strategy: 2 day high with 9 day low results results yoy...

Page | 1 | PHILLIP SECURITIES RESEARCH (SINGAPORE) MCI (P) 020/11/2014 Ref. No.: US2015_0011

QUANT ideas: Trend-following series

Optimizing an N-day breakout on the GLD GLOBAL | EQUITIES| QUANTITATIVE ANALYSIS

23 March 2015

We revise last week’s report to incorporate CFD’s present promotional transaction rate of 0.1% annually and finance costs.

We backtested and optimized an n-day breakout strategy on GLD.

At transaction costs at 0.2%, the optimized results without finance costs yielded an annual gain of 9.9% without leverage, and an annual gain of 20% with 2x leverage based on data from 1 Dec 2004 to 28 Feb 2015.

At transaction costs at 0.1%, the optimized results without finance costs yielded an annual gain of 13.1% without leverage, and an annual gain of 31% with 2x leverage.

The strategy is applied to both up and down markets.

Main Observations: Just because the GLD may be grinding lower doesn’t mean we can’t profit from it. We backtest the GLD with 10 years of data to formulate a matrix of results of various permutations of n-day high and m-day low breakout signals (Donchian Channels – a trend following strategy) for going long and short. Our observations are:

At transaction costs per trade at 0.2% and less, this strategy is viable. At a 0.2% transaction cost level, a 2-day high and 9-day low buy and sell signal would have resulted in a respectable 9.9% geometric annual gain since 2005, or 7.7% when factoring in annual finance costs if using CFDs. The suggested optimum leverage of 1x returned an average of 11.5%, including finance costs.

At transaction costs per trade at 0.1%, the strategy is attractive. The said parameters would have resulted in an attractive 13.1% gain (or 10.4% factoring finance costs) without leverage. With suggested optimum leverage of 2x, the strategy resulted in a 30.9% geometric annual gain, or a 23% annual gain factoring financial costs.

This strategy’s is not viable at any of the parameters when trade transaction costs are at 0.3% per trade or higher which is what some retail investors pay.

We caution clients on blindly using “popular” parameters like a 3-day high and 2-day low on every asset. For the GLD, this was unfruitful at all commission levels.

Strategy: 2 Day High with 9 Day LowTrading

Results

(Arith)

Long Gold

Results yoy

(Arith)

Number of

Trades Average ATR

SD of Daily

Returns No.of Gaps

No.of Traded

Gaps

2005 + 7.80% + 17.15% 31 0.475 0.008 133 23

2006 + 31.30% + 23.22% 24 1.197 0.015 122 16

2007 + 14.76% + 28.15% 24 1.090 0.011 86 13

2008 + 8.51% + 10.14% 32 2.325 0.021 122 21

2009 + 9.02% + 23.69% 32 1.809 0.013 119 22

2010 + 20.84% + 27.07% 22 1.725 0.010 116 16

2011 + 7.60% + 11.23% 27 2.633 0.013 124 21

2012 - 12.73% + 7.53% 33 2.159 0.010 119 27

2013 + 17.92% - 30.95% 33 2.049 0.014 123 27

2014 + 11.37% - 1.10% 27 1.362 0.009 129 20

2015 + 1.97% + 2.47% 6 1.515 0.011 20 5

Total + 160.38% + 156.92% Geometric gain

Annual + 9.90% + 9.75% Geometric gain

Commissions: 0.20%, Slippage: 0.05 Source: PSR

Kenneth Koh (+65 6531 1791) [email protected]

Page | 2 | PHILLIP SECURITIES RESEARCH (SINGAPORE)

Gold’s like a rollercoaster… What a rollercoaster gold price has been on. Since our 1st report on 12th Jan 2015 titled “Technical Analysis: Gold, Has Gold reached an intermediate bottom? Soon, if not now”, we stuck out our necks to alert investors to an intermediate bottom when gold price was under $1200 and when most media narratives on gold was bearish. Since topping out at $1300 on 22th Jan, gold price has grinded lower, closing at $1166 on 18th Mar. We had warned investors to have “a slight bearish bias” and look to price ranges “between $1000-$1200” for accumulation in our report titled Technical Analysis: Gold, For uptrend to resume, price needs to recover back above 1250 soon dated 9th Feb 2015. At present, gold has indeed reached our target zone, having hit $1141 on 17th Mar 2015.

