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


Copyright 2011 - 2019 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/.


Listing 5.1/5.2: Download stock prices in R
Last updated August 2019

p = read.csv('stocks.csv')
y=apply(log(p),2,diff)     # calculate returns. note first column is dates
portfolio_value = 1000
p = 0.01                   # probability
		
Listing 5.1/5.2: Download stock prices in MATLAB
Last updated August 2016

stocks = csvread('stocks.csv',1,0);
p1 = stocks(:,1);                   % consider first two stocks
p2 = stocks(:,2);
y1=diff(log(p1));                   % convert prices to returns
y2=diff(log(p2));
y1=y1(length(y1)-4100+1:end);       % length adjustment
y2=y2(length(y2)-4100+1:end);       % length adjustment
y=[y1 y2];
T=length(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 = length(y1)*p              # p percent smallest
VaR1 = -ys[op]*portfolio_value
print(VaR1)
		
Listing 5.3/5.4: Univariate HS VaR in MATLAB
Last updated 2011

ys = sort(y1);       % sort returns
op = T*p;            % p percent smallest
VaR1 = -ys(op)*value
		

Listing 5.5/5.6: Multivariate HS in R
Last updated August 2019

w = matrix(c(0.3,0.2,0.5)) # vector of portfolio weights
		
Listing 5.5/5.6: Multivariate HS VaR in MATLAB
Last updated 2011

w = [0.3; 0.7];       % vector of portfolio weights
yp = y*w;             % portfolio returns
yps = sort(yp);
VaR2 = -yps(op)*value
		

Listing 5.7/5.8: Univariate ES in R
Last updated August 2019

ES1 = -mean(ys[1:op])*portfolio_value
print(ES1)
		
Listing 5.7/5.8: Univariate ES in MATLAB
Last updated 2011

ES1 = -mean(ys(1:op))*value
		

Listing 5.9/5.10: Normal VaR in R
Last updated August 2019

sigma = sd(y1)                             # estimate volatility
VaR3 = -sigma * qnorm(p) * portfolio_value
print(VaR3)
		
Listing 5.9/5.10: Normal VaR in MATLAB
Last updated 2011

sigma = std(y1);                   % estimate volatility
VaR3 = -sigma * norminv(p) * value
		

Listing 5.11/5.12: Portfolio normal VaR in R
Last updated August 2019

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)*portfolio_value
print(VaR4)
		
Listing 5.11/5.12: Portfolio normal VaR in MATLAB
Last updated 2011

sigma = sqrt(w' * cov(y) * w);       % portfolio volatility
VaR4 = - sigma * norminv(p) *  value
		

Listing 5.13/5.14: Student-t VaR in R
Last updated August August 2019

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) *  portfolio_value
print(VaR5)
		
Listing 5.13/5.14: Student-t VaR in MATLAB
Last updated 2011

scy1=y1*100;                                   % scale the returns
res=mle(scy1,'distribution','tlocationscale');
sigma1 = res(2)/100;                           % rescale the volatility
nu = res(3);
VaR5 = - sigma1 * tinv(p,nu) * value
		

Listing 5.15/5.16: Normal ES in R
Last updated June August 2019

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

sigma = std(y1);
ES2=sigma*normpdf(norminv(p))/p * value
		

Listing 5.17/5.18: Direct integration ES in R
Last updated August 2019

VaR = -qnorm(p)
integrand = function(q){q*dnorm(q)}
ES = -sigma*integrate(integrand,-Inf,-VaR)$portfolio_value/p*portfolio_value
print(ES)
		
Listing 5.17/5.18: Direct integration ES in MATLAB
Last updated 2011

VaR = -norminv(p);
ES = -sigma*quad(@(q) q.*normpdf(q),-6,-VaR)/p*value
		

Listing 5.19/5.20: MA normal VaR in R
Last updated June August 2019

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

WE=20;
for t=T-5:T
    t1=t-WE+1;
    window=y1(t1:t);                   % estimation window
    sigma=std(window);
    VaR6 = -sigma * norminv(p) * value
end
		

Listing 5.21/5.22: EWMA VaR in R
Last updated August 2019

lambda = 0.94;
s11 = var(y1[1:30]);                           # initial variance
for (t in 2:length(y1)){
  s11 = lambda * s11  + (1-lambda) * y1[t-1]^2
}
VaR7 = -qnorm(p) * sqrt(s11) * portfolio_value
print(VaR7)
		
Listing 5.21/5.22: EWMA VaR in MATLAB
Last updated 2011

lambda = 0.94;
s11 = var(y1(1:30));                              % initial variance
for t = 2:T
    s11 = lambda * s11  + (1-lambda) * y1(t-1)^2;
end
VaR7 = -norminv(p) * sqrt(s11) * value
		

Listing 5.23/5.24: Three-asset EWMA VaR in R
Last updated August 2019

s = cov(y)                                         # initial covariance
for (t in 2:dim(y)[1]){
  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) * portfolio_value
print(VaR8)
		
Listing 5.23/5.24: Two-asset EWMA VaR in MATLAB
Last updated 2011

s = cov(y);                                              % initial covariance
for t = 2:T
    s = lambda * s +  (1-lambda) * y(t-1,:)' * y(t-1,:);
end
sigma = sqrt(w' * s * w);                                % portfolio vol
VaR8 = - sigma * norminv(p) * value
		

Listing 5.25/5.26: Univariate GARCH in R
Last updated August 2019

library(rugarch)
spec = ugarchspec(variance.model = list( garchOrder = c(1, 1)),
mean.model = list( armaOrder = c(0,0),include.mean = FALSE))
res = ugarchfit(spec = spec, data = y1)
omega = res@fit$coef[1]
alpha = res@fit$coef[2]
beta = res@fit$coef[3]
sigma2 = omega + alpha * tail(y1,1)^2 + beta * tail(res@fit$var,1)
VaR9 = -sqrt(sigma2) * qnorm(p) * portfolio_value
names(VaR9)="VaR"
print(VaR9)
		
Listing 5.25/5.26: GARCH in MATLAB
Last updated August 2016

[parameters,ll,ht]=tarch(y1,1,0,1);
omega = parameters(1)
alpha = parameters(2)
beta = parameters(3)
sigma2 = omega + alpha*y1(end)^2 + beta*ht(end) % calc sigma2 for t+1
VaR9 = -sqrt(sigma2) * norminv(p) * value