In Letmode/quarks: Simple Methods for Calculating and Backtesting Value at Risk and Expected Shortfall

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quarks

The goal of quarks is to enable the user to compute Value at Risk (VaR) and Expected Shortfall (ES) by means of various types of historical simulation. Currently plain historical simulation as well as age-, volatility-weighted- and filtered historical simulation are implemented in quarks. Volatility weighting can be carried out via an exponentially weighted moving average (EWMA) model or other GARCH-type models.

Installation

You can install the released version of quarks from CRAN with:

install.packages("quarks")

Examples

The data set DAX, which is implemented in the quarks package, contains daily financial data of the German stock index DAX from January 2000 to December 2021 (currency in EUR). In the following examples of the (out-of-sample) one-step forecasts of the 97.5$\%$-VaR (red line) and the corresponding ES (green line) are illustrated. Exceedances are indicated by the colored circles.

library(quarks)         # Call the package

# Calculating the returns
prices <- DAX$price.close
returns <- diff(log(prices))

Example 1 - plain historical simulation

results1 <- rollcast(x = returns, p = 0.975, method = 'plain', nout = 250,
                     nwin = 250)
results1

Visualize your results with the plot method implemented in quarks.

plot(results1)

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Example 2 - age weighted historical simulation

results2 <- rollcast(x = returns, p = 0.975, method = 'age', nout = 250,
                     nwin = 250)
results2

plot(results2)

---

Example 3 - volatility weighted historical simulation - EWMA

results3 <- rollcast(x = returns, p = 0.975, model = 'EWMA',
                     method = 'vwhs', nout = 250, nwin = 250)
results3

plot(results3)

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Example 4 - filtered historical simulation - GARCH

set.seed(12345)
results4 <- rollcast(x = returns, p = 0.975, model = 'GARCH',
                     method = 'fhs', nout = 250, nwin = 250, nboot = 10000)
results4

plot(results4)

To assess the performance of these methods one might apply backtesting.

For instance, by employing the Traffic Light Test, Coverage Tests or by means of Loss Function.

Example 5 - Traffic Light Test

# Calculating the returns
prices <- SP500$price.close
returns <- diff(log(prices))

results <- rollcast(x = returns, p = 0.99, model = 'GARCH',
                     method = 'vwhs', nout = 250, nwin = 500)
trftest(results)

Example 6 - Coverage Tests

# Calculating the returns
prices <- HSI$price.close
returns <- diff(log(prices))

results <- rollcast(x = returns, p = 0.99, model = 'GARCH',
                     method = 'vwhs', nout = 250, nwin = 500)
cvgtest(results, conflvl = 0.95)

Example 7 - Loss Functions

# Calculating the returns
prices <- FTSE100$price.close
returns <- diff(log(prices))

results <- rollcast(x = returns, p = 0.99, model = 'GARCH',
                     method = 'vwhs', nout = 250, nwin = 500)
lossfun(results)

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Functions

In quarks ten functions are available.

Functions - version 1.1.3:

• cvgtest: Applies various coverage tests to Value at Risk
• ewma: Estimates volatility of a return series by means of an exponentially weighted moving average
• fhs: Calculates univariate Value at Risk and Expected Shortfall by means of filtered historical simulation
• hs: Computes Value at Risk and Expected Shortfall by means of plain and age-weighted historical simulation
• lossfun: Calculates of loss functions of ES
• plop: Profit & Loss operator function; Calculates weighted portfolio returns or losses
• rollcast: Computes rolling one-step-ahead forecasts of Value at Risk and Expected Shortfall
• runFTS: Starts a shiny application for downloading data from Yahoo Finance
• trftest: Applies the Traffic Light Test to Value at Risk
• vwhs: Calculates univariate Value at Risk and Expected Shortfall by means of volatility weighted historical simulation

For further information on each of the functions, we refer the user to the manual or the package documentation.

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Data Sets

• DAX: Daily financial time series data of the German Stock Market Index (DAX) from January 2000 to December 2021
• DJI: Daily financial time series data of the Dow Jones Industrial Average (DJI) from January 2000 to December 2021
• FTSE100: Daily financial time series data of the Financial Times Stock Exchange Index (FTSE) from January 2000 to December 2021
• HSI: Daily financial time series data of the Hang Seng Index (HSI) from January 2000 to December 2021
• NIK225: Daily financial time series data of the Nikkei Heikin Kabuka Index (NIK) from January 2000 to December 2021
• SP500: Daily financial time series data of Standard and Poor`s (SP500) from January 2000 to December 2021

Letmode/quarks documentation built on Sept. 6, 2022, 9:03 p.m.