… our recent technical report summarizes the motivations for introducing this model backtest According to our most recent report, “Technical Analysis: Gold, Downside bias with long tailed upside risk” dated 23rd March 2015 we conclude that going forward:

Macroeconomic drivers are net bearish – strengthening US dollar, rising US interest rates, and slowly improving global economy

Meaningful retracements and bottoming behavior will likely increase – Grexit deadline in June, gold price closer to break-even production costs, US dollar starting to be overstretched, and commercial gold hedging getting closer to bullish contrarian upper limit. In fact, a short term upcycle may have started, though it’s hard to predict how long it will be.

Under these conditions, our best recommendation is to adopt the right trading system instead of a plain vanilla long term buy or sell call

Hence, we introduce this trend following strategy because traders can be reactive to both up and down cycles without having to know for certain how long each cycle will last. The table below shows a summary of geometric annual gains for parameters n and m. The backtested from data range is from 1 Dec 2004 to 28 Feb 2015. This assumes a 0.20% transaction fee and 0.05USD slippage per trade. The results range from 2-3 Days High and 4-10 Days Low already looks interesting for further study. The next section starts our technical and quantitative discussion. For brevity, all results do not include finance (borrowing) costs unless specifically stated. N-day breakout strategy results Results Table with gaps (0.20% commissions, 0.05USD slippage per trade)

1 2 3 4 5 6 7 8 9 10 15 20 55 Days High

1 -24.8% -14.6% -10.9% -11.7% -9.7% -9.1% -9.1% -10.0% -9.8% -8.4% -9.3% -6.5% -7.3%

2 -13.4% -4.4% -3.8% -3.7% -3.6% -3.9% -4.9% -6.3% -6.1% -4.7% -5.6% -3.2% -5.6%

3 -7.3% -0.3% 2.5% 3.6% 1.5% 1.6% 0.7% -0.5% 0.3% 2.1% -1.5% 1.5% -1.1%

4 -0.1% 7.5% 8.3% 7.4% 5.9% 6.4% 5.7% 5.4% 6.1% 8.5% 4.5% 7.7% 3.1%

5 0.0% 8.5% 7.9% 5.9% 5.0% 5.0% 4.8% 4.0% 5.2% 7.5% 3.7% 6.2% 1.6%

6 -0.2% 6.3% 6.0% 3.3% 3.1% 4.0% 3.6% 2.4% 3.8% 6.2% 2.6% 6.0% 0.7%

7 1.2% 7.4% 7.6% 4.3% 3.8% 4.8% 4.2% 3.3% 4.2% 5.7% 2.5% 5.9% -0.5%

8 4.3% 9.9% 9.6% 5.8% 5.0% 5.6% 5.1% 4.4% 5.4% 6.4% 2.2% 5.5% -0.1%

9 4.8% 9.9% 9.1% 5.7% 4.8% 5.6% 5.3% 4.9% 5.1% 5.4% 2.2% 5.7% 0.9%

10 6.3% 8.7% 8.3% 4.9% 4.3% 5.4% 5.1% 5.3% 5.8% 6.1% 3.3% 7.0% 0.7%

15 9.0% 6.2% 3.7% 1.8% 2.3% 4.6% 1.7% 1.9% 1.9% 2.8% 1.6% 5.4% 0.4%

20 11.9% 7.4% 5.2% 2.5% 2.4% 4.0% 1.2% 1.9% 1.4% 2.5% 0.1% 3.3% 0.3%

55 13.9% 10.9% 8.5% 5.8% 5.1% 6.8% 5.9% 5.5% 6.0% 5.7% 4.0% 3.1% -2.0%

Days low Source: PSR

http://internetfileserver.phillip.com.sg/POEMS/Stocks/Research/SectorStrategy/SG/TechnicalGold20150112.pdf






Quant section Technical Analysis: It helps, if used correctly. There is a growing body of evidence that technical analysis, when used appropriately, and not in isolation, can increase profit performance. For instance, during high-sentiment periods, hedge funds using technical analysis exhibit higher returns, lower risk, and superior market-timing ability than those non users [Smith, Wang, Wang and Zychowicz (2014)]. Additionally, Han, Yang and Zhou (2011), show that an application of an appropriate trend following strategy of technical analysis to certain high volatility portfolios often outperform buy-and-hold strategies substantially. Unfortunately, there is much subjectivity in the world of technical analysis. What can seem like a reversal pattern could turn into a continuation pattern, a posteriori. Subjective TA, at first blush, seem to convey knowledge. However, when examined critically, lacks in knowledge precision. The purpose for this backtesting series is to help clients to bridge the subjectivity gap of technical analysis to get closer to justified true belief rooted in objectivity, which is a useful definition of “knowledge”.

