CPPI.m

%% Backtest a CPPI product
% CPPI stands for Constant Proportion Portfolio insurance. It is one of
% the simplest hedging strategy.
% this porduct is portfolio with 2 assets : one risk free (tipically, a
% bond) . The other asset is a risky one, but in practice, only assets with
% low volatilities (ie, funds) are used. the typical asset is a fund of
% fund.
%
% The basis of this strategy is to warranty an amount at Expiry, but to
% take advantage of the potential increase of the risky asset. so  CPPI
% provides downside protection.
%
% 3 parameters therefore drive the mechanism :
% - The warratnied amount (Floor). The less you warranty, the more you can potentially take
% advantage of the risky asset
% - the multiplicator : this is the degree of exposure of the bank
%
%
% - Transaction cost : a percentage. If 0.02, then cost to trade 100 is 2
% hedging is less than this value
% To avoid too much trading costs, 3 other parameters are set :
% - A treshold level (for example 0.05) -> we do not hedge if the percentage of
% hedging is less than this value
% - A smothing factor After computation opf the volume of asset to hedge,
% we just trade but we adjust the volume using this smothing factor

%% Clear all the data
clear all;
close all;

%% Set the warrantied amount and fundamental parameters of the CPPI
Floor = 100;
MaxMultiplier = 10;
NumberOfMultiplierStep = 100;
SmoothingFactor = 0.8;
TransactionThreshold = 0.02;
TransactionCost = 0.005;
HedgingFrequencyInDays = 1;

%% Retrieve the data used for the backtesting
% We use the Eurstoxx50 in this case

Mode = 'Historical';

[Prices,dates,StartDate,EndDate] = SimpleXlsReader('1998_BackTest.xls');

Returns = Prices(2 :end)./ Prices (1:end - 1) - 1;

%% Set the number of Multiplier to generate the 3D surface
%Here we just set the number of multiplier we want to evaluate.
Multipliers = linspace(1,MaxMultiplier,NumberOfMultiplierStep);

%% Get the risky asset path (to compare with the CPPI evolution)
NormalizedPrices  = ret2price(Returns,100,  1);
TimeLength = size(NormalizedPrices,1);

%% Compute the CPPI value for each multiplier

for i = 1 : 1: NumberOfMultiplierStep
    [PortFolioValue(i,:) , TradedAmount(i,:), PercentageOfTradingDates(i),DynFloor(i,:),Exposure(i,:)]= CPPI_PayOff_From_Returns_2(100, Floor,Multipliers(i),Returns, 0.03,SmoothingFactor, TransactionThreshold, TransactionCost, HedgingFrequencyInDays);
end;

%% Plot the surface of CCPI value

h1 = figure;
set(h1,'WindowStyle','Docked');
hold on;
surf(PortFolioValue);
shading interp;
set(gca,'YTick',linspace(1 , NumberOfMultiplierStep ,5)');
set(gca,'YTickLabel',num2str( linspace(1 , MaxMultiplier,5)') );
dateaxis('x',12,StartDate);
PlotTitle  = ['BackTesting from ' datestr(StartDate,'dd/mm/yyyy') ' to ' datestr(EndDate,'dd/mm/yyyy')];
title(PlotTitle);
zlabel('Performance, on a 100 basis');
zlim([0.8 * Floor 1.2 * max(max(PortFolioValue))]);
ylim([1 NumberOfMultiplierStep]);
xlim([1 TimeLength-1]);
%zlim([50 max(PercentageOfTradingDates)*1.2]);
grid on;

ViewPoint = [0.7986   -0.6018    0.0000   -0.0984;    0.2825    0.3749    0.8829   -0.7702; ...
    0.5314    0.7052   -0.4695    8.2767;     0         0         0    1.0000];
view(ViewPoint);
%% Plot the risky asset path


XCoor = (NumberOfMultiplierStep) * ones(TimeLength,1);
plot3(1 : TimeLength,XCoor ,NormalizedPrices);
topValue = max(zlim);
%zlim([1 topValue]);


