Does trend following work on stocks? Part II

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1 Does trend following work on stocks? Part II Trend following involves selling or avoiding assets that are declining in value, buying or holding assets that are rising in value, and actively managing the amount of risk taken. It is commonly associated with the managed futures industry and is the core strategy of many commodity trading advisors. However, it is rarely considered as an approach to stock market investing. Does this mean trend following doesn t work on stocks? We attempt to answer this question by applying several basic trend following systems to a broad universe of U.S. stocks using 20 years of historical data ( ). By our definition, a complete trend following system is a rules-based process that determines what to buy and when to buy, what to sell and when to sell, as well as how much to buy or sell. The process must be clear, executable, and repeatable. What to buy/sell Our trend following systems will consider approximately the 3,000 most liquid stocks during each year of the simulation period. This universe of stocks is estimated to represent 95% to 98% of the investable U.S. equity market in any given year. When to buy/sell A simple channel entry/exit method is perhaps the easiest trend following approach to understand. For example, using an 18 month setting, a stock is purchased after it appreciates to an 18 month high (channel top). Likewise, a stock is sold after falling below an 18 month low (channel bottom). $100 $10 Trend follwing isn't just concerned with up-trends. Avoiding down-trends is just as important. $1 Ambac Financial 18 month low 18 month high How much to buy/sell For this project we use a simplified version of the same management framework used to manage our clients assets. Starting with a portfolio risk target 1 of 25% we attempt to spread no more than this amount of risk across all portfolio holdings on an equal risk basis. An individual position s actual risk is estimated to be the (current stock price) minus the (channel bottom price), multiplied by the (number of shares owned). If any position s actual risk exceeds equal risk by a factor of two, the position is rebalanced the following day. This process works to keep portfolio risk under control and individual stocks approximately equal risk weighted. During periods of high volatility, restricting portfolio risk to approximately 25% will often force the portfolio to hold a cash balance. Likewise, during periods of low volatility the portfolio will often use a variable amount of leverage (appendix B). Unlike most traditional investments the goal here is to take a prudent amount of risk rather than to stay at all times. Results are also shown without this management framework. In this scenario no attempt is made to limit future worst case portfolio declines. In other words, the portfolio is forced to remain at all times, like a typical or mutual fund. 1. Portfolio risk target represents the desired limit with respect to the future worst-case decline in portfolio value

