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Question: Explain the main assumptions made in estimating the regression models

22 Oct 2022,9:54 PM

 

Section A (30 Marks, maximum 500 words)

Download monthly share price data covering the most recent 5-year period for five companies of your choice within the FTSE 100 index and perform the following tasks:

 

 1.     Calculate monthly simple returns on shares of the selected companies and comment on the data referring to appropriate descriptive statistics measures.(5 marks) 2.     Construct a variance-covariance matrix of the returns and present the results in an appropriate matrix format. Comment on the key features of this matrix.(5 marks) 3.     Calculate the expected return of an equally weighted portfolio of the five companies.(10 marks) 4.     Calculate the standard deviation of the above equally weighted portfolio using matrix algebra. Briefly comment on the trade-off between risk and return. (10 marks)Show all calculations and formulas in the first sheet of the submitted spreadsheet.

 

Section B: (30 marks, maximum 500 words)

 

Download monthly share prices of five UK investment trusts of your choice for the period October 2010 to October 2020 (10 years at monthly frequency). Also download data from  the FTSE All Share Index for the same period. Convert all prices into logarithmic returns for the period and perform the following tasks:

 

  1. Estimate the below linear regression model for each of the five investment trusts and explain which one of them is the riskiest and why.

 

Please assume the following in the next task:

The dependent variable is the return of each of the five UK investment trusts. The independent variable () is the return on the FTSE All Share Index (used as a proxy for market returns).

Present the results of the above regression model in a suitable tabular format. .

 

(10 marks)

  1. Based on the results of the above regression model, identify the investment trust with the best risk-adjusted performance over the sample period. Briefly explain your selection.  Calculate the R-squared of the above regression model and comment on the amount of variation in the returns of the five investment trusts which is explained by the variation in the returns of the market .

 

(10 marks)

  1. Estimate the variance-covariance matrix of the returns of the five investment trusts and calculate the  for each trust. You should present all the formulas and calculations together with the explanation of the meaning of the coefficient.

 

 

(5 marks)

 

  1. Explain the main assumptions made in estimating the regression models in question 1 above.

 

(5 marks)

 

Show all calculations and formulas in the second sheet of the submitted spreadsheet.

  

Section C (40 marks, maximum 500 words)

Download and record the following information relating to the bond issued by Legal and General Finance Plc from London Stock Exchange. Use the following link:

https://www.londonstockexchange.com/stock/71PP/legal-general-finance-plc/company-page

 

  1. Face value per bond (par value)
  2. Closing Market Value per bond
  3. Coupon rate
  4. Frequency of coupon payments
  5. Next Coupon payment date (only the month and the year)
  6. Maturity date (only the month and the year)

 

Address the following tasks based on the information that you have recorded on a given date (this must be the day on which you chose to perform the data collection exercise for this task)

  1. Express the market price of the bond along with other relevant information that you recorded above in terms of the relevant polynomial equation.

 

(10 marks)

  1. Calculate the market value of the bond using the above information and assuming the yield to maturity (YTM) of 5%.

 

(10 marks)

  1. Calculate the market values (NPV) of the bond for a range of YTMs and present the result as a graph and a table.

 

(10 marks)

  1. Calculate the actual YTM of the bond by using linear approximation. You must clearly explain the steps involved and present the linear equation. Assume that the market price of the bond is the clean price.

Expert answer

 

In order to understand the main assumptions made in estimating regression models, it is first necessary to understand what a regression model is. A regression model is a statistical tool used to predict the value of a dependent variable based on the values of one or more independent variables. The main assumptions made in estimating regression models are that the relationship between the dependent and independent variables is linear, that the errors are normally distributed, and that there is no multicollinearity between the independent variables.

 

Assuming a linear relationship between the dependent and independent variables means that we expect the dependent variable to change by a fixed amount for each unit change in the independent variable. This assumption is often violated in real-world data, but can be overcome by transforming either the dependent or independent variables (or both) to create a linear relationship.

 

The assumption that the errors are normally distributed means that we expect the majority of the error terms to be small, with only a few large errors. This assumption is also often violated in real-world data, but can be overcome by using a robust regression technique.

 

The final assumption, that there is no multicollinearity between the independent variables, means that we expect the independent variables to be uncorrelated with each other. This assumption is important because if the independent variables are correlated with each other, it becomes difficult to interpret the individual coefficients in the regression model. This assumption can be checked using a correlation matrix.

 

In conclusion, understanding the main assumptions made in estimating regression models is important for both interpreting the results of the model and for ensuring that the model is accurately predicting the dependent variable.

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