Boğaziçi University, Department of Economics

Course Code: EC 58D

Course Name: Selected Topics in Financial Econometrics

Problem Set1

Lecturer: Burak Saltoglu

Deadline (13 April 2017)

Data set: EC58D.xls

Instructions:

  • This is a group project, each group can have up to 2 students
  • We will be using this data set for future assignements.
  • This may be a comprehensive project you may have specific questions. You can bring your data with you so that we can discuss at the beginning of each class.
  • You should update the data where possible. Yahoo is a good source bu you can try others.
  • In below there is a sample R code for doing some of the analysis. You can use it as a start.

QUESTIONS

  1. Descriptive ANALYSIS OF FINANCIAL TIME SERIES (STYLIZED FACTS)
  2. In the following data set you are give a large daily data set:
  3. ISE100 series (both the index many different individual stocks),source: IMKB or reuters
  4. Dow Jones Industrial Average and SandP500, and an individual stock (google) (source yahoo finance)
  5. TL/FX Series (USD, EURO)
  6. Spot Gold price in USD,
  7. Crude Oil (Brent and WTI, in USD).
  1. Find the sample mean, sample variance, skewness, and excess kurtosis estimates on these daily (and convert them to study weekly and monthly)return series.
  2. compare your findings on different years. For instance for the Turkish data divide the sample into 4 economically sensible samples and see whether the mean, variance, skewness etc change in these years.
  3. For Dow Jones compare the two crisis periods namely 1929 and 2008. 1929-1933 and 2007 October-2009 October.
  4. Sharp Ratio is given as E(X)/Variance(X) is a critical performance measure. For the above stocks and FX series calculate the Sharpe ratio and comment on your results. (Hint: The higher this ratio the higher the risk adjusted return is).
  5. Calculate autocovariance and autocorrelations (r(t),r(t-i), daily returns i=1,...50, for weekly and monthly it can be lesser) (use R, EVIEWS or MATLAB). Comment on your findings very carefully.
  1. RETURN PREDICTABILITY

Be very clear in commenting on your findings for the following comparisons:

  1. What are the differences and similarities of the time series behaviour of daily, weekly, and monthly series.
  2. Hint: what happens to mean, variance, kurtosis, skewness and ACF properties of same series with different frequencies. Which series are more predictable.
  3. What are the differences and similarities between individual stocks and stock indices (AKB vs ISE, Google vs DJ etc), (use the hint i).
  4. What are the differences between the skewness and kurtosis properties of FX and stock returns (in TL). (using the hint i.)
  5. How can you compare the stocks in Turkey and US by using (use Hint i.)
  1. TIME SERIES ANALYSIS

In this analysis use only Turkish real GDP (the new and old) and unemployment series and cpi.

do the following time series exercise,

  1. Give your descriptive statistics on Turkish macro variables (including the old and new GDP data). Briefly comment your results.
  2. Try various AR processes and choose the optimal lag-length by using Akike and Schwartz Bayesian Information Criterion. By using Box Ljung test statistic what can you say about the normality of residuals for the fitted data.
  3. Try various AR processes and choose the optimal lag-length by using Akike and Schwartz Bayesian Information Criterion.By using Box Ljung test statistic what can you say about the normality of residuals for the fitted data.
  4. Try various ARMA processes and choose the optimal lag-length by using Akike and Schwartz Bayesian Information Criterion.By using Box Ljung test statistic what can you say about the normality of residuals for the fitted data.
  5. By using your results on a, b, and c which model would you use please justify your reasons.
  1. FORECASTING

For the above three macro series estimate an AR(1) model. Then do a forecasting experiment. Reserve the last 10% of your data for forecasting experiment.

  1. Plot your actual your point forecasts.
  2. Do your forecasting experiment in both dynamic and static fashion (notein dynamic forecasting, the previous estimate is treated as a realized value whereas in static one we need the actual value).
  3. Calculate Root Mean Square Error statistics both the dynamic and static forecasts.
  4. Discuss the differences in RMSE in between the dynamic and static cases.
  5. What do you observe if you consider weekly and monthly frequencies.
  6. You can use EVIEWS forecast menu but your excel spreadsheet would be also useful.
  7. You can also update your AR(1) coefficients in forecasting. (i.e. you will re-estimate your AR(1) coefficient).
  8. Compare your RMSE you obtained from this practice with updated coefficients.
  9. Using EVIEWS conduct a forecasting experiment for your optimal model produced in question 3.
  10. What can you say about return predictability of various frequencies (i.e. daily vs weekly monthly).
  1. CAPM

You are given 6 daily Turkish stocks and ISE index and Google and SandP500.

