%   Copyright (c) 2001-2009 by Ales Cerny

%************************************************************************%
% chapter4sect3.m - supplementary program to                            %
% Ales Cerny (2009) Mathematical Techniques in Finance (2nd ed.)         % 
% Princeton University Press http://press.princeton.edu/titles/9079.html %
%************************************************************************%
    
% This code is provided 'as-is', without any express or implied warranty.  
% 
% Permission is granted to anyone to use this code for any purpose, 
% subject to the following restrictions:
% 
% 1. The origin of this code must not be misrepresented; you must not
%    claim that you wrote the original code.
% 2. Modified code versions must be plainly marked as such, and must not 
%    be misrepresented as being the original code.
% 3. This notice may not be removed from any source distribution.

% NOTICE TO STUDENTS: To avoid accusations of plagiarism, if you use this 
% code or its modifications in assessed work you should prepend it with a 
% note stating: 
%   "This is the original/modified version of the code chapter4sect3.m by 
%    Ales Cerny (2009), Mathematical Techniques in Finance (2nd ed.),  
%    Princeton University Press. The original version is available from 
%    http://www.martingales.info/mtfweb2".
% A similar acknowledgement should appear prominently inside your written 
% report.

% One period optimal investment with CRRA utility, incomplete markets,
% single risky asset Japanese NIKKEI 225 real return data,year on year
% returns, monthly data  1960-2000.

clear;
clc;

%*******************%
%    parameters     %
%*******************%
% row vector of rates of return from -35% to 90% in 5% increments
Risky1 = -0.35 : 0.05 : 0.90; 
RiskFreeRate = 0.02;

%****************************************%
%     global parameters for utility      %
%      maximizing procedure CRRAmax      %
%****************************************%
outputflag = 1;      
gama=5;
CEqTol=10^-5;
% relative frequency of annual real returns on NIKKEI 225
XDistr = [0.011 0.023 0.021 0.041 0.034 0.061 0.112 0.095 0.097...
          0.081 0.091 0.068 0.074 0.049 0.047 0.028 0.015 0.008...
          0.013 0.021 0.000 0.000 0.004 0.000 0.002 0.004 ]; 
X = Risky1-RiskFreeRate;

%*********************************************%
% Computations for quadratic utility investor %
%*********************************************%
EX = X*XDistr';                           % E[X]  
EX2 = X.^2*XDistr';                       % E[X^2]

%****************************% 
% main body of the programme %
%****************************%
[CE,alpha] = CRRAmax(X, XDistr, gama, CEqTol, outputflag) ;
disp(' ');
disp(sprintf('Certainty equivalent wealth/Safe wealth  %12.4f  ', CE));
disp(sprintf('CRRA alpha                               %12.4f  ', alpha));
disp(sprintf('quadratic utility alpha                  %12.4f  ', EX/EX2/gama));
disp('');