Methodology: N-day breakout – a trend following strategy At every daily price, let Days High be the maximum of n-days of prior high and Days

Low be the minimum of m-days of prior lows. Define n and m.

When today’s price moves higher than Days High within the day, buy/long the asset immediately. If price gaps above Days High at the start of the day, buy/long the asset immediate at opening.

When today’s price moves lower than Days Low within the day, sell/short the asset immediately. If price gaps below Days Low at the start of the day, sell/short the asset immediately at opening.

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GLD Price with Trading Channel Signals

Previous 2 Days High Previous 9 Days LowBuy signal Sell signal

2 Day High with 9 Day Low

For example, using the above GLD price chart with channel signals from 01 Dec 2014 to 27 Feb 2015, you can see there were 4 buy signals and 3 sell signals. The table on the right shows the summarized results of each trade pair.

Pair Date Range Result

Buy-

Sell

7 Nov 2015 –

16 Dec 2015

+2.8%

Sell-

Buy

16 Dec 2015 –

26 Jan 2015

-0.8

Buy-

Sell

26 Jan 2015 –

1 Jan 2015

-2.3%

Sell-

Buy

2 Jan 2015 – 5

Jan 2015

-2.5%

Buy-

Sell

5 Jan 2015 –

29 Jan 2015

+5.8%

Sell-

Buy

29 Jan 2015 –

13 Feb 2015

+3.1%

Buy-

Sell

13 Feb 2015 –

17 Feb 2015

-1.7%

Sell-

Buy

17 Feb 2015 –

26 Feb 2015

-0.4%

TOTAL 7 Nov 2015 –

26 Feb 2015

+4.0%


Our specific backtest specifications: 1) We went long on the buy signal. However, on the sell signal, we not only sold off our

entire position but went further to a net short position. 2) We will only have 1 active trade at the time. A long position will stay long until a

short signal is generated and vice versa. 3) Every trading position size was all of our trading capital at the time 4) We are always in the market, either long or short. 5) We started in Dec 2004 with a buy.

What parameters of n and m did we use? As a value service to our clients, we did a whole range of them so that we can observe the various patterns of performance and outperformance! In addition, after choosing one of them, we optimized it to give you the Kelly ratio (the leverage ratio that gives the optimal long term profit) as well. Data Range (Dec 2004 – Feb 2015)

Data for the GLD ETF started only at end 2004.

Within this range, there a moderate mix of market conditions - approximately 2 years of a choppy sideways market action, about 5 years of bullish action, and about 3 years of bearish action.

The Results 1st Screen Observations (refer to Appendix 1) Our first matrix of results are data tables tabulating the theoretical gains by backtesting actual GLD price data from 1 Dec 2004 to 28 Feb 2015. We vary n (days high) and m (days low) and calculate the returns for multiple permutations from commission rates 0.1% to 0.3% with a fixed slippage amount (the actual traded buy price is higher than the buy signal price and vice versa for selling) of 0.05USD per trade. Observation 1: If you applied the “popular” parameters of 3-day high and 2-day low, or 4-day high and 3 day low, the strategy is either loss making, or significantly underperforms other parameters at any of the commission levels. This emphasizes the need for analysis and backtesting on specific strategies on specific instruments, and not to simply take “all-in-one” parameter strategies by other practitioners on blind faith. Observation 2: At transaction commissions 0.3% or larger, the backtested results were not attractive at all, yielding an average of low single digit gain. Observation 3: As long as transaction and finance costs are manageable, we conclude that the using the GLD for trend trading is conducive, because they are profitable with a wide range of parameters, over long periods of time. This is corroborated by our belief that gold price is majorly serially correlated to longer term economic cycles, but with some shorter correlations to crisis sentiment. Observation 4: We showcase the parameters 2 day high and 9 day low (2, 9) as the optimal candidate for further study. This returned a geometric annual return of 9.9%.


2nd Screen Observations (refer to Appendix 2) This second matrix consists of the same parameters, but we changed the backtesting data range from 1 Dec 2004 to 31 Dec 2012 in order to determine whether the results change significantly. Observation 1: The main profitable regions stayed profitable. Even relative performances to other parameters stayed within an acceptable small variance. This increases the “robustness” of the strategy. Observation 2: The 2 day high, 9 day low’s relative performance still remained good at 8.8% annually. We conclude that the GLD is viable for an n-day breakout trading strategy and we shall use the 2 day high, 9 day low parameters for further study.