2 HYPOTHETICAL PERFORMANCE DISCLAIMER: HYPOTHETICAL PERFORMANCE RESULTS HAVE MANY INHERENT LIMITATIONS, SOME OF WHICH ARE DESCRIBED BELOW. NO REPRESENTATION IS BEING MADE THAT ANY ACCOUNT WILL OR IS LIKELY TO ACHIEVE PROFITS OR LOSSES SIMILAR TO THOSE SHOWN. IN FACT, THERE ARE FREQUENTLY SHARP DIFFERENCES BETWEEN HYPOTHETICAL PERFORMANCE RESULTS AND THE ACTUAL RESULTS SUBSEQUENTLY ACHIEVED BY ANY PARTICULAR TRADING PROGRAM. ONE OF THE LIMITATIONS OF HYPOTHETICAL PERFORMANCE RESULTS IS THAT THEY ARE GENERALLY PREPARED WITH THE BENEFIT OF HINDSIGHT. IN ADDITION, HYPOTHETICAL TRADING DOES NOT INVOLVE FINANCIAL RISK, AND NO HYPOTHETICAL TRADING RECORD CAN COMPLETELY ACCOUNT FOR THE IMPACT OF FINANCIAL RISK IN ACTUAL TRADING. FOR EXAMPLE, THE ABILITY TO WITHSTAND LOSSES OR TO ADHERE TO A PARTICULAR TRADING PROGRAM IN SPITE OF TRADING LOSSES ARE MATERIAL POINTS WHICH CAN ALSO ADVERSELY AFFECT ACTUAL TRADING RESULTS. THERE ARE NUMEROUS OTHER FACTORS RELATED TO THE MARKETS IN GENERAL OR TO THE IMPLEMENTATION OF ANY SPECIFIC TRADING PROGRAM WHICH CANNOT BE FULLY ACCOUNTED FOR IN THE PREPARATION OF HYPOTHETICAL PERFORMANCE RESULTS AND ALL OF WHICH CAN ADVERSELY AFFECT ACTUAL TRADING RESULTS. Please see appendix A of this document for disclosure of assumptions used in calculating hypothetical performance. These include transaction costs (slippage and commissions), delisted stocks, corporate actions (mergers, spin-offs, distributions, dividends, etc.), liquidity filters, and interest rates applied to cash and/or margin balances. Portfolio results were generated using The Power System Tester from RDB Computing, Inc. Simulated performance with management 18 month 12 month 9 month 6 month 3 month 2 month 1 month S&P 500 Russell % 31.9% 31.9% 30.8% 28.6% 27.8% 24.0% 32.0% 16.3% % -6.1% -5.8% -7.6% -3.1% -2.0% -4.0% -3.4% -19.5% % 33.4% 30.9% 30.4% 29.9% 26.9% 24.7% 31.0% 46.0% % 12.7% 12.7% 12.2% 13.1% 11.6% 7.9% 7.6% 18.4% % 17.2% 15.3% 13.9% 12.2% 12.0% 12.2% 10.2% 18.9% % -2.2% -2.4% -3.9% -3.1% -3.4% -5.5% 1.2% -1.8% % 33.1% 30.6% 28.9% 27.5% 26.3% 25.8% 38.0% 28.5% % 20.0% 19.1% 17.9% 16.2% 15.9% 14.1% 23.1% 16.5% % 25.8% 25.0% 23.5% 20.1% 20.4% 20.0% 33.7% 22.4% % 3.1% 3.8% 5.5% 2.6% 1.7% -1.0% 28.7% -2.5% % 15.8% 14.3% 14.1% 14.7% 13.7% 13.8% 21.1% 21.3% % 9.4% 9.6% 10.7% 9.1% 9.5% 9.5% -9.1% -3.0% % 5.3% 4.1% 2.2% 0.2% -1.2% 0.3% -12.0% 2.5% % -5.4% -7.9% -8.8% -8.5% -10.7% -11.7% -22.3% -20.5% % 34.3% 35.2% 35.1% 29.7% 28.7% 28.1% 28.7% 47.3% % 16.0% 16.2% 17.5% 15.3% 12.8% 13.1% 10.8% 18.3% % 9.5% 9.0% 7.6% 6.3% 5.6% 3.0% 4.8% 4.6% % 18.8% 18.0% 17.8% 17.0% 15.9% 13.4% 15.7% 18.4% % 6.5% 6.3% 6.5% 3.4% 0.6% -2.1% 5.5% -1.6% % -25.0% -26.4% -24.1% -20.6% -16.3% -20.4% -37.2% -33.8% Annualized Return 11.9% 11.6% 10.9% 10.5% 9.7% 9.0% 7.5% 8.4% 7.9% Annualized Volatility 12.4% 11.1% 10.8% 10.6% 9.7% 9.5% 10.0% 14.4% 18.6% Sharpe Ratio (rf=4.6%) Beta (S&P 500) Maximum Drawdown -30.8% -28.7% -29.5% -27.7% -24.5% -22.4% -27.9% -44.9% -43.0% Total Return 853% 803% 690% 634% 537% 465% 321% 405% 354% Please see appendix B for leverage/cash balances resulting from management.

3 Simulated performance without management 18 month 12 month 9 month 6 month 3 month 2 month 1 month S&P 500 Russell % 28.7% 29.3% 29.5% 29.4% 29.0% 24.1% 32.0% 16.3% % -7.3% -7.8% -9.3% -9.6% -9.9% -13.6% -3.4% -19.5% % 37.2% 37.4% 40.3% 44.5% 43.2% 35.4% 31.0% 46.0% % 15.4% 15.2% 13.2% 15.1% 13.9% 10.9% 7.6% 18.4% % 19.7% 18.4% 17.8% 16.8% 16.7% 15.3% 10.2% 18.9% % -2.9% -3.4% -5.8% -6.5% -7.0% -9.7% 1.2% -1.8% % 35.8% 34.5% 34.2% 35.2% 34.4% 33.0% 38.0% 28.5% % 24.4% 24.4% 22.6% 20.1% 19.9% 17.4% 23.1% 16.5% % 31.6% 31.6% 29.3% 28.5% 27.3% 21.7% 33.7% 22.4% % 1.7% 0.8% -0.1% -2.0% -2.2% -4.4% 28.7% -2.5% % 25.6% 25.6% 26.7% 25.1% 24.6% 22.5% 21.1% 21.3% % 10.5% 11.4% 12.9% 12.1% 14.3% 17.1% -9.1% -3.0% % 7.5% 6.0% 3.4% -3.2% -7.2% -1.9% -12.0% 2.5% % -7.6% -13.0% -16.5% -18.7% -21.6% -20.0% -22.3% -20.5% % 45.0% 46.5% 45.6% 43.3% 41.3% 37.9% 28.7% 47.3% % 21.4% 21.5% 20.4% 17.7% 16.1% 14.4% 10.8% 18.3% % 11.4% 11.0% 10.1% 7.3% 6.5% 3.2% 4.8% 4.6% % 21.1% 20.9% 19.4% 18.6% 17.5% 15.5% 15.7% 18.4% % 6.7% 7.0% 7.6% 3.7% -0.8% -4.8% 5.5% -1.6% % -41.9% -42.5% -39.7% -42.8% -40.8% -46.1% -37.2% -33.8% Annualized Return 12.1% 12.2% 11.7% 11.0% 9.5% 8.5% 6.2% 8.4% 7.9% Annualized Volatility 15.9% 15.7% 15.9% 15.7% 15.8% 15.6% 15.8% 14.4% 18.6% Sharpe Ratio (rf=4.6%) Beta (S&P 500) Maximum Drawdown -47.0% -45.6% -45.9% -43.6% -47.3% -47.5% -53.3% -44.9% -43.0% Total Return 876% 907% 808% 712% 510% 416% 231% 405% 354% Money management versus at all times Entry/Exit Annualized Return Annualized Volatility Sharpe Ratio (rf=4.6%) Beta (S&P 500) Maximum Drawdown Total Return 18 months 11.9% 12.1% 12.4% 15.9% % -47.0% 853% 876% 12 months 11.6% 12.2% 11.1% 15.7% % -45.6% 803% 907% 9 months 10.9% 11.7% 10.8% 15.9% % -45.9% 690% 808% 6 months 10.5% 11.0% 10.6% 15.7% % -43.6% 634% 712% 3 months 9.7% 9.5% 9.7% 15.8% % -47.3% 537% 510% 2 months 9.0% 8.5% 9.5% 15.6% % -47.5% 465% 416% 1 month 7.5% 6.2% 10.0% 15.8% % -53.3% 321% 231% Average 10.2% 10.2% 10.6% 15.8% % -47.2% 615% 637%

