Posted: April 14th, 2024

Data Analysis in Finance Learning Exercise 1 Financial Returns and Volatility

Instructions: Complete this assignment by downloading the data, R codes and then answering the questions in this word document. Then submit it electronically.  Go to the page in Blackboard where the assignment is posted, double click on the link “Learning Exercise 1”,then click on Browse and attach the answer file.   Click Submit to finish.  Note: Blackboard submission is set only before the deadline. Late assignments can’t be submitted.

 

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1. Using the attached R code (volatility_le1.R) get the daily equity prices data for the Japanese Nikkei 225 stock index for the period 2000/01/01-2018/07/29 from finance.yahoo.com (use ticker ^N225) and answer questions 1-3.

 

1. Compute the log returns for Nikkei and find the statistics below.
2. a) Find the mean annualized return.
3. b) Find the annualized volatility (standard deviation for the whole sample).
4. c) Find the skewness and kurtosis and explain if there is any asymmetry and fat tails?
5. d) Formulate and test the efficient market hypothesis (EMH) using the Q test for returns for k=15 autocorrelations.
6. e) Formulate and test the null hypothesis of no volatility clustering using the Q test for squared returns for k=15 autocorrelations.

 

2. Using the same data find annualized Monthly and Annual historical volatilities forthe whole period. Here use moving average standard deviations with monthly (22 days) window and annual (252 days) window. In both cases annualize the volatilities using sqrt(252) multiplier since we use daily data. Present a plot of both volatilities on one graph. Do you observe that volatilities are changing over time? What are the main events that caused volatility peaks for Nikkei index?

 

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3. Find exponentially weighted volatilities (EWMA) using .94 and .98 as the smoothing parameter. Plot both of these serieson the same graph and attach it.  Which parameter gives smoother volatility graph?

 

 

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2000. Use the attached excel data of daily equity prices of JPM starting in 2000. Load data into R code and answer questions 4-8.

 

4. Estimate various ARCH and GARCH models below. In each case estimate the model with an intercept. Explain which model has the best fit using Schwarz information criterion (SIC).
5. a) Estimate an ARCH(1) model and report the SIC
6. b) Estimate an ARCH(8) model and report the SIC
7. c) Estimate a GARCH(1,1) model and report the SIC
8. d) Estimate a GARCH(2,1) model and report the SIC
9. e) Pick another order GARCH model and report the SIC
10. f) Estimate the GARCH(1,1) with student-t distribution. Now what is the SIC criterion? Does it find this estimate preferable?

 

5. Using theGARCH(1,1) model with normal distribution estimate the time series of annualized volatilities and show on a graph. Explain when did the peaks of volatility happen, what was the maximum level of volatility and which news for JPM were related to that.

 

6. Now perform the Q test of no autocorrelation of the standardized residuals and the squared standardized residuals with 10 lags. What do the results say about the appropriateness of the GARCH(1,1) model?

 

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7. Present the skewness and kurtosis of the JPM returns and of the standardized residualsafter you estimated the GARCH model. Compare the results and explain what was the effect on standardized residuals after removing GARCH?

 

8. Now perform an out of sample forecast for 1 year for daily volatility ofJPM and graph the forecasts. Do you expect the volatility to go up or down in the long run? Why is it so?

 

9. No computer work is needed for this question. In theory what should be the GARCH (1,1) volatility pattern in each case below:
10. When the sum of alpha plus beta is small?
11. When the sum of alpha plus beta is bigger than one?
12. When alpha is small and beta is big with a sum slightly less than one?
13. When alpha is big and beta is small with a sum slightly less than one?

 

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