  1. As we discussed in the class this well-known model is estimated with the given regression equation.
  2. Estimate daily, weekly and monthly beta’s for each stocks do a statistical analysis on them and comment on your findings. How does the model fit? Which frequency seems to be more suitable for practical use of betas.
  3. Note that the beta’s are linearly additive i.e if there are 6 stocks with different wealths, w1, w2, w3.., and w6 then the portfolio constituted from these stocks are given as. Discuss how can you allocate your stocks to get a portfolio beta close to 1.
  4. How would you allocate your portfolio beta under recessionary environment.
  1. GRANGER CASUALITY

The granger causality test examines the causality between series, the direction of the relation. We can test whether GNP causes money supply to increase or a monetary expansion lead GNP to rise, under conditions defined by Granger.

Granger Causality Test

  1. Steps for testing x (granger) causes y;

Regress y on all lagged y to obtain RSS1

Regress y on all lagged y and all lagged x obtain RSS2

The null is’s are alll zero.

Test statistics;

  1. Steps for testing y (granger) causes x;

Regress x on all lagge x to obtain RSS1

Regress x on all lagged x and all lagged y obtain RSS2

The null is’s are alll zero.

If we obtain Granger casuality both from a and b then we will have bivariate casuation.

Now we will apply this test for Stock Market Volume relationship. By using the daily data between 1929-2009 we can test whether volume causes stock returns. Also test whether stock returns causes volume.

  1. EVENT STUDIES

As we discussed in the class Testing for Semi-strong form of Market efficiency is known as ‘event studies’. It tests whether market reacst to announcements, fastly and correctly. The test involves the following steps. You will have some material from Copeland and Weston. Classical Reference: Fama, Fisher, Jensen, Roll (1969), The Adjustment of Stock Prices to New Information, International Economic Review, 10, 1-21.

  1. Run CAPM regression for company i,
  2. We do the analysis surrounding an economic event of interest (i.e. dividend announcements, stock splits, changing in accounting regimes, FOMC meetings etc).
  3. Then the Average Abnormal Return
  4. In the final stage we will calculate the Cumulative Abnormal Returns , T=the number of months being summed (T=1,..,M)

M=the total number of months in the sample.

  1. Under market efficiency prices willcorrect in a speedy way so abnormal returns won’t be observed. Therefore, They (CAR) would fluctuate around zero and average would equal to zero.
  2. More information can be found in Copeland and Weston (I have distributed the copies).
  3. Given your weekly data set from ISE, look at whether these 6 individual stocks show any abnormal returns during Earnings seasons. From ISE find which months are the earnings seasons and make an analysis what happens to CAR 4 weeks before and after the earnings announcement.
  1. How much of the increase in SandP is due to Weaker Dollar: is it buble or is it Dollar valuation?

In the data given EC683.xls calculate SandP500 series in terms of

a.)EURO’s (i.e. what is the value of SandP500 index in terms of EUROS?).

b.)Compare your index values of both Dollars and Euros between 2009 March and 2009 October. How much of the recent change can be attributed to the weaker Dollar? Or how much money could an European investor can make by investing on SandP?

c.)Do the same for in Spot gold prices. İndex now is in terms of one spot gold price.

d.)Do the same for crude oil prices?

e.)Comment your finding carefully. How much overvaluation can you notice?

f.)Do the same for ISE returns and comment on it…can you see any pattern when ISE dollars.

R CODE

library(tseries)

library(zoo)

price = get.hist.quote(instrument = "^gspc", start = "2000-01-01", quote="AdjClose")

y=diff(log(price))

plot(y)

y=coredata(y)

RCODE

library(moments)

mean(y)

sd(y)

min(y)

max(y)

skewness(y)

kurtosis(y)

acf(y,1)

acf(y^2,1)

jarque.bera.test(y)

Box.test(y, lag = 20, type = c("Ljung-Box"))

Box.test(y^2, lag = 20, type = c("Ljung-Box"))