Rajesh Shekhar Data Mining Prof. Chris Volinsky

◦ Use Data Mining techniques to build a portfolio with superior return/risk characteristics using technical indicators  Maximize return  Minimize risk ◦ Build different momentum based strategies

◦ Risk Diversification  Select stocks across sectors for a natural diversification.  Virtual sectors created using k-means cluster algorithm ◦ Return maximization  Use momentum based indicators to predict future returns  Try different trading algorithms

 Investment Universe: Large Market Cap Stocks (Top 100/300/500)  Data collected for everyday stock prices from WRDS (CRSP database) for the entire stock universe from  Custom benchmark of top 100/300/500 stocks was created as composition of S&P 500 was not known over the period

IssueApproach Large Dataset (Entire stock universe from 1999 to 2009; more than 5 GB) Use database (SQL Server) and query to get subset of the data and create proper indexes. Ticker name change.Use permno Dividends: The price change for stocks does not give the true return as it ignores the dividend paid. Use daily adjusted return which adjusts for the dividend. Missing ReturnsUse average to fill the returns Duplicates Use ‘select distinct’ SQL query to filter the data Null Values:Use average to fill the returns

 Used k-means cluster to create virtual clusters  11 clusters for 300/500 stock universe and 10 clusters for 100 stock universe  Input: β, Market Cap (Liquidity), P/E (Price/Earning)  β stock = cov(R stock, R market )/var(R marke )  β captures long term adjusted equilibrium rate of return

◦ Different models tried for capturing momentum indicators (linear models (based on APT)  Best model to capture model momentum was:  Based on time decay of historical returns  r = k j *r j where r = predicted stock return j = time period (j=0 for the current time) k = constant achieved after calibration  More weights on recent data ◦ Two years of moving window for prediction ◦ Portfolio analysis and rebalancing every two weeks

 Long Only  Short Only  Long-Short  Sector Rotation  Sector Portfolio Optimization

 Basic Idea: Long top “n” performing stocks in each sector based on market cap  Portfolio Weights: All selected stocks are equally weighted in portfolio Basic Idea: Short bottom “n” performing stocks in each sector based on market cap Portfolio Weights: All selected stocks are equally weighted in portfolio Short Only

 Basic Idea: Combination of Long and Short  Portfolio Weights: All selected stocks are equally weighted in portfolio Basic Idea: Long top performing sectors & short on bottom performing ones Portfolio Weights: Weight in each sector is proportional to return (More weight on the more outperforming sector; shorting allowed) Sector Rotation

 Basic Idea: Select stocks using long only strategy.  Portfolio Weights: Decided by Markowitz Portfolio optimization techniques ◦ Sector Constraints : (weights vary from 1.1 to 0.9 of the target sector weights) ◦ Asset Constraints (Shorting and leverage allowed): (weights vary from -0.1 to 1.1) ◦ Allocation on the efficient frontier

(SQL Server) Database Portfolio Engine (MATLAB Code) Portfolio Reports &Graphs Risk Analysis (MATLAB Code) Performance & Risk Report MATLAB (Object Oriented) SQL Server database (> 5 GB of raw data and with indexes 12GB)

 Vary Input parameters ◦ Stock universe (100/300/500) ◦ Stock selected (10/20/40) ◦ Running time window ( , ) ◦ Rebalancing period (15/21/30/45 days)

Results: 300 stocks universe

Performance Measurement : Risk Metrics (100 stocks) Long Only Short Only Long Short Sector Rotation Sector PortOpt Return (annual) 20.16%37.10%16.18%52.15%14.49% Sigma (annual) 32.93%55.44%36.73%47.04%30.01% Alpha (annual) 37.35%54.29%33.36%69.34%31.68% SharpeRatio (annual) InfoRatio (annual) Var (95% Daily) -2.91%-3.93%-3.28%-3.96%-2.81% CVAR (95% Daily) -3.72%-7.23%-5.56%-5.97%-3.69% MaxDD (Daily) 15.39%43.56%27.95%30.36%13.40% (100 stocks) Long Only Short Only Long Short Sector Rotation Sector PortOpt Return (annual) 25.55%0.53%6.00%22.43%33.30% Sigma (annual) 15.29%15.71%12.49%16.77%16.23% Alpha (annual) 15.43%-9.59%-4.12%12.30%23.18% SharpeRatio (annual) InfoRatio (annual) Var (95% Daily) -1.31%-1.51%-1.22%-1.52%-1.37% CVAR (95% Daily) -1.71%-2.15%-1.52%-1.91%-1.79% MaxDD (Daily) 8.64%8.04%5.90%8.59%7.78% (300 stocks) Long Only Short Only Long Short Sector Rotation Sector PortOpt Return (annual) 37.91%90.17%57.09%105.86%61.34% Sigma (annual) 42.74%66.97%48.95%54.23%42.79% Alpha (annual) 54.26%106.53%73.44%122.21%77.69% SharpeRatio (annual) InfoRatio (annual) Var (95% Daily) -3.58%-4.69%-4.40%-4.17%-3.52% CVAR (95% Daily) -4.53%-8.36%-6.78%-6.33%-4.48% MaxDD (Daily) 17.55%45.84%27.92%33.22%24.54% (300 stocks) Long Only Short Only Long Short Sector Rotation Sector Port Opt Return (annual) 70.02%25.05%45.07%51.91%69.17% Sigma (annual) 21.68%19.03%17.62%22.98%23.96% Alpha (annual) 58.18%13.22%33.24%40.08%57.33% Sharpe Ratio (annual) Info Ratio (annual) VaR (95% Daily) -1.44%-1.54%-1.29%-1.72%-1.61% CVAR (95% Daily) -1.89%-2.24%-1.83%-2.43%-2.34% Max DD (Daily) 10.99%10.09%8.27%13.61%15.98%

 Benchmark : Custom Benchmark  Value-added Return = Pure sector allocation + Allocation/Selection interaction + Within-sector selection R V = + + Rv = the value-added return w P,j = portfolio weight of sector j w B,j = benchmark weight of sector j R P,j = portfolio return of sector j R B,j = benchmark return of sector j R B = return in the portfolio’s benchmark S = number of sectors

 Transaction Costs: ◦ Slippage cost and explicit costs are taken into account ◦ Market impact and other implicit costs are ignored  Leverage costs are not taken into account  Portfolio Turnover not taken into account

 Virtual sectors works reasonably well.  Time decay returns is a decent predictor of future returns in stable market for short time periods.  Statistically relevant for large market caps.