% logngraf.m. Makes graphs of lognormal and portfolio calculations. 
close all;

lnr = (-5:0.02:2)';
fill = ones(size(lnr,1),1); 
sig = 1;
mu = [ 0 (-1/2*sig^2)];
pr = (1/(2*pi*sig^2)^0.5).*exp(-1/2*((lnr*[1 1]-fill*mu).^2)/sig.^2);

% what is pr ( loss) in each case? 
cdf('Normal',0,mu(1),sig)
cdf('Normal',0,mu(2),sig)

plot(100*(exp(lnr)-1),pr(:,1)./(exp(lnr)*ones(1,size(pr(:,1),2))),'-k');
hold on; 
plot(100*(exp(lnr)-1),pr(:,2)./(exp(lnr)*ones(1,size(pr(:,2),2))),'--k');
axis([-100 400 0 inf]);
xlabel('Percent arithmetic return');
%ylabel('Probability');
text(-30,0.9,'E(lnR) = -50%, E(R) = 0%, 50% lose $'); 
text(30,0.35,'E(lnR) = 0%, E(R) = 67%, 69% lose $'); 
set(gca,'Ytick',[]); 
%_pline = (1~6~100*(exp((mu[1]+1/2*sig^2))-1)~0~
%              100*(exp((mu[1]+1/2*sig^2))-1)~0.5~1~15~0);
%_pmsgstr = "Mean";
%_pmsgctl =  100*(exp((mu[1]+1/2*sig^2))-1)~0.53~0.2~90~1~15~0;

print -depsc2 logn.eps;