%% Plot the warrantied amount plane in transparency
% The CPPI si supposed to be always above except incase of big Krach
FloorPlane = PortFolioValue;
FloorPlane(:,:) = Floor;
surf(FloorPlane,'FaceColor','b','EdgeColor','none','FaceAlpha',0.15);
ylim([1 NumberOfMultiplierStep]);

%% Plot the percentage of hedging days for each multiplier

UntradedDays = (TradedAmount == 0);
h = figure;
set(h,'WindowStyle','Docked');
area(PercentageOfTradingDates');
hold on;

%% Put some labeling 
grid on;
set(gca,'XTick',linspace(1 , NumberOfMultiplierStep ,5)');
set(gca,'XTickLabel',num2str( linspace(1 , MaxMultiplier,5)') );
ylabel('Percentage of trading dates');
xlabel('Multiplier');
title('Percentage of trading dates according to value of Multiplier');


%% Plot the surface of the trading amount
%As expected, the higher is the risk the more we have to hedge, and so the
%higher are the transaction costs.

h3 = figure;
set(h3,'WindowStyle','Docked');
surf(TradedAmount);
shading interp;

set(gca,'YTick',[1 25 50 75 100']);
set(gca,'YTickLabel',num2str( linspace(1 , MaxMultiplier,5)' ) );

dateaxis('x',StartDate);
title('Traded Amount');

grid on;
ylim([1 100]);
ylabel('Multiplier');
xlabel('Time');
xlim([1 TimeLength]);
dateaxis('x',12,StartDate);
zlabel('Traded Amount , on a 100 basis');


TotalTradedAmount = sum(TradedAmount,2);
h4 = figure;
set(h4,'WindowStyle','Docked');
plot(TotalTradedAmount );
grid on;
set(gca,'XTick',linspace(1 , NumberOfMultiplierStep ,5)');
set(gca,'XTickLabel',num2str( linspace(1 , MaxMultiplier,5)') );
ylabel('Total Traded Amount');
xlabel('Multiplier');
title('Total Traded Amount depending on the value of Multiplier');


%% Bonus -> Let's compare to the Allianz EEP version .... We use the
% multiplier giving the maximum result
%[ MaxVal,BestStrategy] = max(PortFolioValue(:,end));
BestStrategy = 45;
MaxVal = PortFolioValue(BestStrategy,end);
h5 = figure;
set(h5,'WindowStyle','Docked');
plot(dates(2:end),Prices(2:end)./Prices(1).*100,'k');
hold on;
AdjustedDates = dates(2: 1 : 1 + size(PortFolioValue,2));
plot(AdjustedDates,PortFolioValue(BestStrategy,:),'b');
plot(AdjustedDates,DynFloor(BestStrategy,:),'r');
legend(get(h5,'CurrentAxes'),'Risky Asset','CPPI (Best Multiplier)','Floor');
grid on;
xlim([AdjustedDates(1) AdjustedDates(end)])
ylim([80 max(NormalizedPrices)]);
title(['Performance of the EEP from ' num2str(datestr(StartDate,'dd/mm/yyyy')) ' to ' num2str(datestr(EndDate,'dd/mm/yyyy')) ' for the best Strategy, with a Multplier of ' num2str(Multipliers(BestStrategy))]);
MyDateTick(12,dates,StartDate,EndDate,60);
h6 = figure;
set(h6,'WindowStyle','Docked');
plot(AdjustedDates,Exposure(BestStrategy,:)./100,'k');
xlim([AdjustedDates(1) AdjustedDates(end)]);
MyDateTick(12,dates,StartDate,EndDate,60);
grid on;
title(['Exposure of the EEP from ' num2str(datestr(StartDate,'dd/mm/yyyy')) ' to ' num2str(datestr(EndDate,'dd/mm/yyyy'))]);
ylabel('% of the EEP Exposed');
disp(['Best Multiplier is ' num2str(Multipliers(BestStrategy)) ' Giving a absolute result of ' num2str(MaxVal - 100) ' % from ' num2str(datestr(StartDate,'dd/mm/yyyy')) ' to ' num2str(datestr(EndDate,'dd/mm/yyyy'))]);