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LinkedIn에 올라온 글을 읽다가 우연히 한 논문을 보았습니다. 공동 저자를 보니까 이정현(Jeong-Hyun Lee)이라는 한국이름이 보이더군요. New York University의 Courant Institute of Mathematical Sciences에 재직하는 듯 합니다. 공동 저자인 Marco Avellaneda도 경력이 화려합니다.
He has also held positions as vice-president in the Morgan Stanley Derivative Products Group, portfolio manager in equity volatility Strategies at Gargoyle Strategic Investments LLC, Head of Volatility Arbitrage at Capital Fund Management and Portfolio Manager in quantitative equity strategies at the Galleon Group in New York. He is known as the inventor of the Uncertain Volatility model and for his work on the Weighted Monte Carlo algorithm and the theory of Dispersion Trading, as well as for several other papers in quantitative finance and derivatives. Marco has extensive experience in the fields of derivatives, quantitative strategies in equities and volatility trading from the point of view of hedge funds and Wall Street firms.
위키페이다를 보니까 ‘A well documented empirical study which confirms that StatArb profitability dropped after 2002 and 2003’라고 평가를 해놓았습니다.
이정현씨는 대한수학회 수리과학정보센터에 또다른 논문도 기고한 적이 있네요.
Generalized Brownian motions with application to finance
Machine Learning in Statistical Arbitrage라는 논문을 보면 인용논문중 하나로 나옵니다.
2.
Numerical Method라는 중국계 회사가 있습니다. 이 회사가 중국대학에 조성현씨가 했던 알고리즘트레이딩전략개발교육과 비슷한 과정을 개설해 운영하고 있습니다.
Introduction to Algorithmic Trading Strategies
2011년 Nanyang Technological University이 개설한 과정에 참여했던 Seow Kian Ping, Parambill Koyachamveettil Manu Chad, Fang Zhi Heng, Cher Zhong Ming등이 ‘Statistical Arbitrage in the U.S. Equities Market’을 실제로 구현하는 프로젝트를 진행하였습니다. 그리고 결과물을 발표했습니다.
Statistical Arbitrage in the U.S. Equities Market Presentation
Statistical Arbitrage in the U.S. Equities Market report
Statistical Arbitrage in the U.S. Equities Market code
이중 개발소스중 PCA와 관련한 부분입니다. 이런 소개를 하는 이유는 국내외 논문을 읽고 분석,구현하는 훈련을 하는 것이 퀀트 트레이더에게 필요하다는 생각이기때문입니다.
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function main_ETF() close all;clear all % Read the ETF, stock and date information % ETF.mat contains the etf data in structured format % StockInfo.mat contains the stock data in structured format tic fprintf('============================================================\n') fprintf('PARAMETERS OPTIMIZATION\n') fprintf('------------------------------------------------------------\n') fprintf('Performing optimization...skipped! (This will take one day)\n') fprintf('------------------------------------------------------------\n') %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Optimization %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if 0 load('ETF.mat'); load('Stocks.mat'); % Select date in YYYYMMDD StartDate = 20060104; EndDate = 20081231; % Number of Stocks and ETF used NoOfStock = length(Stocks); NoOfETF = length(ETF); % Sort the desired data for selected date from ETF and stock. for ii = 1:NoOfETF ETFused(ii).name = ETF(ii).name; ETFused(ii).Return = ETF(ii).Return(find(ETF(ii).Date==StartDate):find(ETF(ii).Date==EndDate)); ETFused(ii).Date = ETF(ii).Date(find(ETF(ii).Date==StartDate):find(ETF(ii).Date==EndDate)); end for ii = 1:NoOfStock Stocksused(ii).name = Stocks(ii).name; Stocksused(ii).Return = Stocks(ii).Return(find(Stocks(ii).Date==StartDate):find(Stocks(ii).Date==EndDate)); Stocksused(ii).Date = Stocks(ii).Date(find(Stocks(ii).Date==StartDate):find(Stocks(ii).Date==EndDate)); end % Find the optimal stock for the trading strategy with the optimise score % levels. TradingParameters = []; profit = []; ProfitAll = []; Signal = []; Wealth = []; for ii = 1:NoOfStock [profit,SSO,SSC,SBO,SBC,Sigtmp,wealthtmp,stocktmp,indretur] = optimizeOmegaETF(ETFused,Stocksused,ii); TradingParameters = [TradingParameters;[SSO,SSC,SBO,SBC]]; ProfitAll = [ProfitAll;profit]; % This is the omega for Optimise omega