%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Empirical Financial Econometrics Matlab Class Code part 1
% Updated Spring 2021
% This Matlab code facilitates to ASSN 1-2. 
% Copyright at Chaoyi Chen (BCE & MNB)
% All rights reserved. For use by registered students only.
% Please do not distribute without express written consent.
% Email: chaoyi.chen@uni-corvinus.hu
% Web: www.chenchaoyi.com
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%
clear all % clean workspace


%%
%%%%%%%%%%%%%%%%%%%%%%%%% Data load and transformation %%%%%%%%%%%%%%%%%%%%%%%%%
% Load data
load YMOPD1901 % This is mat. file, which stores data that the MATLAB program uses

%{ 
Remarks:
1). The mat file should be stored under the "Current Folder"
2). If your data stored as csv., you can use readtable('myfile.csv') function;
3). If your data stored as xlsx., you can use readtablexlsread('myfile.xlsx','Variable') function;
you should save your data at the "Current Folder". Otherwise the Matlab cannot detect your data
%}

year = YMOPD(:,1); 
price = YMOPD(:,2);
lagprice = lagmatrix(price,1);
RiskFree = YMOPD(:,3);
n=size(year,1);

%{
Remarks:
Suppose your dataset, say X, is of n rows by k columns size, where eacg column stores a variable
1). X_i = X(:,i) means you store the ith columnn to X_i, so the X_i will be of size n
by one.
2). X_j = X(j,:) means you store the jth row to X_j, so the X_j will be of size
one by k.
3). Similarly, X_ij = X(i,j) means you store the element at ith columnn and jth row of X.
4). size(X) function shows the size of the matrix. In addition, size(X,1)
shows the row size of X (=n in our example) and size(X,2)shows the column
size of X (=k in our example). 
5). lagmatrix(X,Lags) creates a lagged (shifted) version of a time series
matrix. Type lagmatrix and see examples from HELP for more references
%}

% Define log versions 
p = log(price);
p = p(2:end);
lp = log(lagprice);
lp = lp(2:end);

%{
Remarks:
Since lagprice is the first-lag matrix of price, we lose one observation
initially (You will see NA in lagprice). So we need to re-match the data by deleting the first
observation for all data. p=p(2:end) means we restore data p with its two
to end rows.
%}

% Define ratios and returns
y = p - lp; 
riskfree = RiskFree(2:end);
%{
Remarks:
Remember Log(x_t)-Log(x_{t-1}) approx = return of x at period t by 
first order Taylor expansion. See lecture note "Notation and Concept" for
details
%}

% mean, variance, skewness and kurtosis
mean_y = mean(y);
var_y = var(y);
skew_y = skewness(y);
kurtosis_y = kurtosis(y); 

% Print statistic descriptives
%---------TABLES-----------%
diary results; 
    disp('---------------------------');
    disp('Mean of SP500');
    disp('---------------------------');
    disp(mean_y);
    disp('---------------------------');
    disp('Variance of SP500');
    disp('---------------------------');
    disp(var_y);
    disp('---------------------------');
    disp('Skewness of SP500');
    disp('---------------------------');
    disp(skew_y);
    disp('---------------------------');
    disp('Kurtosis of SP500');
    disp('---------------------------');
    disp(kurtosis_y);
diary off;

% Plot the series
year = year(2:end,1);
base = zeros(size(y,1),1); % break-even investment point
set(0,'DefaulttextInterpreter','latex');
plot(year, y, 'LineWidth',4);
hold on
plot(year, base, '-.', 'LineWidth',4);
hold on
plot(year, riskfree,'--', 'LineWidth',4);
legend({ 'SP 500','Break-even', 'Risk Free'},'Interpreter','latex','location','SW','FontSize',15);
xlabel('Date','FontSize',10);
ylabel('Return','FontSize',10);
title('SP 500 and Risk Free Daily Return, 1901-2015','FontSize',15)
grid on;

%%%%%%%%%%%%%%%%%%%%%%%%% Static Portfolio with weight=1 or 0 %%%%%%%%%%%%%%%%%%%%%%%%%
%%
%{ 
Suppose you invested $100 at the end of year 1901 and put full weight
on risky asset (sp500 in our example), your cumulative return until the end
of 2015 will be 100*(1+y_{1902})*(1+y_{1903})*...*(1+y_{2015}). You can
make use of a loop to compute for the number as below:
%}

principle = 100; 
years_invest = size(year,1);
cumu = principle; % cumulative value / initial cumulative = principle
cumu_yearly = zeros(years_invest,1); % store cumulative value for each investment year

for i=1:years_invest
    cumu = cumu*(1+y(i)); % update by each period return
    cumu_yearly(i) = cumu;
end

Sharpe_ratio = mean(y-riskfree)/std(y); % Here we assume the variance of risk free =0 (not true however)