2 day high, 9 day low trading results analysis The anatomy of trading results with market movements

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GLD Price with Strategy Returns


Annual strategy returns:

+ 7.80% + 31.30% + 14.76% + 8.51% + 9.02% + 20.84% + 7.60% - 12.73% + 17.92% + 11.37%

Total strategy returns:

+ 160.38%

GLD Total Returns:

+ 156.9%

Source: PSR

Note: Annual returns are based on realized gains, not marked–to-market.

The above chart shows the actual GLD price chart from Dec 2004 to Feb 2015. The bottom numbers are the yearly returns for the 2,9 strategy. We think these parameters are worth considering due to its robustness:

This strategy was unprofitable only one year out of ten.

The years that have been profitable were of different behavior. Some were bullish, some were bearish, and some were moderately range bound. There were also differences in cycle magnitudes and time length.

The strategy was profitable in the two most recent years.

The biggest single drawdown was only -6%. If the strategy is profitable under various bull, bear and sideways markets, which factors determine reduces the profitability of the strategy?

Results Summary Table

Buy Breakout Period 2

Sell Breakout Period 9

Arithmatic Returns + 114.83%

Geometric Returns + 160.38%

Buy Signals 147

Sell Signals 147

+ve Trade 111

-ve Trade 183

Total Trades 294

Average Days per trade 8.8

Annual Gain Arth + 11.33%

Annual Gain Geo + 9.90%

Trades Data

% Profitable trade 38%

Stdev 3.7%

Average 0.39%

Biggest Profit + 20.35%

Biggest Drawdown - 6.28%


Performance Analysis


Results

(Arith)

Long Gold

Results yoy

(Arith)

Number of

Trades Average ATR

SD of Daily

Returns No.of Gaps

No.of Traded

Gaps

2005 + 7.80% + 17.15% 31 0.475 0.008 133 23

2006 + 31.30% + 23.22% 24 1.197 0.015 122 16

2007 + 14.76% + 28.15% 24 1.090 0.011 86 13

2008 + 8.51% + 10.14% 32 2.325 0.021 122 21

2009 + 9.02% + 23.69% 32 1.809 0.013 119 22

2010 + 20.84% + 27.07% 22 1.725 0.010 116 16

2011 + 7.60% + 11.23% 27 2.633 0.013 124 21

2012 - 12.73% + 7.53% 33 2.159 0.010 119 27

2013 + 17.92% - 30.95% 33 2.049 0.014 123 27

2014 + 11.37% - 1.10% 27 1.362 0.009 129 20

2015 + 1.97% + 2.47% 6 1.515 0.011 20 5



Commissions: 0.20%, Slippage: 0.05 Source: PSR

From the above table, we observe that performance tends to suffer when the number of gaps traded is large, and to lesser extents, higher number of trades and the daily volatility of price movements.

Factors affecting performance Number of gaps traded. Gaps can occur in the GLD when there is excessive movement in the futures market during the non-trading hours. The COMEX gold market operates from Sunday to Friday, 6pm – 5:15pm. The typical NYSE trading hours are from 9:30pm – 4:00pm. If the gap occurs that triggers a trading signal in our strategy, our traded price will not be as favorable if it were triggered without a gap. Hence, the more gaps that are traded, the less likely we will be profitable. Number of trades. Higher number of trades in a year imply that traded trends tended to be shorter, decreasing profitability. In addition, there were also more transaction costs. Volatility with no prevailing trend. High intraday volatility as measured by average true range (ATR) combined with smaller long term trend tend to reduce performance. These help to explain the following observations:

The loss-making year in 2012 was characterized by the largest number of traded gaps (27) and number of trades (32), in a range bound market.

In trending markets, lower volatility tended to yield better results.

Although the number of traded gaps in 2012 and 2013 are the same, 2013 the year of a big downtrend that offset the effect of number of gaps traded.


