Chapter 5. Implementing Risk Forecasts (in R/Python)


Copyright 2011, 2016, 2018 Jon Danielsson. This code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The GNU General Public License is available at: https://www.gnu.org/licenses/.
The original 2011 R code will not fully work on a recent R because there have been some changes to libraries. The latest version of the Matlab code only uses functions from Matlab toolboxes.
The GARCH functionality in the econometric toolbox in Matlab is trying to be too clever, but can't deliver and could well be buggy. If you want to try that, here are the docs (estimate). Besides, it can only do univariate GARCH and so can't be used in Chapter 3. Kevin Sheppard's MFE toolbox is much better, while not as user friendly, it is much better written and is certainly more comprehensive. It can be downloaded here and the documentation here is quite detailed.


Listing 5.1/5.2: Download stock prices in R
Last updated August 2016

library(tseries)
library(zoo)
prices = zoo(read.csv('stocks.csv',header=TRUE,sep=','))
## convert prices of first two stocks to returns and adjust length
y1=tail(diff(log(coredata(prices[,1]))),4100)
y2=tail(diff(log(coredata(prices[,2]))),4100)
TT=length(y1)
y=cbind(y1,y2)
value = 1000                                             # portfolio value
p = 0.01                                                 # probability
		
Listing 5.1/5.2: Download stock prices in Python
Last updated June 2018

import numpy as np
p = np.loadtxt('stocks.csv',delimiter=',',skiprows=1)
p = p[:,[0,1]]                                        # consider two stocks
## convert prices to returns, and adjust length
y1 = np.diff(np.log(p[:,0]), n=1, axis=0)
y2 = np.diff(np.log(p[:,1]), n=1, axis=0)
y1 = y1[len(y1)-4100:]
y2 = y2[len(y2)-4100:]
y = np.stack([y1,y2], axis = 1)
T = len(y1)
value = 1000                                          # portfolio value
p = 0.01                                              # probability
		

Listing 5.3/5.4: Univariate HS in R
Last updated August 2016

ys = sort(y1)        # sort returns
op = TT*p            # p percent smallest
VaR1 = -ys[op]*value
print(VaR1)
		
Listing 5.3/5.4: Univariate HS in Python
Last updated June 2018

ys = np.sort(y1)           # sort returns
op = int(T*p)              # p percent smallest
VaR1 = -ys[op - 1] * value
print(VaR1)
		

Listing 5.5/5.6: Multivariate HS in R
Last updated 2011

w = matrix(c(0.3,0.7)) # vector of portfolio weights
yp = y %*% w           # obtain portfolio returns
yps = sort(yp)
VaR2 = -yps[op]*value
print(VaR2)
		
Listing 5.5/5.6: Multivariate HS in Python
Last updated June 2018

w = [[0.3], [0.7]]               # vector of portfolio weights
yp = np.squeeze(np.matmul(y, w)) # portfolio returns
yps = np.sort(yp)
VaR2= -yps[op - 1] * value
print(VaR2)
		

Listing 5.7/5.8: Univariate ES in R
Last updated 2011

ES1 = -mean(ys[1:op])*value
print(ES1)
		
Listing 5.7/5.8: Univariate ES in Python
Last updated June 2018

ES1 = -np.mean(ys[:op]) * value
print(ES1)
		

Listing 5.9/5.10: Normal VaR in R
Last updated 2011

sigma = sd(y1)                   # estimate volatility
VaR3 = -sigma * qnorm(p) * value
print(VaR3)
		
Listing 5.9/5.10: Normal VaR in Python
Last updated June 2018

sigma = np.std(y1, ddof=1)                # estimate volatility
VaR3 = -sigma * stats.norm.ppf(p) * value
print(VaR3)
		

Listing 5.11/5.12: Portfolio normal VaR in R
Last updated 2011

sigma = sqrt(t(w) %*% cov(y) %*% w)[1] # portfolio volatility
## Note: the trailing [1] is to convert a single element matrix to float
VaR4 = -sigma * qnorm(p)*value
print(VaR4)
		
Listing 5.11/5.12: Portfolio normal VaR in Python
Last updated June 2018

## portfolio volatility
sigma = np.sqrt(np.mat(np.transpose(w))*np.mat(np.cov(y,rowvar=False))*np.mat(w))[0,0]
## Note: [0,0] is to pull the first element of the matrix out as a float
VaR4 = -sigma * stats.norm.ppf(p) * value
print(VaR4)
		

Listing 5.13/5.14: Student-t VaR in R
Last updated August 2016

library(QRM)
scy1=(y1)*100                            # scale  the returns
res=fit.st(scy1)
sigma1=res$par.ests[3]/100               # rescale the volatility
nu=res$par.ests[1]
VaR5 = - sigma1 * qt(df=nu,p=p) *  value
print(VaR5)
		