code. Wealth = [Wealth;wealthtmp]; Signal = [Signal;Sigtmp]; save('ETFresultsOptimizeOmega.mat','TradingParameters','ProfitAll','Wealth','Signal'); end [maxProfit maxStockind] = max(ProfitAll); fprintf('==============================================\n') fprintf('The optimal stock chosen is %s with a profit of $%.2f\n',StocksUsed(maxStockind).name,maxProfit); fprintf('==============================================\n') end %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Outsample Test %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if 1 clear all load('ETF.mat'); load('Stocks.mat'); % This is the results from optimization load('ETFresultsOptimizeOmega.mat') % Select date in YYYYMMDD StartDate = 20090102; EndDate = 20101231; % Number of Stocks and ETF used NoOfStock = length(Stocks); NoOfETF = length(ETF); ETFused = []; Stocksused = []; ProfitAll(33) = 0; fprintf('============================================================\n') fprintf('BACKTESTING\n') fprintf('------------------------------------------------------------\n') fprintf('Performing Outsample test...') % Sort the desired data for selected date from ETF and stock. for ii = 1:NoOfETF ETFused(ii).name = ETF(ii).name; ETFused(ii).Return = ETF(ii).Return(find(ETF(ii).Date==StartDate):find(ETF(ii).Date==EndDate)); ETFused(ii).Date = ETF(ii).Date(find(ETF(ii).Date==StartDate):find(ETF(ii).Date==EndDate)); end for ii = 1:NoOfStock Stocksused(ii).name = Stocks(ii).name; Stocksused(ii).Return = Stocks(ii).Return(find(Stocks(ii).Date==StartDate):find(Stocks(ii).Date==EndDate)); Stocksused(ii).Date = Stocks(ii).Date(find(Stocks(ii).Date==StartDate):find(Stocks(ii).Date==EndDate)); end [maxOmega maxStockind] = max(ProfitAll); OptTradingPara = TradingParameters(maxStockind,:); OptWealth = Wealth(maxStockind,:); [TradeSignalBackTest,WealthBackTest,OmegaBackTest] = outSampleTest(ETFused,Stocksused,maxStockind,OptTradingPara); figure(1115);plot(WealthBackTest,'linewidth',2) title(sprintf('Outsample Test: P&L of %s over a 3 years period (2008-2010) with omega of %.2f for ETF','ATI',1.15),'fontsize',12) ylabel('Capital $','fontsize',12) xlabel('Time (Days)','fontsize',12) set(gca,'linewidth',2) set(gca,'fontsize',10) grid on fprintf('Completed!~\n') fprintf('------------------------------------------------------------\n') end %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% BootStrapping %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if 1 clear all; load('ETF.mat'); load('Stocks.mat'); % This is the results from optimization load('ETFresultsOptimizeOmega.mat') % Number of Monte Carlo MonteCarloRuns = 50; % Select date in YYYYMMDD StartDate = 20060104; EndDate = 20101231; % Number of Stocks and ETF used NoOfStock = length(Stocks); NoOfETF = length(ETF); ETFused = []; Stocksused = []; % Number of Bootstrapping samples SampleNo = 500; ProfitAll(33) = 0; % Optimal parameter to use [maxOmega maxStockind] = max(ProfitAll); OptTradingPara = TradingParameters(maxStockind,:); OptWealth = Wealth(maxStockind,:); TradeSignalBS = []; WealthBS = []; OmegaBS = []; fprintf('Performing Bootstrapping - 50 Monte Carlos runs...') for ii = 1:MonteCarloRuns fprintf('%d...',ii); % Bootstrapping to select SampleNo randomly from population [ETFused,Stocksused]=SampleBootstrap(ETF,Stocks,SampleNo,NoOfStock,NoOfETF); [TradeSignalBackTest,WealthBackTest,OmegaBackTest] = outSampleTest(ETFused,Stocksused,maxStockind,OptTradingPara); TradeSignalBS = [TradeSignalBS;TradeSignalBackTest]; WealthBS = [WealthBS;WealthBackTest]; OmegaBS = [OmegaBS;OmegaBackTest]; if ~isempty(find(ii == [3:13:MonteCarloRuns])) fprintf('\n') end end a = toc; fprintf('Completed Bootstrapping!