SELECTED PAST EXAMS QUESTION

Jan2012- Q1.

1. Explain the meaning and significance of: confidence intervals; the critical regions; the critical value; the null hypothesis and the alternative hypothesis within the context of the analysis of portfolio returns.
   (20 per cent of the marks)
2. The information provided below illustrates the performance of funds X and Y as well as the Ft-All Share index over the last full year of trading:
   
   
   You are required to set up and test the following hypotheses:
   1. Fund X has significantly outperformed Fund Y.
   2. Fund X has significantly outperformed the FT All Share index.
   3. Fund Y has significantly outperformed the FT All Share index.
      (50 per cent of the marks)
3. Compare and contrast the Poisson and Binomial distributions and provide examples of when they could be used in Finance.
   (30 per cent of the marks)
   Jan2011 -Q3.
   1. Within the context of share return analysis, explain the meaning and significance of Type I and Type II errors and the relationship between the confidence interval and the associated hypothesis.

(20 per cent of the marks)

(b) Compare and contrast the normal and student t -distributions and assess the implications of each for the analysis of share returns.

(20 per cent of the marks)

(c) The following information has been made available for the monthly returns generated by two fund managers and the FT All Share Index over the last full calendar year:

You are required to set up and test the following hypotheses:

(i) Manager A has significantly outperformed Manager B.

(ii) Manager A has significantly outperformed the FT All Share Index.

(iii) Manager B has significantly outperformed the FT All Share Index. (60 per cent of the marks)

JAN2010- Q3.

(a) The following information has been made available for the monthly returns generated by two fund managers and the FT All Share Index over the last full calendar year:

You are required to set up and test the following hypotheses:

(i) Manager A has significantly outperformed Manager B.

(ii) Manager A has significantly outperformed the FT All Share Index.

(iii) Manager B has significantly outperformed the FT All Share Index.

JAN2012- Q4.

The following is the result of a logistic regression analysis based on a sample of 113 acquired UK companies which are matched by size, industry, and year of accounts with 113 non-acquired companies. The dependent variable takes a value of 1 if the company was acquired and 0 if it was not acquired. The independent variables are sales growth (sg_1) in percent; the debt to equity ratio (de_1) in per cent; the after-tax profit margin (pm_1) in per cent and total assets divided by sales (tasls_1), all in the year prior to acquisition.

Logistic Regression

Block 1: Method = Enter

You are required to write a report evaluating the performance of this model from both a financial and statistical perspective.

JAN2011 -

Q5. The following logistic regression output has been made available which was run on a sample of 90 failed UK companies and 90 non-failed companies matched by year and industry. The following notation is used:

Status is the dependent variable which takes a value of 1 for a failed company and 0 for a non-failed company.

pm1 is the after-tax profit margin in the year prior to failure.

de1 is the debt to equity ratio in the year prior to failure.

tasls1 is the total assets to sales ratio in the year prior to failure.

slsg2_1 is the sales growth rate in the year prior to failure.

Logistic Regression

Block 0: Beginning Block

Block 1: Method = Enter

You are required to write a report explaining the meaning of this information and critically assessing the performance of the estimated model from both a financial and statistical perspective.

JAN2010- Q5.

The following output has been provided which summarises the results of a logistic regression undertaken on paired samples of failed and non-failed UK publicly quoted companies. The independent variables employed are as follows:

PBTCL_1 is profit before tax divided by current liabilities.

CLTA_1 is current liabilities to total assets.

NCI_1 is the no-credit interval which is a measure of how long (in days) a company can continue trading with no revenue being generated.

CATL_1 is current assets to total liabilities.

All of these are calculated using data taken from the last accounts published prior to failure.

The dependent variable is dichotomous with failed companies being assigned 1 and non-failed companies 0.

Block 0: Beginning Block

Block 1: Method = Enter

You are required to undertake a financial and statistical evaluation of this information.

Jan2010 - Q6.

(a) Explain and critically discuss the validity of the various tests available to test for stochastic non-stationarity?

(40 per cent of the marks)

(b) Explain the meaning and significance of the concept of cointegration with the aid of appropriate examples.

(30 per cent of the marks)

(c) Explain the stylized facts as to why financial data cannot generally be explained effectively by using linear time series models. Which of these features could be modelled using a TGARCH (p, q) process?

(30 per cent of the marks)

JAN2012 - Q2.

Consider the following data on the returns of the price of Gold Bullion (London Bullion Market) in US$/Troy Ounces for the period from November 2009 to October 2011:

You are required to:

1. Explain the concept of decomposing a time series.
   (20 per cent of the marks)
2. Explain and discuss the basic time series models of random walk (RW), historical mean (HM), moving averages (MA) and exponential smoothing (ES).
   (30 per cent of the marks)
3. Calculate the RW, MA for three months and ES with alpha = 0.2 for this data, and evaluate them using the Mean Squared Errors (MSE)
   technique.
   (50 per cent of the marks)
   JAN2011 Q6.
   (a) Consider the following data for the Nikkei 225 returns for the period between January 2009 and December 2009:

   Date	Nikkei 225 Returns
   Jan-09 Feb-09 Mar-09 Apr-09 May-09 Jun-09 Jul-09 Aug-09 Sep-09 Oct-09 Nov-09 Dec-09	6.22 -12.04 -5.74 9.65 8.26 7.56 3.91 4.71 0.95 -3.64 -1.68 -6.28

   
   You are required to:
   1. Explain the basic time series models of the random walk (RW), historical mean (HM), moving average (MA) and exponential smoothing (ES). (20 per cent of the marks)
   2. Calculate the RW, MA at three months, HM and ES with alpha = 0.1 for these data. (40 per cent of the marks)

(b) Critically discuss the consequences of including a non-stationary series in a regression model and identify and explain possible means of addressing and testing for this problem. (40 per cent of the marks)

Jan2009 -

Q3.

(a) Explain the relationship between a confidence interval and the corresponding hypothesis test within the context of the analysis of historical share returns. (10 per cent of the marks)

(b) Compare and contrast the main characteristics of the binomial and poisson distributions using examples from finance where each would be applicable. (20 per cent of the marks)

JAN2012

Q3. The following regression model is to test whether the Metals & Mining industry stock returns are sensitive to commodity price changes and global market changes for the period from January 2000 to September 2011:

where:

\[{{R}_{t}}\] : log return on the S&P Metals & Mining Industry index in month t

\[{{R}_{MSCI\_world,t}}\] : log return on the MSCI world market index in month t

\[{{R}_{SP1500,t}}\] : log return on the SP1500 in month t

\[{{R}_{oil,t}}\] : log return on the WTI crude oil price in month t

\[{{R}_{Gold,t}}\] : log return on the Gold price in month t

\[{{D}_{t}}\] : is a dummy variable which equals 1 during the recent international financial crisis (August 2007 – September 2011) and 0 before.

You are required to:

1. Identify the key underlying assumptions of the linear regression model and discuss the available statistical tests for examining these assumptions.
   (40 per cent of the marks)
2. Hypothesise and explain the expected signs of the coefficients and compare the actual signs with your hypotheses.
   (20 per cent of the marks)
3. Critically evaluate the performance of the regression model taking full account of the assumptions underpinning the estimation technique.

(40 per cent of the marks)

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Solution: The downloadable solution consists of 42 pages, 5282 words and 80 charts.
Deliverable: Word Document