Multi-algorithm analysis for FB (Facebook)

Today, I'll just throw out some more results from the multi-algorithmic testing I've been doing with SignalSolver. This time for Facebook (symbol FB). This is a stock which moved a lot in the time-frames used in the study. Could SignalSolver correctly predict and capitalize on these price movements? Let's see...

Optimizations for June 2015 through June 2016

As described in the methodology and the AMZN results, two optimizations were run on the June 2015 through June 2016 stock price data, one which rewarded raw returns using the Percentage Band, the other which rewarded more consistent returns and using the EMA band. First, lets look at Buy-hold performance for the subsequent periods:

Now lets see if the algorithms were able to exploit these price movements.

Results of the Return Optimization:

Now, the results for the Figure of Merit optimizations:

and the multi-algorithm averages:

One difference to note is that the return optimized algorithms were started out in a long state (because the End State vote indicated Long 7 to 1), whereas the FOM optimized algorithms were started out of the market because there was no good consensus. Accordingly, these returns would have been realized with lower capital.

Jan 2015 to Jan 2016 FOM Results

Here's the buy-hold results:

A pretty dramatic rise at the end of Jan 16. Luckily, all the algorithms were started long, so we got a piece of the action:


Averaging more algorithms simultaneously gave better results, for the most part. In fact for the 25 and 50 day we actually beat Buy-hold for the higher averages.




FB Sept 2014 to Sept 2105 FOM Optimizations


Another impressive set of returns (if you had guessed long). How did the algorithms do?

Good 10 and 25 day results, but hanging on for 50 trading days would have knocked a big hole in your profits. But,  had you held on for 99 days you would have beaten buy-hold very nicely.

Preliminary results of multi-algorithm testing

The portfolio and methodology for this multi algorithm study are described in my previous post. Here are links to the results spreadsheets:

EMA/Figure of merit optimization periods: Sept 2014-15  Jan 2014-15 June 2015-16

PB/Return optimization period:  Jun 2015-16

On these spreadsheets you can use the autofilter to include and exclude stocks of interest. For any stock you can click on the + sign on the left to see detailed results for each of the 8 algorithms used in the analysis. If you change the "Algs Included" cell, it will change the number of algorithms included in the averaging and summarized below the portfolio. For example, if you set it to 5 the top 5 algorithms for each stock in the portfolio (that is in the autofiltered list of stocks) will be averaged. If you set it to one, you will only include the top (best performing) algorithm. These calculations are also done automatically in the data tables below, and displayed on the graphs.

A-Z Portfolio June 2015-16 Optimizations

The top graph in each set shows the average return on $10K on running from one to 8 algorithms for a 10day, 25 day, 50 day or 90 day period on the out-of-sample data immediately following the 250 days of data the optimization were run on. So, for example, for the stock A (Agilent), the algorithms were found by using the data from June 15 2015 to June 9th 2016. The 10 day result was on the data from June 13th 2016 to June 24th 2016. The 25 day result was on data June 13th through July 18th 2016, and so on. These are trading days, not calendar days.

The buy-hold performance of this portfolio is shown below:

So if you had correctly guessed to go short for the 10 day period and long after that, you would have made more profit. On the other hand, if you had guessed wrongly, you would have been better off following the algorithms.


Percentage Band/Return optimization vs. EMA Band/Figure of Merit optimization

A three algorithm average for the PB/Return optimization for June 2015-16 gave the best Annualized Return (AR) results overall, much better than just running one algorithm. But there seems to be little point in running them beyond 10 days--profits barely increased for the next 15 days and by 50 days had soured into a loss.

The EMA/FOM algorithms had better longevity and, on average, were not lossy until after 50 days. Peak profits were at 25 days and slightly better than those for PB/Return, but best AR was still at 10 days, the same as the PB/Return result but in most cases lower.

The Figure of Merit optimizations gave more consistent results than simply optimizing for return, especially when averaged over several algorithms.

A-Z Portfolio Jan 2015-16 Optimizations

Again we see a breakdown in returns for the 99 day runs, but the shorter time-frame runs are all positive. Buy-hold performance for the same periods are shown below:

Running a single algorithm on each stock in the portfolio realized most of the potential profit for the 10 and 25 day periods, but running for 50 or 99 days gave disappointing results. Averaging across many algorithms did not lead to improvements.


A-Z Portfolio Sept 2014-15 Optimizations

Clearly, the best results for this timeframe were achieved when more algorithms were averaged, however the results were tepid at best and did not exploit the potential of the data, which is hinted at in the buy-hold performance for the portfolio in same time-frame, shown below:




Multi-algorithm trading strategy testing- Portfolio and Methodology

"Two heads are better than one", the saying goes. But can averaging improve trading systems? Can a multi-algorithm technique improve profitability and lower risk? After compiling the "Summary of Strategy Performance", I was very curious to quantify if and for how long strategies such as those published here were profitable for. To do that, I used out-of-sample testing which is very easy to do with SignalSolver.