%{
If put full weight on risk free asset 
%}

cumu_rf = principle;
cumu_yearly_rf = zeros(years_invest,1);
for i=1:years_invest
    cumu_rf = cumu_rf*(1+riskfree(i)); % update by each period return
    cumu_yearly_rf(i) = cumu_rf;
end

% Print cumulative value
%---------TABLES-----------%
diary results; 
    disp('---------------------------');
    disp('Initial value at 1901');
    disp('---------------------------');
    disp(100);
    disp('---------------------------')
    disp('cumulative value of investing SP500, 1901-2015');
    disp('---------------------------');
    disp(cumu);
    disp('---------------------------');
    disp('cumulative value of investing risk free, 1901-2015');
    disp('---------------------------');
    disp(cumu_rf );
    disp('---------------------------');
diary off;

% Plot the cumulative value series
set(0,'DefaulttextInterpreter','latex');
subplot(2,1,1);
plot(year, cumu_yearly, 'LineWidth',4);
hold on
plot(year, cumu_yearly_rf, '-.', 'LineWidth',4);
hold on
legend({ 'SP 500', 'Risk Free'},'Interpreter','latex','location','SW','FontSize',15);
xlabel('Date','FontSize',10);
ylabel('Cumulative value','FontSize',10);
title('SP 500 and Risk Free Cumulative Value, 1901-2015','FontSize',15)
grid on;

% Now suppose you invested $100 after WWII and re-study the question
% Full weight on risky asset
year_1947 = year(46:end);
y_1947 = y(46:end);
rf_1947 = riskfree(46:end);
years_invest_1947 = size(year_1947,1);
cumu_1947 = principle; % cumulative value / initial cumulative = principle
cumu_yearly_1947 = zeros(years_invest_1947,1); % store cumulative value for each investment year
for i=1:years_invest_1947
    cumu_1947 = cumu_1947*(1+y_1947(i)); % update by each period return
    cumu_yearly_1947(i) = cumu_1947;
end
% Full weight on riskfree asset
cumu_rf_1947 = principle;
cumu_yearly_rf_1947 = zeros(years_invest_1947,1);
for i=1:years_invest_1947
    cumu_rf_1947 = cumu_rf_1947*(1+rf_1947(i)); % update by each period return
    cumu_yearly_rf_1947(i) = cumu_rf_1947;
end

Sharpe_ratio_1947 = mean(y_1947-rf_1947)/std(y_1947); % Here we simply assume the variance of risk free =0 (not true however)

% Print cumulative value
%---------TABLES-----------%
diary results; 
    disp('---------------------------');
    disp('Initial value at initial 1947');
    disp('---------------------------');
    disp(100);
    disp('---------------------------')
    disp('cumulative value of investing SP500, 1947-2015');
    disp('---------------------------');
    disp(cumu_1947);
    disp('---------------------------');
    disp('cumulative value of investing risk free, 1947-2015');
    disp('---------------------------');
    disp(cumu_rf_1947);
    disp('---------------------------');
diary off;

% Plot the WWII cumulative value series
set(0,'DefaulttextInterpreter','latex');
subplot(2,1,2);
plot(year_1947, cumu_yearly_1947, '-.', 'LineWidth',4);
hold on
plot(year_1947, cumu_yearly_rf_1947, '-.', 'LineWidth',4);
hold on
legend({ 'SP 500', 'Risk Free'},'Interpreter','latex','location','SW','FontSize',15);
xlabel('Date','FontSize',10);
ylabel('Return','FontSize',10);
title('SP 500 and Risk Free Cumulative Value, 1947-2015','FontSize',15)
grid on;

%%%%%%%%%%%%%%%%%%%%%%%%% Home Work %%%%%%%%%%%%%%%%%%%%%%%%%
% Rewrite the loop of computing cumulative values using "while" instead of "for" 

%%
%%%%%%%%%%%%%%%%%%%%%%%%% Static Portfolio with equal weights %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%% Now assume you choose 1/2 weight on sp and 1/2 weight on rf
% New portfolio return from 1901-2015
y_portfolio = 0.5*y+0.5*riskfree;
cumu_portfolio = principle; % cumulative value / initial cumulative = principle
cumu_yearly_portfolio = zeros(years_invest,1); % store cumulative value for each investment year
for i=1:years_invest
    cumu_portfolio = cumu_portfolio*(1+y_portfolio(i)); % update by each period return
    cumu_yearly_portfolio(i) = cumu_portfolio;
end

Sharpe_ratio_portfolio = mean(y_portfolio- riskfree)/(1/2*std(y_portfolio)); % Again, here we simply assume variance of rf = 0 which is not true

