ln(P_t-1), which stabilizes the variance and normalizes the distribution. Treasury yields and CPI are used directly or transformed into relevant variables such as inflation rates for better model interpretation. Data cleaning involves handling missing values and ensuring alignment of data periods across variables.

Exploratory Data Analysis

The analysis begins with descriptive statistics summarizing each variable's distribution: mean, median, standard deviation, minimum, maximum, skewness, and kurtosis, as shown in Table 1. For example, the stock returns may display positive skewness, indicating occasional large positive returns, while the CPI and T-bill yields might exhibit skewness toward the lower end due to economic downturns. Understanding these distributions helps in diagnosing model suitability and selecting appropriate transformations.

Estimation and Testing of Classical Assumptions

Using EViews, the model specified earlier is estimated through Ordinary Least Squares (OLS). The residuals are then subjected to tests for homoscedasticity, serial correlation, and normality. The Breusch-Pagan test assesses heteroscedasticity; the Durbin-Watson test detects serial correlation; and the Shapiro-Wilk or Jarque-Bera tests evaluate residual normality. Given potential violations, corrections such as robust standard errors for heteroscedasticity, the Cochrane-Orcutt procedure for serial correlation, or transformations to improve normality are considered. Ensuring the residuals satisfy these classical assumptions validates the model's reliability.

Hypotheses Testing

To assess the significance of individual variables, hypotheses are formulated as: H₀: β_i = 0 (the variable has no effect) versus H₁: β_i ≠ 0. A t-test evaluates each coefficient’s significance. The overall model significance is examined through the F-test: H₀: All β_i = 0 versus H₁: At least one β_i ≠ 0, indicating whether the model explains a significant portion of the variation in stock prices.

Model Evaluation and Interpretation

The R-squared and adjusted R-squared indicate the proportion of variance in stock prices explained by the model; higher values suggest better fit but must be interpreted with caution. The F-statistic tests the joint significance of all regressors. The estimated coefficients’ signs reveal the direction of each variable's impact: positive coefficients suggest a direct relationship with stock prices, while negative ones imply inverse relationships. The significance levels (p-values) determine the robustness of these effects. For example, a significant positive β₁ for the S&P 500 indicates that increases in market index levels are associated with higher stock prices, consistent with market efficiency theories.

Conclusion

This analysis demonstrates how the Arbitrage Pricing Theory can be operationalized using macroeconomic variables to model stock prices effectively. Ensuring the classical assumptions of regression are satisfied enhances confidence in the results. The significance of variables like the S&P 500, Treasury yields, and CPI aligns with economic intuition, reinforcing their roles as risk factors influencing asset returns. Proper data handling, rigorous testing, and clear interpretation collectively contribute to robust financial modeling, aiding investors and policymakers in understanding market dynamics.

References

• Brooks, C. (2014). Introductory Econometrics for Finance. Cambridge University Press.
• Asteriou, D., & Hall, S. (2016). Applied Econometrics. Palgrave Macmillan.
• Ross, S. A. (1976). The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory, 13(3), 341-360.
• FRED Economic Data. (2023). Federal Reserve Bank of St. Louis. https://fred.stlouisfed.org
• Yahoo Finance. (2023). https://finance.yahoo.com
• World Bank. (2023). World Bank Data. https://data.worldbank.org
• IMF. (2023). International Monetary Fund Data. https://www.imf.org/en/Data
• Barrow, M. (2017). Statistics for Economics, Accounting and Business Studies. Pearson.
• Brooks, C. (2008). Introductory Econometrics for Finance. Cambridge University Press.
• Damodar N. Gujarati, Dawn C. Porter. (2009). Basic Econometrics. McGraw-Hill Education.