4 Summary Our goal was to illustrate the potential of trend following as a general approach to stock market investing. A simple trend following system with very few moving parts was purposely chosen, to avoid curve-fitting. This system was applied to all reasonably liquid U.S. stocks that traded from 1989 to 2008, including delisted stocks. Results are shown for a broad spectrum of practical time frames, from 1 month s to 18 month s. Simulated performance results with management suggest that even a very simple approach to trend following over the last 20 years would have yielded substantially higher Sharpe ratios than traditional stock market indices. Trend following would have enjoyed higher annual returns, lower volatility, and modest beta relative to the general stock market. Simulated performance results without management are less impressive, as expected. However, annual returns and Sharpe ratios are still significantly higher to those of traditional stock market indices, while drawdowns and annual volatilities are approximately the same. Eric Crittenden Cole Wilcox Blackstar Funds, LLC Research Director Managing Director 1850 North Central Ave. Ste 630 eric@blackstarfunds.com cole@blackstarfunds.com Phoenix, AZ USA Appendix A Annualized performance data Monthly data points were used for annualized volatility, beta, and maximum drawdown calculations. Sharpe ratio calculations used the time-period relevant monthly Federal Funds rate to calculate excess return. Transaction costs & trade executions Combined slippage and commissions were estimated to be 0.5% per trade, half of which was applied on the day of entry and half on the day of exit. Executions were assumed at the market open on the day following the entry or exit signal. Delisted stocks The scope of this project included over 30,000 individual securities that traded on U.S. exchanges (AMEX, NYSE & NASDAQ), including 16,218 delisted securities. Corporate actions Cash dividends were assumed re on the relevant ex-dividend date. Price data was proportionately back-adjusted for cash dividends to yield format. Stock splits, stock dividends, reverse splits, mergers, divestitures, etc. were also proportionately back adjusted for. Buy and sell signals, as well as profits and losses, were calculated from data. Liquidity filters Simulated trading was limited to stocks above $5 (actual price, not split-adjusted) and among the approximately 3,000 most liquid U.S. stocks (at the time of the trade). Liquidity estimates used only price and volume data that was available prior to trade signal (to avoid postdictive error). Interest rates Cash balances were assumed to collect (annualized Federal Funds rate at the time, less 0.25%) expressed in daily terms. Margin balances were assumed to pay (annualized Federal Funds rate at the time, plus 0.25%) expressed in daily terms.

5 Net Exposure Appendix B Average exposure for all systems was less than, indicating cash balances. Maximum exposures rarely exceeded 120%, indicating very modest use of leverage. 140% Exposure by system 120% 80% 60% Average Maximum Minimum 40% 20% 0% 18 months 12 months 9 months 6 months 3 months 2 months 1 month 18 months 12 months 9 months 6 months 3 months 2 months 1 month All Average 83% 76% 73% 72% 67% 66% 69% 72% Maximum 126% 126% 120% 120% 110% 108% 112% 117% Minimum 26% 25% 23% 21% 15% 12% 15% 20%