% Print cumulative value including portfolio with equal weight
%---------TABLES-----------%
diary results; 
    disp('---------------------------');
    disp('Initial value at 1901');
    disp('---------------------------');
    disp(100);
    disp('---------------------------')
    disp('cumulative value of investing SP500, 1901-2015');
    disp('---------------------------');
    disp(cumu);
    disp('---------------------------');
    disp('cumulative value of investing risk free, 1901-2015');
    disp('---------------------------');
    disp(cumu_rf );
    disp('---------------------------');
    disp('cumulative value of investing equal weight portfolio, 1901-2015');
    disp('---------------------------');
    disp(cumu_yearly_portfolio );
    disp('---------------------------');
diary off;

% Print Sharpe Ratio Compare
%---------TABLES-----------%
diary results; 
    disp('---------------------------');
    disp('Full weight on risky asset');
    disp('---------------------------');
    disp(Sharpe_ratio);
    disp('---------------------------')
    disp('Half weight on risky asset');
    disp('---------------------------');
    disp(Sharpe_ratio_portfolio);
diary off;

% Plot the cumulative value series
set(0,'DefaulttextInterpreter','latex');
subplot(2,1,1);
plot(year, cumu_yearly, 'LineWidth',4);
hold on
plot(year, cumu_yearly_rf, '-.', 'LineWidth',4);
hold on
plot(year, cumu_yearly_portfolio, '-.', 'LineWidth',4);
hold on
legend({ 'SP 500', 'Risk Free', 'Portfolio(equal weight)'},'Interpreter','latex','location','SW','FontSize',15);
xlabel('Date','FontSize',10);
ylabel('Cumulative value','FontSize',10);
title('SP 500, Risk Free, Equal Weight Portfolio Cumulative Value, 1901-2015','FontSize',15)
grid on;

% New portfolio return from WWII to 2015
y_portfolio_1947 = 0.5*y_1947+0.5*rf_1947;
cumu_portfolio_1947 = principle; % cumulative value / initial cumulative = principle
cumu_yearly_portfolio_1947 = zeros(years_invest_1947,1); % store cumulative value for each investment year
for i=1:years_invest_1947
    cumu_portfolio_1947 = cumu_portfolio_1947*(1+y_portfolio_1947(i)); % update by each period return
    cumu_yearly_portfolio_1947(i) = cumu_portfolio_1947;
end

Sharpe_ratio_portfolio_1947 = mean(y_portfolio_1947- rf_1947)/(1/2*std(y_portfolio_1947)); % Again, here we simply assume variance of rf = 0 which is not true

% Print cumulative value
%---------TABLES-----------%
diary results; 
    disp('---------------------------');
    disp('Initial value at initial 1947');
    disp('---------------------------');
    disp(100);
    disp('---------------------------')
    disp('cumulative value of investing SP500, 1947-2015');
    disp('---------------------------');
    disp(cumu_1947);
    disp('---------------------------');
    disp('cumulative value of investing risk free, 1947-2015');
    disp('---------------------------');
    disp(cumu_rf_1947);
    disp('---------------------------');
    disp('cumulative value of investing equal weight portfolio, 1947-2015');
    disp('---------------------------');
    disp(cumu_portfolio_1947);
    disp('---------------------------');
diary off;


% Print Sharpe Ratio Compare after WWII
%---------TABLES-----------%
diary results; 
    disp('---------------------------');
    disp('Full weight on risky asset, after WWII');
    disp('---------------------------');
    disp(Sharpe_ratio_1947);
    disp('---------------------------')
    disp('Half weight on risky asset, after WWII');
    disp('---------------------------');
    disp(Sharpe_ratio_portfolio_1947);
diary off;

% Plot the WWII cumulative value series
set(0,'DefaulttextInterpreter','latex');
subplot(2,1,2);
plot(year_1947, cumu_yearly_1947, '-.', 'LineWidth',4);
hold on
plot(year_1947, cumu_yearly_rf_1947, '-.', 'LineWidth',4);
hold on
plot(year_1947, cumu_yearly_portfolio_1947, '-.', 'LineWidth',4);
hold on
legend({ 'SP 500', 'Risk Free', 'portfolio (equal weight)'},'Interpreter','latex','location','SW','FontSize',15);
xlabel('Date','FontSize',10);
ylabel('Return','FontSize',10);
title('SP 500, Risk Free, Equal Weight Portfolio Cumulative Value, 1947-2015','FontSize',15)
grid on;

