Calculating VaR and ES on Japanese Yen

Overview

The goal of this quiz is to test your understanding of using R to estimate VaR and ES using the Japanese Yen exchange rate data from FRED. You should be able to do all the calculations after completing Exercises 5-8.

Exchange Rate Data from FRED

Retrieve the data on the exchange rate between the Japanese Yen and the US Dollar from FRED:

DEXJPUS

Remove the NA observations of this series.

Restrict the dates of this series from 1979-12-31 to 2017-12-31.

Special note: This series gives the number of Japanese Yen per US Dollar, which is the convention for quoting this exchange rate in the foreign exchange market. However, to make this series comparable to the Wilshire 5000 Index and price of Gold, we need to change the exchange rate to be the number of US Dollars per Japanese Yen, i.e., replace the series by its inverse,

1 / DEXJPUS

after removing the NA observations.

Calculate the daily log returns and discrete returns of the price of Japanese Yen in terms of US Dollars.

Use the daily log return data to estimate the VaR and ES at the 99% confidence level. (Note that this is a different confidence level than the 95% confidence level used in the lectures and exercises.)

Question 1 Follow the instructions in the attached PDF and use the results to complete the quiz. What is the estimated mean of daily log returns? Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 2 What is the estimated standard deviation of daily log returns? Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 3 What is the VaR of daily log returns, using the formula that assumes normality? Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 4

What is the ES of daily log returns, using the formula that assumes normality?

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 5

What is the VaR of daily log returns, simulating from a normal distribution with the same mean and standard

deviation as the data?

Please set the seed value to 123789, and draw a sample of 100,000. If you are using R version 3.6.0 or higher, please add the following command BEFORE setting the seed value: RNGkind(sample.kind=Rounding)

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 6

What is the ES of daily log returns, simulating from a normal distribution with the same mean and standard deviation as the data?

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 7

What is the VaR of daily log returns, simulating from the empirical distribution of the data?

Please set the seed value to 123789, and draw a sample of 100,000. If you are using R version 3.6.0 or higher, please add the following command BEFORE setting the seed value: RNGkind(sample.kind=Rounding)

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 8

What is the ES of daily log returns, simulating from the empirical distribution of the data?

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 9

Suppose a hedge fund invests $1000 million in the Japanese Yen. What is the most conservative (e.g. most negative) expected shortfall of its assets over a day, at the 99% confidence level?

Enter the answer using two decimal places, i.e., n.nn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

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Calculating VaR and ES on British Pound

Overview

The goal of this quiz is to test your understanding of using R to estimate VaR and ES using the British Pound exchange rate data from FRED. You should be able to do all the calculations after completing Exercises 5-8.

Exchange Rate Data from FRED

Retrieve the data on the exchange rate between the British Pound and the US Dollar from FRED:

DEXUSUK

Remove the NA observations of this series.

Restrict the dates of this series from 1979-12-31to 2017-12-31.

Special note: This series gives the number of US Dollar per British Pound, which is the convention for quoting this exchange rate in the foreign exchange market.

Calculate the daily log returns and discrete returns of the price of British Pound in terms of US Dollars.

Use the daily log return data to estimate the VaR and ES at the 99% confidence level. (Note that this is a different confidence level than the 95% confidence level used in the lectures and exercises.)

Question 1

Follow the instructions in the attached PDF and use the results to complete the quiz.

What is the estimated mean of daily log returns?

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 2

What is the estimated standard deviation of daily log returns?

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 3 What is the VaR of daily log returns, using the formula that assumes normality? Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 4

What is the ES of daily log returns, using the formula that assumes normality?

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 5

What is the VaR of daily log returns, simulating from a normal distribution with the same mean and standard deviation as the data?

Please set the seed value to 123789 and draw a sample of 100,000. If you are using R version 3.6.0 or higher, please add the following command BEFORE setting the seed value: RNGkind(sample.kind=Rounding)

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 6

What is the ES of daily log returns, simulating from a normal distribution with the same mean and standard deviation as the data?

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 7 What is the VaR of daily log returns, simulating from the empirical distribution of the data?

Please set the seed value to 123789, and draw a sample of 100,000. If you are using R version 3.6.0 or higher, please add the following command BEFORE setting the seed value: RNGkind(sample.kind=Rounding)

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 8

What is the ES of daily log returns, simulating from the empirical distribution of the data?

Enter the answer using six decimal places, i.e., n.nnnnnn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.

Question 9

Suppose a hedge fund invests $1000 million in the British Pound. What is the most conservative (e.g. most negative) expected shortfall of its assets over a day, at the 99% confidence level?

Enter the answer using two decimal places, i.e., n.nn (where n is an integer). If this is a negative number, please add a minus (-) sign in front. If this is a positive number, there is no need to add a plus sign in front.