In out-of-sample testing, you first find a strategy which worked for a specific time period. You then see how that strategy performed on data outside that specific time period. You can either go forward or backwards in time, but in these tests I go forward because that's pretty much how you would do it in reality. By multi-algorithm I mean running several algorithms simultaneously on the same stock. We look at running from 1 to 8 algorithms on each stock in a portfolio. Every stock has a different set of algorithms, found by optimization.

To get a handle on average success rates, I needed to analyze a reasonable number of stocks. Accordingly, I will report on 30 stocks with 128 out-of-sample results on each, a total of 960 algorithms each run for 4 time periods.

The A-Z Portfolio

I tried to create a portfolio which didn't look like I had cherry-picked stocks to put a rosy face on things. Accordingly, I used stock symbols A though Z which comprises 24 stocks (because symbols J and U are not assigned at this time). This I will call the "A-Z" portfolio. Other stocks were tested: AMZN, DUST, FAS, FB, NUGT, SPY and UWTI. I will report on these later, but the results are also in the spreadsheets if you are interested ahead of time. 


I have been careful to ensure that anyone with a recent copy of SignalSolver can reproduce the results I report. You just need to make sure the Settings are as per the Settings tab on the results spreadsheets. Also, you will need to adjust the Web Query end date to get the exact OHLC data I used, (or increase the Offset to move the data back in time).

First, load the daily OHLC data for the stock into SignalSolver by typing the symbol and making sure data interval was set at "Daily". Set the "Days To Analyze" to 250 days which is almost a year of data and the Offset set to 100 days leading to an exclusion of the most recent 100 days. For example, for stock symbol "A" the included data was 6/15/15 to 6/9/16, the excluded data 6/10/16 to 10/31/16. Other exclusion days tested were 200 and 300 days. The buy and sell scan ranges were set to -20% to +20%, and the investment style set to "Long and Short", starting in the "Out" state. I'll talk about optimizations later.

Clear all the algorithms on the Algorithm tab (select the rows and press delete) so SignalSolver won't scan through any pre-configured strategies. Set the Seek/Scan level to "Seek level 2". and press Solve.  This will search 1000 algorithms using about 400,000 backtests. The seek doesn't search the same 1000 algorithms each time, but follows logic as to what may constitute a good strategy. It would take about 5 minutes to finish on my machine after which the top 100 algorithms will appear on the Algorithms tab, with the top 8 being transferred to the Strategy and Report Tabs.

For this study, I looked only at the top 8 strategies found. Here is an example Seek result:

Example of a seek result

Example of a seek result

Notice that the strategies are ordered with the highest Figure of Merit first, as this was a FOM optimization (see below).

Next step is to see how each of these 8 strategies played out moving forward in time. I started out looking at the next 25, 50 days and 99 days, but it quickly became clear that I'd have to also look at a shorter time interval, so I opted for 10 days.

Start State of out-of-sample testing

Start State is the start state of the backtest and is especially important for the short time results as these may not trade much, if at all. I set the Start State of the out-of-sample test to Out, unless a clear Start State was indicated by the traffic lights on the 250/100 seek result. For example, in the above illustration, 5 algorithms are green (bullish) and 3 are red (bearish). Only if the vote was 6/2, 7/1 or 8/0 would I set the start state to that indicated by the traffic lights, Long for green and Short for red, otherwise use Out.

Reading of the out-of-sample result

After setting the Start State, I would read off the out-of-sample results by setting the "Days to Analyze" and the "Offset". Here is an example, same stock, same algorithms:

Out-of-sample result

Out-of-sample result

Notice the data analyzed starts from 6/16/16. I had to avoid using 6/15/16 data because it is used in the traffic light calculation, that's why I set the offset to 89 and not 90 days. Its vital that none of the backtested data is used in the out-of-sample analysis. After 10/89 I would set the Days To Analyze/Offset to 25/74, then 50/49 then 99/0. Each time I would cut and paste the top 8 Strategies and the Annual Returns into the results spreadsheet.

Optimizations and bands

I followed this procedure for two different Solve optimizations, one using a simple Return optimization on the Percentage Band (PB) (like most of the algorithms on this site), the other a Figure of Merit optimization using a 50 period (H+L)/2 Exponential Moving Average band. Why use an EMA band? It seemed to give better results than the PB band, but I haven't confirmed this properly yet.

