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MANG6299 W1

SEMESTER 1 EXAMINATIONS 2021-22

Quantitative Finance

SECTION A

A1. One important source of free data is EUROSTAT (the database of the statistical office of the European Union). The link is below contain data on employment: https://ec.europa.eu/eurostat/web/lfs/data/database

From this data source, select and download quarterly unemployment rate of a country of your choice. The time series should start in 1990s and contain at least 100 observations

a) This section may be very important to check the rest of your answers. Please, provide the following information of your data source, add a time series plot and compute summary statistics :

1. link with direct access to download the data

2. start date:

3. end date:

4. plot of the time series.

5. Compute the summary statistics of the unemployment rate and comment on it.

[5 marks]

b) Estimate the AR(4) model of unemployment rate (yt). Is the series stationary? Explain.

[10 marks]

c) Obtain a stationary time series based on the unemployment rate. Based on this series, estimate the AR(1) model. Is this a good model? Explain

[10 marks]

d) Estimate the AR(p) model, where p≤4. Is the addition of extra lags useful? Does it help explaining more of the variability of the unemployment rate?

[10 marks]

e) Economic theory proposes inflation may be good at explaining unemployment. If unemployment and inflation were both I(1), how would you propose to test if inflation is good to predict unemployment.

[10 marks]

SECTION B

B2. The Maximum likelihood estimator is very popular in time series analysis:

a) Explain the concept of Maximum Likelihood (ML). When is ML preferred to Ordinary Least Squares?

[8 marks]

b) The main variable of interest is Yt. The following function is proposed to describe the behaviour of Yt = α + εt. This is a special case of the regression line where there is no slope parameter. Find the ML estimator of α.

[12 marks]

B3. You are given a variable Yt.

a) Explain the concept of cluster volatility. Is this very common in Finance? Provide an example.

[8 marks]

b) You perform the diagnostic test of volatility. The sample statistic based on five ARCH effect is 6.5. Describe the diagnostic test. Is there evidence of heteroskedasticity in your data?

[7 marks]

B4. One of the topics of the module has been the ‘Econometric testing of portfolio theory’. This exercise is based on another extension of the CAPM model.

In particular, you will make use of:

Frazzini, A. and Pedersen, L.H. (2014) “Betting Against Beta”. Journal of Financial Economics 111(1):1-24.

Available at: http://docs.lhpedersen.com/BettingAgainstBeta.pdf

a) Explain the betting against beta factor. How does it fit with other factors that may explain the distribution of the return of financial assets?

[8 marks]

b) How does the empirical strategy of the paper to test the “betting against beta” hypothesis differ from the Fama-MacBeth two step methodology? Explain similarities and differences with a hypothetical example.

[8 marks]

c) Imagine yourself as a young analyst in Yahoo Finance. The paper is motivated by some of the practices of large investment institutions. Would you recommend to make use of the “betting against beta” strategy? Why or why not?

[4 marks]