Listing 5.13/5.14: Student-t VaR in Python
Last updated June 2018

scy1 = y1 * 100                       # scale the returns
res = stats.t.fit(scy1)
sigma = res[2]/100                    # rescale volatility
nu = res[0]
VaR5 = -sigma*stats.t.ppf(p,nu)*value
print(VaR5)
		

Listing 5.15/5.16: Normal ES in R
Last updated June 2018

sigma = sd(y1)
ES2 = sigma*dnorm(qnorm(p))/p * value
print(ES2)
		
Listing 5.15/5.16: Normal ES in Python
Last updated June 2018

sigma = np.std(y1, ddof=1)
ES2 = sigma * stats.norm.pdf(stats.norm.ppf(p)) / p * value
print(ES2)
		

Listing 5.17/5.18: Direct integration ES in R
Last updated 2011

VaR = -qnorm(p)
integrand = function(q){q*dnorm(q)}
ES = -sigma*integrate(integrand,-Inf,-VaR)$value/p*value
print(ES)
		
Listing 5.17/5.18: Direct integration ES in Python
Last updated June 2018

from scipy.integrate import quad
VaR = -stats.norm.ppf(p)
integrand = lambda q: q * stats.norm.pdf(q)
ES = -sigma * quad(integrand, -np.inf, -VaR)[0] / p * value
print(ES)
		

Listing 5.19/5.20: MA normal VaR in R
Last updated June 2018

WE=20
for (t in seq(TT-5,TT)){
  t1=t-WE+1
  window= y1[t1:t]                 # estimation window
  sigma=sd(window)
  VaR6 = -sigma * qnorm(p) * value
  print(VaR6)
}
		
Listing 5.19/5.20: MA normal VaR in Python
Last updated June 2018

WE = 20
for t in range(T-5,T+1):
    t1 = t-WE
    window = y1[t1:t]                     # estimation window
    sigma = np.std(window, ddof=1)
    VaR6 = -sigma*stats.norm.ppf(p)*value
    print (VaR6)
		

Listing 5.21/5.22: EWMA VaR in R
Last updated August 2016

lambda = 0.94;
s11 = var(y1[1:30]);                           # initial variance
for (t in 2:TT){
  s11 = lambda * s11  + (1-lambda) * y1[t-1]^2
}
VaR7 = -qnorm(p) * sqrt(s11) * value
print(VaR7)
		
Listing 5.21/5.22: EWMA VaR in Python
Last updated June 2018

lmbda = 0.94
s11 = np.var(y1[0:30], ddof = 1)             # initial variance
for t in range(1, T):
    s11 = lmbda*s11 + (1-lmbda)*y1[t-1]**2
VaR7 = -np.sqrt(s11)*stats.norm.ppf(p)*value
print(VaR7)
		

Listing 5.23/5.24: Two-asset EWMA VaR in R
Last updated 2011

s = cov(y)                                         # initial covariance
for (t in 2:TT){
  s = lambda*s + (1-lambda)*y[t-1,] %*% t(y[t-1,])
}
sigma = sqrt(t(w) %*% s %*% w)[1]                  # portfolio vol
## Note: [1] is to convert single element matrix to float
VaR8 = -sigma * qnorm(p) * value
print(VaR8)
		
Listing 5.23/5.24: Two-asset EWMA VaR in Python
Last updated June 2018

## s is the initial covariance
s = np.cov(y, rowvar = False)
for t in range(1,T):
    s = lmbda*s+(1-lmbda)*np.transpose(np.asmatrix(y[t-1,:]))*np.asmatrix(y[t-1,:])
sigma = np.sqrt((np.transpose(w)*s*w)[0,0])
## Note: [0,0] is to pull the first element of the matrix out as a float
VaR8 = -sigma * stats.norm.ppf(p) * value
print(VaR8)
		

Listing 5.25/5.26: GARCH in R
Last updated 2011

library(fGarch)
g = garchFit(~garch(1,1),y1,include.mean=F,trace=F)
omega = g@fit$matcoef[1,1]
alpha = g@fit$matcoef[2,1]
beta = g@fit$matcoef[3,1]
sigma2 = omega + alpha*y[TT]^2 + beta*g@h.t[TT]     # calc sigma2 for t+1
VaR9 = -sqrt(sigma2) * qnorm(p) * value
print(VaR9)
		
Listing 5.25/5.26: GARCH VaR in Python
Last updated June 2018

from arch import arch_model
am = arch_model(y1, mean = 'Zero', vol='Garch', p=1, o=0, q=1, dist='Normal')
res = am.fit(update_freq=5)
omega = res.params[0]
alpha = res.params[1]
beta = res.params[2]
## computing sigma2 for t+1
sigma2 = omega + alpha*y1[T-1]**2 + beta * res.conditional_volatility[-1]**2
VaR9 = -np.sqrt(sigma2) * stats.norm.ppf(p) * value
print(VaR9)
## Note: arch_model's GARCH optimization has issues with convergence