Optimization of the (2,9) parameters

Backtest range: 1 Dec 2004 to 28 Feb 2015

Results Table with gaps (2 days high, 9 days)

0% 50% 100% 150% 200% 250% 300% 350% 400% Leverage

0.00% 16.4% 24.0% 30.9% 37.2% 42.8% 47.5% 51.3% 54.3% 56.2%

0.05% 14.8% 21.3% 27.2% 32.4% 36.7% 40.2% 42.8% 44.5% 45.3%

0.10% 13.1% 18.7% 23.6% 27.7% 30.9% 33.3% 34.8% 35.4% 35.2%

0.15% 11.5% 16.2% 20.1% 23.2% 25.4% 26.7% 27.2% 26.9% 25.7%

0.20% 9.9% 13.7% 16.7% 18.8% 20.1% 20.5% 20.1% 18.8% 16.9%

0.25% 8.3% 11.3% 13.3% 14.6% 14.9% 14.5% 13.3% 11.3% 8.6%

0.30% 6.8% 8.9% 10.1% 10.5% 10.1% 8.8% 6.9% 4.2% 0.9%

0.35% 5.2% 6.5% 7.0% 6.6% 5.4% 3.4% 0.8% -2.4% -6.2%

0.40% 3.7% 4.2% 3.9% 2.8% 0.9% -1.7% -4.9% -8.7% -12.9%

Transaction Cost In the above table, we optimized the 2,9 N-day breakout model with leverage versus transaction costs.

Factoring in Financial Costs Phillip CFD offers transaction costs of 1.8%, and an average finance cost of 2.75% annually, if trading the GLD. At present, there is a promotional effective rate at 0.1%. Hence, we evaluate both the 0.2% and 0.1% transaction cost basis. Assuming the usage of such CFDs inclusive of the 2.75% finance cost: At 0.2% transaction costs: No leverage: annual gain is 7.2% (9.9% - 2.75% x 1) Suggested leverage of 1x: annual gain is 11.2% (16.7% - 2.75% x 2) At 0.1% transaction costs: No leverage: annual gain is 10.4% (13.1% - 2.75% x 1) Suggested leverage of 2x: annual gain is 22.7% (30.9%% - 2.75% x 3) In summary, the above results factor in the transaction costs, slippage of 0.05USD, and finance costs. Even at rates of 0.2%, we think even the unleveraged case of 7.2% is worth pursuing considering this strategy is meant to work even if we do not know which direction gold prices will be taking in the intermediate term. In addition, by design, the strategy rides longer trends and takes small drawdowns. Result parameter summaries for the 2,9 parameters with 0.1% transaction costs are found in Appendix 3. Results summary table without finance costs

Transaction costs Without leverage Recommended leverage

0.2% 9.9% 16.7% (1x leverage)

0.1% 13.7% 30.9% (2x leverage)

Results summary table with CFD finance costs

Transaction costs Without leverage Recommended leverage

0.2% 7.2% 11.2% (1x leverage)

0.1% 10.4% 22.7% (2x leverage)

Note: both tables are based on 0.05 USD slippage per trade.

http://www.phillipcfd.com/markets-products/commissions-and-finance-charges/


Final Thoughts How well the strategy will work in the future is a matter of probabilities, but we have made these probabilities a little clearer. In the world of the blind, the one-eyed man is king, this is our attempt to give you “an eye”, or at least some hindsight quantitative perspectives. It is key to note that market conditions can change going forward, and that the best parameters of last year may not yield the best results this year. However, there are a few key observations we can broadly agree with:

1. GLD tends to trend more than it doesn’t. Based on the permutations of n-day high/low parameters, the results were profitable over majority of the parameters at all transaction cost levels (0.1% - 0.3%). These were profitable over the whole data range (till Feb 2015), as well as a shortened data range (till Dec 2012). In other words, using a trend trading strategy this year will likely be profitable, although it virtually impossible to be certain which parameters would achieve the best result, or how good the results would be.

2. If we wanted a best guess to the best parameters, we think 2,9 is as good a guess as any as a long term strategy. The merits include: i) having one of the largest annual returns in the back test period, ii) having only one losing year out of ten, and iii) having made gains in the most recent 2 years.

3. “Popular” parameters like 3,2 or 4,3 underperform on the GLD at all commission levels and should be avoided.

4. We feel that transaction costs 0.3% or higher does not make this strategy attractive. 5. At transaction costs 0.2% or lower, the strategy is worth pursuing.


References Smith, M. David, Wang, N., Wang, Y., Zychowicz, E. J., (2014). Sentiment and the Effectiveness of Technical Analysis: Evidence from the Hedge Fund Industry. Han, Y., Yang, K., Zhou, G., (2011). A New Anomaly: The Cross-Sectional Profitability of Technical Analysis.


