% Copyright (c) 2001-2009 by Ales Cerny

%************************************************************************%
% chapter3exe5.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 chapter3exe5.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.

clc;

gama=5;
V0 = 100;
y = 10;
rsafe = 0.02;
v = (1+rsafe)*V0+y;
r = -0.35 : 0.05 : 0.90;   % row vector of rates of return from -35% to 90% in 5% increments%
XDistr = [0.011                 % relative frequency of annual real returns on NIKKEI 225, monthly data 1960-2000
          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 ]'; 
CEqTolerance = 10^(-7);
X=r-rsafe;
EX = X*XDistr';
OmegaX = (X.*XDistr)*X'; 
betaQU = OmegaX\EX;

%****************************%
% main body of the programme %
%****************************%
RR=5; %coefficient of local relative risk aversion
[IP,beta]=HARAmax(X,XDistr,gama,CEqTolerance); 

clc
disp('_________________________________________________________________________')
disp(' ')
disp(sprintf('                            gamma = %1d',gama))        
disp(' ')
disp(sprintf('  Actual risky investment (JPY million)                %12.1f', beta/RR*v))
disp(' ')
disp(sprintf('  Normalized optimal investment                        %12.3f', beta))
disp(' ')
disp(' ')
disp('                  quadratic utility (gamma = -1) ')
disp(' ')
disp(' ')
disp(sprintf('  Actual risky investment (JPY million)                %12.1f', betaQU/RR*v))
disp(' ')
disp(sprintf('  Normalized optimal investment                        %12.3f', betaQU))
disp(' ')
disp('__________________________________________________________________________')
disp(' ')
disp(' ')
disp(' ')