Bands are explained here. The FOM optimization used these weights-

FOM Weights

With these FOM settings we are essentially looking for algorithms with good 250 day return, low standard deviation of returns for each quartus (62 days in this case), a good value for the minimum of all four quartus returns, and good returns for the most recent quartus. By setting up this kind of optimization we hope to avoid algorithms which performed very well for only short period. For more information on FOM, see here.

There is a secondary effect to running multiple algorithms on the same stock; a change in efficiency. All the tests were done using investment style "Long and Short", where you are essentially tying up the capital 100% of the time. If you run 2 algorithms  on the same stock, however, there may be times when algorithm A puts you long while algorithm B puts you short, effectively taking you (mostly) out of the market. Since, as I hope to show, profits on each algorithm average out to be similar, you have essentially increased the effective annual return by reducing the time your capital is in the market. We don't take this effect into account in the Annualized Returns reported here, we assume all capital is in the market for 100% of the time. But I believe this effect is real--please correct me if I am wrong about this.

In the next post, we shall look at the results.


FEYE Trading System: Performance

FEYE Trading System

A trading system which worked for FEYE (FireEye). This is based on daily data, so traded at most once per day.

FEYE Trading System: Performance

FEYE Trading System: Performance

FEYE Trading System: Equity curve, signals and positions

FEYE Trading System: Equity curve, signals and positions

FEYE Trading System: Parameter surface

FEYE Trading System: Parameter surface

FEYE Trading System: Parameter scan

FEYE Trading System: Parameter scan

FEYE Trading System: Trades List

As always, future performance is not guaranteed.

DIS Trading Strategy

Here is a Walt Disney Company (DIS) trading strategy with daily maintenance which had quite nice characteristics; 59% annualized return over the last 2 years.

DIS trading strategy, equity curves, signals and positions.

The performance was better than long buy-hold with lower drawdown and about three times the reward-risk. Signal reinforcement was good, and not many dual signal days.

DIS trading strategy (daily), and performance characteristics over the last 2 years.

Below I show the return for the DIS trading strategy for each 6 month period going back 2 years. Comparing with long buy-hold you can see better consistency (higher minimum and lower StdDev).

DIS.D Longevity Corr1

Please note that this is simply a measurement, not an opinion or financial advice.

This post was corrected 1/8/2016 to correct a miscalculation in the short-side returns.

Update Oct 21st 2016

Strategy peaked 11/23/15, shortly after the stock price peaked.

DIS Trading Strategy (Daily) Update Oct 21st 2016

DIS Trading Strategy (Daily) Update Oct 21st 2016

Two GLD Trading Strategies (Daily)

GLD is the much traded SPDR Gold Trust ETF. I find these two GLD trading strategies interesting because they gave reasonable results (32.6% and 48% annualized return) for each of the four 6 month periods of the analysis. The strategies require daily intervention.

Strategy 1: BCS AHC

This is a buy on fall, sell on rise strategy using the close price as the buy reference and the high price as the sell reference. As you can see from the life chart and the longevity analysis, the lowest return for the last four 6 month periods was close to 30% annualized. You can easily find algorithms with over 50% annualized return for GLD, but they are not as consistent, with lowest quartus returns of around 14%.

I would prefer to see more reinforcement on the signals, but there it is. As of Sat Sept 5th, this strategy is Short with no transactions pending.

You can view the trades in spreadsheet format here: GLD.D Trades

Strategy 2: AOO AHCI

In many ways this strategy shows better results than the BCS AHC strategy, for example there was lower drawdown, higher return, better signal reinforcement and good consistency (minimum 6 month quartus return of 38.43%). On the other hand, signals were cluttered, with 67 dual signal days, 50 buy signal days and 75 sell signal days. Also, its not an trading strategy that makes intuitive sense; buy on rise, sell on rise. Maybe it is one of those serendipitous occurrences, we shall see. Notice the sell strategy is almost the same as for BCS AHC but the sell signal percentage is quite different.

As of Sat Sept 5th, the strategy is Short with no transactions pending. GLD.D2 Table GLD.D2 Longevity GLD.D2 Surface GLD.D2 Life GLD.D2 Time For a list of trades in Excel format: GLD.D2 Trades. For a more detailed explanation of the above charts, please go here.

Algorithms were discovered by SignalSolver.

Please note, the above analysis was corrected on 12/28/2015 to reflect a bug fix in SignalSolver. Original returns were $9530 and $12753 respectively.

Update Oct 21st 2016

Both algorithms peaked 12/30/2015.

GLD Trading Strategy AOO AHCI Update Oct 21st 2016

GLD Trading Strategy AOO AHCI Update Oct 21st 2016

GLD Trading Strategy BCS AHC Update Oct 21st 2016

GLD Trading Strategy BCS AHC Update Oct 21st 2016

TSLA Trading Strategy (Daily)

This TSLA trading strategy would have given a 1062% return over 2.1 years vs. a buy-hold return of 86% for the same period. The strategy is based on buying and selling when the stock price rises above specific thresholds. The buy side keyed off the day’s open price; the buy and cover signal appeared when the price rose 4.27% above the open price of the day, and the buy is at the signal price, so you would have to set up stop orders for the buy and the cover.