Appendix 1: Backtested Results Varying Parameter: Days high, Days low Date Range: 1 Dec 2004 – 28 Feb 2015 1 Dec 2004 - 28 Feb 2015

Results Table with gaps (0.30% commissions, 0.05USD slippage per trade)

1 2 3 4 5 6 7 8 9 10 15 20 55

1 -33.1% -22.1% -17.6% -17.8% -15.4% -14.3% -14.1% -14.8% -14.2% -12.7% -12.9% -9.8% -9.3% Days High

2 -20.3% -10.5% -9.1% -8.5% -8.0% -7.9% -8.7% -9.9% -9.6% -8.1% -8.4% -5.7% -7.2%

3 -13.4% -5.6% -2.1% -0.5% -2.2% -1.8% -2.6% -3.5% -2.6% -0.8% -3.9% -0.6% -2.3%

4 -5.7% 2.7% 4.2% 3.7% 2.5% 3.3% 2.8% 2.6% 3.6% 6.0% 2.4% 5.9% 2.0%

5 -5.0% 4.2% 4.2% 2.6% 2.0% 2.3% 2.2% 1.5% 2.9% 5.3% 1.9% 4.6% 0.6%

6 -4.9% 2.3% 2.6% 0.3% 0.3% 1.5% 1.2% 0.1% 1.7% 4.1% 0.9% 4.5% -0.1%

7 -3.2% 3.9% 4.5% 1.6% 1.3% 2.6% 2.1% 1.2% 2.2% 3.8% 0.9% 4.6% -1.3%

8 0.1% 6.5% 6.7% 3.2% 2.6% 3.5% 3.0% 2.5% 3.6% 4.6% 0.8% 4.2% -0.9%

9 0.9% 6.8% 6.5% 3.3% 2.6% 3.7% 3.4% 3.1% 3.4% 3.8% 0.8% 4.6% 0.2%

10 2.6% 5.7% 5.7% 2.6% 2.1% 3.5% 3.2% 3.6% 4.1% 4.5% 2.0% 5.9% 0.1%

15 6.1% 3.8% 1.6% -0.1% 0.6% 3.1% 0.2% 0.5% 0.6% 1.5% 0.6% 4.5% -0.1%

20 9.5% 5.4% 3.5% 0.9% 0.9% 2.7% -0.1% 0.7% 0.2% 1.4% -0.9% 2.5% -0.2%

55 12.9% 10.0% 7.8% 5.1% 4.4% 6.2% 5.3% 4.9% 5.5% 5.1% 3.6% 2.7% -2.3%

Days low


1 2 3 4 5 6 7 8 9 10 15 20 55 Days High

1 -24.8% -14.6% -10.9% -11.7% -9.7% -9.1% -9.1% -10.0% -9.8% -8.4% -9.3% -6.5% -7.3%

