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
using CSV;
p = CSV.read("stocks.csv",nullable=false);
## convert prices of first two stocks to returns, and adjust length
y1 = diff(log.(p[:,1]));
y2 = diff(log.(p[:,2]));
y1 = y1[length(y1)-4100+1:length(y1)];
y2 = y2[length(y2)-4100+1:length(y2)];
y = hcat(y1,y2);
T = size(y,1)
value = 1000; # portfolio value
p = 0.01; # probability
ys = sort(y1); % sort returns
op = T*p; % p percent smallest
VaR1 = -ys(op)*value
ys = sort(y1) # sort returns
op = convert(Int64, T*p) # p percent smallest
VaR1 = -ys[op] * value
w = [0.3; 0.7]; % vector of portfolio weights
yp = y*w; % portfolio returns
yps = sort(yp);
VaR2 = -yps(op)*value
w = [0.3; 0.7] # vector of portfolio weights
yp = y * w # portfolio returns
yps = sort(yp)
VaR2 = -yps[op] * value
ES1 = -mean(ys(1:op))*value
ES1 = -mean(ys[1:op]) * value
sigma = std(y1); % estimate volatility
VaR3 = -sigma * norminv(p) * value
sigma = std(y1); # estimate volatility
using Distributions;
VaR3 = -sigma * quantile(Normal(0,1),p) * value
sigma = sqrt(w' * cov(y) * w); % portfolio volatility
VaR4 = - sigma * norminv(p) * value
sigma = sqrt(w'*cov(y)*w) # portfolio volatility
VaR4 = -sigma * quantile(Normal(0,1), p) * value
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
## using Distributions;
## res = fit_mle(TDist, y1)
## nu = res.ν (this is the Greek letter nu, not Latin v)
## sigma = sqrt(nu/(nu-2))
## VaR5 = -sigma * quantile(TDist(nu), p) * value
## Julia does not have a function for fitting Student-t data yet
## Currently: there exists Distributions.jl with fit_mle
## usage: Distributions.fit_mle(Dist_name, data[, weights])
sigma = std(y1);
ES2=sigma*normpdf(norminv(p))/p * value
sigma = std(y1)
ES2 = sigma * pdf(Normal(0,1), (quantile(Normal(0,1), p))) / p * value
VaR = -norminv(p);
ES = -sigma*quad(@(q) q.*normpdf(q),-6,-VaR)/p*value
using QuadGK;
VaR = -quantile(Normal(0,1), p)
integrand(x) = x*pdf(Normal(0,1), x)
ES = -sigma * quadgk(integrand, -Inf, -VaR)[1] / p * value
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
WE = 20
for t in range(T-5, 6)
t1 = t-WE
window = y1[t1+1:t] # estimation window
sigma = std(window)
VaR6 = -sigma*quantile(Normal(0,1),p)*value
println(VaR6)
end
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
lambda = 0.94
s11 = var(y1[1:30]) # initial variance
for t in range(2, T-1)
s11 = lambda * s11 + (1-lambda) * y1[t-1]^2
end
VaR7 = -sqrt(s11) * quantile(Normal(0,1), p) * value
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
s = cov(y) # initial covariance
for t in range(2, T-1)
s = lambda * s + (1-lambda) * y[t-1,:] * (y[t-1,:])'
end
sigma = sqrt(w'*s*w) # portfolio vol
VaR8 = -sigma * quantile(Normal(0,1), p) * value
[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
## We use the FRFGarch mini-package again (refer to Chapter 2 above)
using FRFGarch;
res = GARCHfit(y1)
sigma_fc = res.seForecast
## seForecast contains the next-day conditional volatility forecast
VaR9 = - sigma_fc * quantile(Normal(0,1), p) * value
## GARCH estimation will be slightly different from other languages
## this is due to GARCHfit choosing initial conditional vol = sample vol