Financial Investment Analysis Assignment -

1. Please download the following data from the Bloomberg Terminal: The main Germany stock index (DAX) from 04 January 1960 to 28 December 2018 using daily frequency. If successful, you should have 14,840 daily prices (excluding the headers). Log returns can be formed by constructing the variable: r_t = ln[P_t/(P_t-1)], where P_t is the adjusted closing price at time t. Then, answer the following questions:

(a) Using 'an appropriate test', assess the possibility of ARCH effects in r_t. When estimating volatility of returns, why might a GARCH-type model be preferred to simply calculating the historic standard deviation?

(b) Estimate an appropriate model specification for returns over the full sample available, using (i) a GARCH (1, 1) model and (ii) a GARCH-in-mean (1, 1) model. Express each equation in the appropriate equation form and interpret the coefficients. NB: Whilst we did not go through the GARCH-in-mean(1, 1) model in the lab session, we did have a lecture on this and you have the Stata manual on the ARCH, hence you should be able to model this.

(c) Read the following journal: Sun and Tong (2010)'s 'Risk and the January Effect', Journal of Banking and Finance, 34:965-974.

Using the same dataset, estimate (i) model (1) on page 967 in Sun and Tong (2010) and (ii) model (2) in the same article. If the lagged returns are not significant, then delete them from your equations for returns. Express each estimation in the appropriate equation form and interpret the coefficients.

(d) On the basis of the values of the appropriate information criteria, which of your 4 models (i.e. two models from part (b) and two from part (c)) would you prefer? Explain.

(e) Estimate your 'preferred' regression from 1(d) above using observations up to and including 27 November 2018. Forecast the return volatility over the next month as well as the annualised volatility. Briefly comment on the forecasts you obtain.

2. For this problem you are tasked to evaluate the factor(s) that contribute to CEO Salaries and Bonuses following Hauser and Booth (2011) paper using limited dependent variable models. The datasets for this problem are provided on Canvas in excel format ('Data2.xlsx' and 'Data3.xlsx'). Data2 consists of 63 out of 101 FTSE100 companies (after data 'cleaning and adjustments') for 2009 (cross-sectional data). Data3 consists of similar dataset to Data2 with the exception that the time period now runs from 2009 to 2018 (inclusive) as a panel data. Both datasets are given on annual frequency. The following variables are defined:

(i) SID - This refers to the company's unique identification (in no particular order);

(ii) Year - The year the data were taken;

(iii) Ticker - The company's stock ticker;

(iv) Comp. - CEOs' total salaries and cash compensations;

(v) Tenure - The length of the period (in years) a particular CEO was in of?ce;

(vi) Price - The adjusted closing price of a company's share;

(vii) ROE - Return on Equity;

(viii) Sales - The company's annual revenue figures;

(ix) Gsales - The year-to-year growth of the company's sales figures;

(x) Geps - The year-to-year growth of the company's diluted EPS;

(xi) Equity - Total Equity of a company;

(xii) Ret - The one period simple return from previous year;

(xiii) Geq - The year-to-year growth of the company's equity, and;

(xiv) C - A binary variable that indicates (Y = 1) if a CEO experienced an increase in compensation each year and (Y = 0) if a CEO of a particular company either received a decrease in salary and/or cash bonuses or if there was no change in salary and/or cash bonuses.

Now, answer the following questions:

(a) Use dataset 'Data2.xlsx' to answer parts (a) - (e). To remove outliers from the data, perform a similar trimming procedure as outlined on page 303 in Hauser and Booth (2011). Using Linear Probability Model (LPM), run the regression of 'C' against the log of 'Sales', the log of 'Tenure', 'Ret', 'ROE', 'Geps', 'Geq' and 'Gsales' and interpret your results. Highlight any issues with this model.

(b) Now estimate the regression using probit and logit models with the same variables. Interpret your results.

(c) Note that the logit model can be represented as an 'odds ratio' model. What do the coefficients from this model represent (you need to run the regression ?rst)?

(d) Now, compare the LPM, Logit and Probit models' results with their marginal effects evaluated at their means and at the average marginal effects. How do you interpret the results from these marginal effects?

(e) Evaluate the 'goodness-of-fit' from your LPM, logit and probit models. What can you tell from this?

(f) Now use 'Data3.xlsx' from this point on. Perform the same trimming procedure as in (a). Run a conditional logit model with a robust standard error of 'C' against the log of 'Sales', the log of 'Tenure', 'Ret', 'ROE', 'Geps', 'Gsales' and 'Year' and interpret your results. What does the 'Year' in your regression represent?

(g) And lastly, evaluate the 'odds ratio' and the marginal effects (both at means and at average marginal effects) using the same variables. Interpret your results.

3. For this problem, you are given the dataset 'Problem_3.xlsx' provided on Canvas. The dataset consists of monthly data of the US Effective Federal Funds Rate ('ff') as well as the Real Personal Consumption Expenditures ('cpi') from July 1954 to March 2019. The interest rate dataset is reported as annualised rates. It is possible that when you run the optimisation routine that you do not get a solution in some of the models below. If so, what does this indicate about your dataset? Discuss this issue along with the relevant model(s).

(a) Convert the fed funds rates into monthly rates.

(b) Plot the fed funds rate and inflation on the same graph. What do you see? How can you explain the relationship between the two variables?

(c) Fit an AR(4) model to the federal funds rate and interpret the results. Save this as Model 1.

(d) Run an MSDR model on the federal funds rate with 2-state and 3-state transitions. Interpret your results. Save these as Models 2 and 3.

(e) Run a Markov-Switching Autoregressive of order 2 (MSAR(4)) model on the federal funds rate with a 2-state transition, one with constant AR coefficients and the other with state-dependent AR coefficients. Interpret your results. Save these as Models 4 and 5.

(f) Using models 4 and 5, now apply the state-dependent variance to these models and save them as models 6 and 7. Interpret your results.

(g) Estimate the state duration and probability transition matrix for models 6 and 7. What do these results tell you?

(h) Now use the Markov-Switching Dynamic Regression (MSDR) model to estimate the federal funds rate as a function of its lag (1-lag) and inflation. Allow only inflation to 'switch' across 2-states (thus only the constant and the coefficient for inflation are changing). Save this as Model 8. Interpret your results. Which model do you prefer and why?

Attachment:- Assignment Files.rar