2 -13.4% -4.4% -3.8% -3.7% -3.6% -3.9% -4.9% -6.3% -6.1% -4.7% -5.6% -3.2% -5.6%

3 -7.3% -0.3% 2.5% 3.6% 1.5% 1.6% 0.7% -0.5% 0.3% 2.1% -1.5% 1.5% -1.1%

4 -0.1% 7.5% 8.3% 7.4% 5.9% 6.4% 5.7% 5.4% 6.1% 8.5% 4.5% 7.7% 3.1%

5 0.0% 8.5% 7.9% 5.9% 5.0% 5.0% 4.8% 4.0% 5.2% 7.5% 3.7% 6.2% 1.6%

6 -0.2% 6.3% 6.0% 3.3% 3.1% 4.0% 3.6% 2.4% 3.8% 6.2% 2.6% 6.0% 0.7%

7 1.2% 7.4% 7.6% 4.3% 3.8% 4.8% 4.2% 3.3% 4.2% 5.7% 2.5% 5.9% -0.5%

8 4.3% 9.9% 9.6% 5.8% 5.0% 5.6% 5.1% 4.4% 5.4% 6.4% 2.2% 5.5% -0.1%

9 4.8% 9.9% 9.1% 5.7% 4.8% 5.6% 5.3% 4.9% 5.1% 5.4% 2.2% 5.7% 0.9%

10 6.3% 8.7% 8.3% 4.9% 4.3% 5.4% 5.1% 5.3% 5.8% 6.1% 3.3% 7.0% 0.7%

15 9.0% 6.2% 3.7% 1.8% 2.3% 4.6% 1.7% 1.9% 1.9% 2.8% 1.6% 5.4% 0.4%

20 11.9% 7.4% 5.2% 2.5% 2.4% 4.0% 1.2% 1.9% 1.4% 2.5% 0.1% 3.3% 0.3%

55 13.9% 10.9% 8.5% 5.8% 5.1% 6.8% 5.9% 5.5% 6.0% 5.7% 4.0% 3.1% -2.0%

Days low


+ 13.12% 1 2 3 4 5 6 7 8 9 10 15 20 55 Days High

1 -15.4% -6.4% -3.6% -5.1% -3.7% -3.5% -3.8% -5.1% -5.1% -3.9% -5.5% -3.2% -5.2%

2 -5.8% 2.0% 1.8% 1.3% 1.0% 0.3% -0.9% -2.5% -2.5% -1.2% -2.7% -0.6% -4.0%

3 -0.7% 5.2% 7.2% 8.0% 5.5% 5.2% 4.1% 2.7% 3.3% 5.0% 0.9% 3.7% 0.2%

4 5.9% 12.4% 12.6% 11.3% 9.3% 9.5% 8.7% 8.2% 8.8% 11.0% 6.6% 9.5% 4.1%

5 5.4% 12.9% 11.6% 9.3% 8.0% 7.7% 7.4% 6.4% 7.5% 9.7% 5.6% 7.8% 2.5%

6 4.8% 10.4% 9.5% 6.5% 5.9% 6.6% 6.1% 4.7% 6.0% 8.3% 4.3% 7.4% 1.6%

7 5.7% 11.1% 10.7% 7.1% 6.4% 7.1% 6.5% 5.4% 6.1% 7.6% 4.1% 7.2% 0.3%

8 8.6% 13.4% 12.6% 8.5% 7.5% 7.8% 7.2% 6.4% 7.3% 8.2% 3.7% 6.7% 0.7%

9 8.8% 13.1% 11.9% 8.1% 7.1% 7.6% 7.2% 6.7% 6.8% 7.1% 3.5% 6.9% 1.6%

10 10.2% 11.9% 11.0% 7.3% 6.5% 7.4% 7.0% 7.1% 7.4% 7.8% 4.7% 8.1% 1.4%

15 12.0% 8.6% 5.8% 3.7% 4.1% 6.2% 3.2% 3.4% 3.3% 4.1% 2.7% 6.3% 1.0%

20 14.3% 9.3% 6.9% 4.2% 3.9% 5.3% 2.5% 3.1% 2.5% 3.7% 1.0% 4.0% 0.8%

55 14.9% 11.7% 9.3% 6.5% 5.8% 7.4% 6.5% 6.0% 6.5% 6.2% 4.5% 3.5% -1.7%

Days low


Appendix 2: Backtested Results Varying Parameters: Days high and Days low Date range: 1 Dec 2004 – 31 Dec 2012

1 Jan 2005 to 31Dec 2012


1 2 3 4 5 6 7 8 9 10 15 20 55 Days high

1 -25.7% -17.4% -14.1% -14.6% -11.8% -12.9% -13.3% -14.8% -14.1% -12.0% -14.1% -12.9% -14.0%

2 -10.8% -3.3% -2.8% -1.9% -1.4% -5.1% -6.2% -8.8% -8.8% -7.1% -8.4% -7.7% -11.4%