\n') fprintf('Total time elapsed --> %.2f\n',a) fprintf('============================================================\n') figure(888);plot(WealthBS.') title(sprintf('50 Monte Carlo runs for Stock ATI using ETF approach (Bootstrapping)'),'fontsize',12) ylabel('Capital $','fontsize',12) xlabel('Time (Days)','fontsize',12) set(gca,'linewidth',1.2) set(gca,'fontsize',10) grid on figure(889);plot(OmegaBS,'linewidth',3) title(sprintf('Omega Stock ATI using ETF approach with mean of 1.0485 (Bootstrapping)'),'fontsize',12) ylabel('Omega','fontsize',12) xlabel('No. of Monte Carlo Runs','fontsize',12) set(gca,'linewidth',1.2) set(gca,'fontsize',10) grid on end PlotProfit function [Sigtmp,wealthtmp1,OmegaRatios] = outSampleTest(ETFData,StockData,StockInd,OptTradingPara) SSO = OptTradingPara(1); SSC = OptTradingPara(2); SBO = OptTradingPara(3); SBC = OptTradingPara(4); Sbo = SBO; Sso = SSO; Sbc = SBC; Ssc = SSC; % Number of Stocks and ETF used NoOfStock = length(StockData); NoOfETF = length(ETFData); %Optmization starts here NoOfTradingDays = length(StockData(1).Date); StockPortfolio = 0; lastTransactionDay = 0; %stores the index of the last day when stock was bought or sold ETFBetas = zeros(NoOfETF,1); %Define the initial set of betas as Zeros. wealthtmp1 = []; Sigtmp = []; PortfolioReturn = ones(NoOfTradingDays,1); %Optimzation w.r.t Omega for getting the best set of boundary values for the given stock Wealth = 1e6; StockPortfolio = 0; ETFReturn = 1; PortfolioReturn = ones(NoOfTradingDays,1); for i = 61:NoOfTradingDays IndexReturn(i) = 0; %Calculate the ETF Return for the current position for k=1:NoOfETF IndexReturn(i) = IndexReturn(i)+ ETFData(k).Return(i)*ETFBetas(k); end stockReturn = 1; IndexRet = 1; stockReturn = stockReturn * (1+StockData(StockInd).Return(i)); IndexRet = IndexRet*(IndexReturn(i)+1); %Mark to market if a there is an exposure if(StockPortfolio == 1) Wealth = Wealth*(1-IndexRet+stockReturn); elseif(StockPortfolio == -1) Wealth = Wealth*(1+IndexRet-stockReturn); end %This function call need to be MODIFIED according to the interface [Signal, Betas,ssssssss] = ETFregression(ETFData, StockData(StockInd).Return, i, Sbo, Sso, Sbc, Ssc, StockPortfolio); if(Signal == 1) if (StockPortfolio == -1) StockPortfolio = 0; %Update PandL for transaction cost Wealth = Wealth*(1-.0005); elseif(StockPortfolio == 0) % Go Long StockPortfolio = 1; ETFBetas = Betas; %Update PandL for transaction cost Wealth = Wealth*(1-.0005); end elseif(Signal == -1) if(StockPortfolio == 0) % Steps for Going Short StockPortfolio = -1; ETFBetas = Betas; %Update PandL for transaction cost Wealth = Wealth*(1-.0005); elseif(StockPortfolio == 1) StockPortfolio = 0; %Update PandL for transaction cost Wealth = Wealth*(1-.0005); end end wealthtmp1 = [wealthtmp1,Wealth]; Sigtmp = [Sigtmp,Signal]; end %Portfolio return on each day PortfolioReturn = wealthtmp1(2:end)./wealthtmp1(1:end-1)-1; %Get the PandL and Omega for the corresponding strategy %Omega calculation iAbove = 0; iBelow = 0; iAboveMeanCount = 0; iBelowMeanCount = 0; for i=1:size(wealthtmp1,2)-1 if(PortfolioReturn(i) > 0) iAbove = iAbove + PortfolioReturn(i); iAboveMeanCount = iAboveMeanCount + 1; elseif(PortfolioReturn(i) < 0) iBelow = iBelow - PortfolioReturn(i); iBelowMeanCount = iBelowMeanCount + 1; end end OmegaRatios = ((iAbove/iAboveMeanCount)*(iAboveMeanCount/(iAboveMeanCount+iBelowMeanCount)))/((iBelow/iBelowMeanCount)*(iBelowMeanCount/(iAboveMeanCount+iBelowMeanCount))); %Profit and Loss update PandL = Wealth - 1e6; function [ETFused,Stocksused] = SampleBootstrap(ETF,Stocks,SampleNo,NoOfStock,NoOfETF) a = 1; b = length(Stocks(1).Return); sampleInd = round(a + (b-a).*rand(SampleNo,1)); for ii = 1:NoOfETF ETFused(ii).name = ETF(ii).name; ETFused(ii).Return = ETF(ii).Return(sampleInd); ETFused(ii).Date = ETF(ii).Date(sampleInd); end for ii = 1:NoOfStock Stocksused(ii).name = Stocks(ii).name; Stocksused(ii).Return = Stocks(ii).Return(sampleInd); Stocksused(ii).Date = Stocks(ii).Date(sampleInd); end |
