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Am I missing something? Currently implementing a VaR and CVaR measure assuming normality of wealth value. after executing the following script, VaR is always greater than CVaR, as expected, but convexity does not match. I would expect VaR and CVaR to be a convex function of a.

clear all
x=2.05798*randn(500000,1)+100;
varr=zeros(100,1);
cvar=zeros(100,1);
cv=zeros(100,1);
for i=1:100
 varr(i,1)=prctile(x,0.01*i);
 cvar(i,1)=mean(x(x<prctile(x,0.01*i)));
 cv(1,i)=0.01*i;
end
hold on
plot(varr,'r')
hold on 
plot(cvar)
legend('Var','CVar')

enter image description here

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