%%
%%%%%%%%%%%%%%%%%%%%%%%%% Static Portfolio with different weights %%%%%%%%%%%%%%%%%%%%%%%%%
% Now assume you invest w on risky asset nd (1-w) on risk free asset
% from 1901 - 2015
% We evaluate the cumulative value and Sharpe ratio with w = [0,0.1,0.2,...,0.9,1] by a loop

weight_choice = [0:0.1:1]; % generate a vector storing all weight candidates
SR = zeros(size(weight_choice,2),1); % SR(j) stores the Sharpe ratio when w=j. All results assume variance of rf = 0 but not true 
cumu_portfolio_all = principle*ones(size(weight_choice,2),1); % cumu_portfolio(j,1) stores the cumulative value when w=j
cumu_yearly_portfolio_all = zeros(years_invest,size(weight_choice,2)); % cumu_yearly_portfolio(:,j) store cumulative value for each investment year when w=j

for j=1:size(weight_choice,2)
    w = weight_choice(j);
    y_portfolio_w = w*y+(1-w)*riskfree;
    std_port_w = w*std(y);  
    SR(j) =  mean(y_portfolio_w)/std_port_w; 
    for i=1:years_invest
    cumu_portfolio_all(j,1) = cumu_portfolio_all(j,1)*(1+y_portfolio_w(i)); % update by each period return
    cumu_yearly_portfolio_all(i,j) = cumu_portfolio_all(j,1);
    end
end

% Print cumulative value including portfolio with equal weight
%---------TABLES-----------%
diary results; 
    disp('---------------------------');
    disp('Initial value at 1901');
    disp('---------------------------');
    disp(100);
    disp('---------------------------')
    disp('cumulative value of investing SP500, 1901-2015');
    disp('---------------------------');
    disp(cumu);
    disp('---------------------------');
    disp('cumulative value of investing risk free, 1901-2015');
    disp('---------------------------');
    disp(cumu_rf );
    disp('---------------------------');
    disp('cumulative value of investing portfolio, 1901-2015, weights are in order of 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1');
    disp('---------------------------');
    disp(cumu_portfolio_all);
    disp('---------------------------');
diary off;

% Print Sharpe Ratio Compare after WWII
%---------TABLES-----------%
diary results; 
    disp('---------------------------');
    disp('Full weight on risky asset, after WWII');
    disp('---------------------------');
    disp(Sharpe_ratio);
    disp('---------------------------')
    disp('Differenet weights on risky asset, 1901-2015, weights are in order of 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1');
    disp('---------------------------');
    disp(SR);
diary off;

% Plot the cumulative value series
set(0,'DefaulttextInterpreter','latex');
subplot(2,1,1);
plot(year, cumu_yearly_rf, 'LineWidth',2);
hold on
plot(year, cumu_yearly_portfolio_all(:,2), '-.', 'LineWidth',2);
hold on
plot(year, cumu_yearly_portfolio_all(:,3), '-.', 'LineWidth',2);
hold on
plot(year, cumu_yearly_portfolio_all(:,4), '-.', 'LineWidth',2);
hold on
plot(year, cumu_yearly_portfolio_all(:,5), '-.', 'LineWidth',2);
hold on
plot(year, cumu_yearly_portfolio_all(:,6), '--', 'LineWidth',2);
hold on
plot(year, cumu_yearly_portfolio_all(:,7), '--', 'LineWidth',2);
hold on
plot(year, cumu_yearly_portfolio_all(:,8), '--', 'LineWidth',2);
hold on
plot(year, cumu_yearly_portfolio_all(:,9), ':',  'LineWidth',2);
hold on
plot(year, cumu_yearly_portfolio_all(:,10),':',   'LineWidth',2);
hold on
plot(year, cumu_yearly_portfolio_all(:,11),':',  'LineWidth',2);
hold on
legend({ 'Risk Free', 'w = 0.1', 'w = 0.2', 'w = 0.3', 'w = 0.4', 'w = 0.5',...
    'w = 0.6', 'w = 0.7', 'w = 0.8', 'w = 0.9', 'w = 1'},'Interpreter','latex','location','SW','FontSize',15);
xlabel('Date','FontSize',10);
ylabel('Cumulative value','FontSize',10);
title('SP 500, Risk Free, Weighted Portfolio Cumulative Value, 1901-2015','FontSize',15)
grid on;

% Plot the Sharpe ratio
set(0,'DefaulttextInterpreter','latex');
subplot(2,1,2);
plot(weight_choice(2:end),SR(2:end), '-.', 'LineWidth',4);
hold on
legend({ 'Sharpe Ratio'},'Interpreter','latex','location','SW','FontSize',15);
xlabel('Weight','FontSize',10);
ylabel('Sharpe Ratio','FontSize',10);
title('Sharpe Ratio of Different Portfolios','FontSize',15)
grid on;

%%%%%%%%%%%%%%%%%%%%%%%%% Home Work %%%%%%%%%%%%%%%%%%%%%%%%%
%{
1. Why the Sharpe ratio is monotonically decreasing over time? (Hint: recall our assumption)
2. At home, re-produce the last two figures with data after WWII 
%}
%%%%%%%%%%%%%%%%%%%%%%%%% The End %%%%%%%%%%%%%%%%%%%%%%%%%