3 -5.1% 1.0% 3.9% 5.9% 4.4% 0.9% -0.2% -2.8% -1.5% 1.2% -3.1% -1.9% -5.7%

4 2.4% 7.1% 8.6% 8.8% 8.6% 6.0% 5.1% 3.2% 4.4% 7.8% 3.5% 4.7% -0.5%

5 0.5% 5.0% 5.3% 4.1% 4.5% 2.1% 1.8% 0.0% 1.6% 4.5% 0.7% 1.9% -3.3%

6 0.8% 2.9% 3.5% 1.4% 2.6% 1.2% 0.6% -1.7% 0.1% 3.1% -0.5% 1.7% -4.3%

7 3.0% 4.6% 5.8% 3.0% 3.9% 2.0% 1.0% -1.0% 0.2% 2.2% -1.0% 1.1% -5.6%

8 7.7% 8.6% 9.3% 5.7% 6.4% 3.8% 3.0% 1.4% 2.8% 4.0% -0.4% 1.3% -4.9%

9 8.3% 8.8% 8.7% 5.5% 5.7% 3.6% 2.8% 1.6% 2.6% 3.1% -0.4% 1.8% -3.6%

10 9.9% 8.2% 8.5% 5.5% 6.0% 4.1% 3.4% 3.0% 4.0% 4.5% 1.6% 3.8% -3.4%

15 12.8% 6.2% 4.0% 2.8% 4.7% 4.5% 0.9% 0.5% 1.0% 1.8% 0.4% 2.3% -3.2%

20 18.5% 11.3% 9.5% 7.4% 8.5% 7.4% 3.9% 4.1% 4.4% 4.9% 1.8% 2.5% -2.3%

55 18.8% 14.3% 12.5% 9.9% 8.8% 9.4% 8.1% 8.2% 9.8% 9.1% 6.9% 3.7% -2.5%

Days low 1 Jan 2005 to 31 Dec 2012,


1 2 3 4 5 6 7 8 9 10 15 20 55 Days High

1 -16.8% -9.4% -6.3% -7.1% -5.5% -7.5% -7.5% -9.6% -9.7% -7.8% -11.1% -9.5% -12.7%

2 -1.4% 5.4% 4.9% 4.4% 5.1% 0.4% -0.8% -3.1% -3.9% -2.2% -4.9% -4.4% -9.8%

3 2.2% 7.4% 9.2% 10.4% 9.2% 5.7% 4.1% 1.7% 2.4% 5.0% 0.4% 1.2% -4.1%

4 9.6% 12.8% 13.3% 12.6% 12.9% 10.4% 9.2% 7.7% 8.2% 11.3% 6.8% 7.4% 1.1%

5 7.4% 10.3% 9.9% 6.8% 8.2% 6.4% 5.6% 4.2% 5.2% 8.0% 3.8% 4.5% -1.8%

6 7.4% 7.7% 7.7% 3.8% 6.1% 5.4% 4.3% 2.3% 3.4% 6.5% 2.6% 4.4% -2.8%

7 9.0% 9.2% 10.1% 6.1% 7.8% 6.0% 4.8% 3.1% 3.4% 5.5% 1.6% 3.5% -4.4%

8 13.5% 13.2% 13.3% 8.7% 9.8% 7.7% 6.6% 5.2% 5.6% 7.0% 2.2% 3.7% -3.7%

9 13.6% 13.1% 12.2% 8.7% 9.0% 6.8% 5.9% 4.7% 5.3% 5.8% 1.8% 4.1% -2.5%

10 15.1% 12.7% 12.2% 8.9% 9.4% 7.3% 6.2% 5.8% 6.1% 6.7% 3.1% 5.7% -2.6%

15 16.1% 9.5% 6.7% 5.2% 6.8% 6.5% 3.0% 2.7% 3.0% 3.8% 1.8% 3.5% -2.1%

20 19.8% 13.1% 10.9% 8.9% 9.6% 8.5% 5.3% 5.6% 5.7% 6.3% 2.6% 3.2% -1.7%

55 18.9% 15.0% 13.6% 11.3% 10.3% 11.0% 9.8% 9.9% 11.1% 10.5% 8.6% 5.6% -1.3%

Days low


Appendix 3: Results summaries for commission levels of 0.1%. No leverage.


Results

(Arith)

Long Gold

Results yoy

(Arith)

Number of

Trades Average ATR

SD of Daily

Returns No.of Gaps

No.of Traded

Gaps

2005 + 11.10% + 17.15% 31 0.475 0.008 133 23

2006 + 33.70% + 23.22% 24 1.197 0.015 122 16

2007 + 17.16% + 28.15% 24 1.090 0.011 86 13

2008 + 11.71% + 10.14% 32 2.325 0.021 122 21

2009 + 12.22% + 23.69% 32 1.809 0.013 119 22

2010 + 23.04% + 27.07% 22 1.725 0.010 116 16

2011 + 10.30% + 11.23% 27 2.633 0.013 124 21

2012 - 9.43% + 7.53% 33 2.159 0.010 119 27

2013 + 21.22% - 30.95% 33 2.049 0.014 123 27

2014 + 14.07% - 1.10% 27 1.362 0.009 129 20

2015 + 2.57% + 2.47% 6 1.515 0.011 20 5



Commissions: 0.10%, Slippage: 0.05

0

20

40

60

80

100

120

140

160

180

200

20

05

20

06

20

07

20

08

20

09

20

10

20

11

20

12

20

13

20

14

20

15

GLD Price with Strategy Returns


Annual strategy returns:

+ 11.10% + 33.70% + 17.16% + 11.71% + 12.22% + 23.04% + 10.30% - 9.43% + 21.22% + 14.07%

Total strategy returns:

+ 249.06%

GLD Total Returns:

+ 156.9%


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strategy: 2 day high with 9 day low results results yoy...

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