The sell and short signals came along when the price rose 2.82% above the previous day’s high, and the sell actions occured at the subsequent open using market orders. Every day you would have to recalculate the buy or sell point to find the new buy or sell price. SignalSolver will re-calculate the prices each time you update the prices from the web or enter the latest prices manually. Here is the list of trades.

The equity curve shows the return of $10,000 over time for the algorithm (yell0w) and buy-hold (gray):

This algorithm spent 64% of its time short. Looking at the signals at the bottom of the chart, you may notice that they are fairly thin, and there are 21 dual signal days, 28 buy signal days and 36 sell signal days. There is occasional reinforcement of signals, OK but not great.

From the performance table you can see that the long side of the algorithm worked much harder than the short side (the leftmost two columns), but the combination (always being long or short) gave annualized return of 223%.

Lets look at sensitivity to the buy and sell parameters.

The dotted line is buy-hold annualized return at 34.45%. The colored lines are the return for different values of buy and sell percentage in different time periods. The blue line is the overall performance for the whole 2.1 year period (528 daily data points), the other green, red, yellow and white lines each represent one quarter of the data (which I call a quartus). As you move the buy or sell point out of the region, you can see that some quartus’s would have been lossy. The worst performing quartus for the chosen buy and sell points was the most recent one, 02/19/15 to 08/26/15, and the annualized return was 161%. The algorithm was found by instructing SignalSolver to find strategies with the best minimum quartus return.

If you map the return for a large range of buy and sell points you notice that the overall surface is a little peaky.

While there is a fair amount of space under the peaks, there are also steep cliffs in the vicinity, so if the buy and sell points were to move around over time you would be in trouble. For that reason I would not expect such high gains in the future.

I will be paper trading this strategy for a while and will post the results from time to time.



The above analysis has been corrected 12/29/15 for a bug in the short side return.

Update 12/29/2015:

TSLA.D Update 12-29-15

Update Oct 21st 2016

TSLA Trading Strategy (Daily) Update Oct 21st 2016

TSLA Trading Strategy (Daily) Update Oct 21st 2016

TSLA Trading Strategy (Daily) Update Oct 21st 2016

TSLA Trading Strategy (Daily) Update Oct 21st 2016


OMER Trading Strategy (Daily)

Frequent reversals characterize this strategy for Omeros Corporation

This OMER trading strategy is signal rich; there were 174 dual signal days out of the 528 days in the analysis. Added to that 151 buy signal only days and 39 sell signal only days and you get 364 signal days, of which 250 were actionable signals leading to trades, of which only 146 were good. Still, all that activity led to a theoretical $311,341 profit from $10K invested over the 2 year period from 7/12/13 to 8/14/15.

The algorithm itself is a bit of an odd one with buys triggering off price changes from the open price and sells triggering off price changes from the previous day’s open price. Is it just a fluke that it has worked so consistently? In its worst quartus (132 trading days in this case) this algorithm returned 250% annualized or 93% actual return.

You can see from the list of trades and the equity chart that there were several periods of daily reversals from long to short and back again. You might think that ignoring dual signals would work better, but it doesn’t–it leads to an 80% reduction in returns.

This strategy was found by optimizing for minimum quartus returns and then doing some minor tweaking by hand, which is quite easy to do since the Scan charts in Signalsolver are interactive. I just moved the buy and sell points to areas away where there were lower returns. I’m just going to post the charts, if you need help interpreting them I would refer you to yesterday’s AAPL post where I discuss the methodology in detail.

By the way, OMER took off today gapping up 70% or so. I was working on it before that so this change doesn’t show on the data, but the proceeds would have jumped to $929,212. It would be cheating to track this strategy knowing it had already added 70%, so I’m not planning on doing so.



Equity curve for the OMER trading strategy showing $545,057 in returns over a 2 year period.

OMER Daily Trading Strategy, sync up info

OMER Daily algorithm–current and pending trades, if you are looking for synchronization info.

Follow up 12/29/2015

This algorithm peaked and then failed dramatically immediately after the 70% gap up on Aug 18th, very shortly after publication. Here is the 528 day equity curve:

OMER.D Equity Followup

Here are the stats:


OMER.D Table Followup

Buy-hold would have been a much better option. For a profit, one solution was a buy point of 2.0% and a sell point of 4.4%, which would have given a return of $13,964 over the 94 days. Unfortunately, these parameter changes don’t appear to be predictable.