# Peering into the future with Monte Carlo Simulations

## August 31, 2009

Armed with track records spanning 2-5 years (on average), many investors believe they have enough data to get a good feeling of what is going to occur with their managed futures investment. The fact of the matter is that they only know what DID happen (in past tense) instead of what COULD happen (future tense).

The problem, as we all know, is that moving forward into the future introduces the element of randomness. Past performance does not guarantee future results is not just a clever phrase the lawyers make brokers use, it is a fact of life. The fact that the future will not look the same as the past is as certain as death and taxes. Random events will happen, causing trading systems to experience smaller or larger returns and drawdowns than were expected. While getting larger returns than expected in the future would be welcome, larger drawdowns than expected can be deadly to an investors psyche and ability to stick with a particular system.

So how do you get a better idea of what COULD happen, rather than being mesmerized by what did happen? One tool statisticians use to peer into future probabilities is called a Monte Carlo Simulation.

Monte Carlo Simulation

The crux of the problem in predicting future returns is that the only available data is past data. You can "make up" future data, or test your program/model/trading system on the data of another market to simulate future returns, but neither of those really show you how the program works on the market environment you are concerned about.

The answer for some is to take the historical return data, mix it up, then put it back together randomly. This is commonly referred to as a Monte Carlo simulation. To understand the premise of a Monte Carlo simulation, imagine a case in which all of the historical trade results of a particular trading system are tossed into a hat. We then shake the hat around, and create new track records by pulling out those trades out of the hat at random one by one, then doing it again and again. One new return stream may include a long streak of winning trades which wasn’t in the original, while another has a disturbing streak of losing trades; but most will include a mixture of winners and losers roughly proportionate to what happened in real time.

While the underlying data is the exact same as the actual trading performance, the order in which that performance occurred has changed. A Monte Carlo simulation is basically letting us know what could have happened if a big losing day wasn’t followed by a winning day, or that streak of losing days pushed on a few days longer, and so on.

This introduces randomness into the results, which is what we’re after when trying to ascertain possible future scenarios; and can cause drastic differences from a program’s actual past track record.  Looking at these differences begins to show you what COULD happen, instead of what DID happen.

To run a Monte Carlo simulation, all the trade results of a particular model, or daily profit/loss numbers for a managed futures program are compiled, then a set number of trades(or days) are pulled out and put together in a randomized, new 'return stream'. The table below illustrates a very simple Monte Carlo simulation with the original return stream, plus four new randomized return streams.

You can see that the far left column has a return of \$5,676 across 15 trades, with a drawdown of -\$3925 (trades 3-5). Such a track record may look impressive to many, and an investor using only this as her barometer for investing may expect a similar return and drawdown in the future.

However, the next four columns of the table show return streams using random samplings of the past return stream, and you will quickly see that the possible drawdowns looking ahead may be much more than what was experienced in the past. While 1 of the DDs was less, and two were only a little higher, 1 out of 4 future return streams produced a drawdown of -\$6,210.06; which is nearly twice the DD of what was experienced in the past.

The table below is intended to be an example and exhibit of the topic discussed herein. The profits/losses are for educational and illustrative purposes only, and do not represent trading in actual accounts.

 Past Random Random Random Random Return Return Return Return Return Trade Stream Stream 1 Stream 3 Stream 3 Stream 4 1 (\$1,250.00) (\$900.00) (\$1,625.00) \$3,650.00 (\$300.00) 2 \$2,375.00 \$1,980.00 (\$825.00) (\$1,400.00) (\$1,400.00) 3 (\$900.00) \$2,250.00 (\$900.00) \$2,375.00 \$3,650.00 4 (\$1,400.00) \$2,375.00 \$2,375.00 (\$1,625.00) \$2,375.00 5 (\$1,625.00) (\$1,250.00) (\$1,153.58) (\$1,250.00) (\$1,625.00) 6 \$900.00 \$900.00 \$2,250.00 (\$300.00) \$900.00 7 \$650.00 \$2,231.47 (\$1,250.00) (\$900.00) \$650.00 8 \$1,980.00 (\$1,625.00) (\$1,400.00) \$900.00 \$2,231.47 9 (\$825.00) (\$906.48) \$650.00 (\$825.00) (\$900.00) 10 \$2,250.00 (\$1,400.00) \$3,650.00 (\$906.48) \$2,250.00 11 (\$300.00) (\$825.00) \$1,980.00 \$650.00 \$1,980.00 12 (\$906.48) (\$300.00) \$900.00 \$1,980.00 (\$906.48) 13 \$2,231.47 (\$1,153.58) (\$300.00) \$2,250.00 (\$1,250.00) 14 \$3,650.00 \$650.00 \$2,231.47 (\$1,153.58) (\$825.00) 15 (\$1,153.58) \$3,650.00 (\$906.48) \$2,231.47 (\$1,153.58) Total Profit \$5,676.41 \$5,676.41 \$5,676.41 \$5,676.41 \$5,676.41 Max DD (\$3,925.00) (\$6,210.06) (\$3,350.00) (\$4,075.00) (\$4,135.06) 25% of DDs Below \$ (3,351.00) 50% of DDs Below \$ (4,076.00) 75% of DDs Below \$ (4,136.00) 100% of DDs Below \$ (6,211.00)

We hope this simplistic example drives home the point that the order of winners and losers can be just as important as the magnitude of winners and losers in creating a drawdown environment. A program could have the exact same winning percentage, average profit, average loss, worst loss, and so on in the future (basically doing exactly as you would hope and expect based off its past track record) – yet still have a drawdown double what was seen in the past simply due to the order in which the winners and loser fall. Simple randomness can have that big of an impact on future performance.

This example used only four randomly generated return streams, and is therefore not a very robust sampling. True Monte Carlo simulations are run with as many data points (trades or days) as you have, and are run thousands of times. Attain usually runs its Monte Carlo simulations across 5,000 to 100,000 trials, meaning the table above would have up to one hundred thousand columns showing different return and drawdown combinations.

In reviewing such large numbers of simulations, investors must understand the concept of percentiles. While percentiles are most often associated with scores on standardized tests, it has a valid use when analyzing results. A percentile is simply a value between 1 and 100 indicating the percent of samples (return streams) taken from all results that is equal to or below the given value. For example, a 25% Drawdown at the 99th percentile level means 99% of the returns streams in the simulation had a drawdowns below 25%.

Example: APA Modified

As an example of how a Monte Carlo simulation can be put to good use - we ‘went back in time’ so to speak, and ran a Monte Carlo simulation as of Dec 31, 2008 on the then 22 month historical track record of our own APA Modified program to see what the simulation would have told us COULD happen over the next year.

The Modified program was at all time highs at the end of December, with the historical track record showing a max intramonth (daily) drawdown of about -22% (or -\$55,000) and the programs backtesting having shown a historical max drawdown of -40%. Since then, the program has unfortunately struggled thus far in 2009, seeing a new max DD of close to -40%.

What would a Monte Carlo simulation have shown us at the end of December 2008 was possible in 2009? What would a Monte Carlo simulation have shown us COULD happen in 2009?

Using the daily performance record of the APA Modified program, we plugged the past return stream into the Monte Carlo simulator. We then took 240 days (roughly equal to a year of trading) "out of the hat" of all days, and saw what the possible drawdowns were. We repeated this 10,000 times, thus simulating 10,000 different possible years across 2.4 million days. You gotta love computers.

Past Performance is Not Necessarily Indicative of Future Results

 APA Modified Intramonth DDs (daily) across 10,000 fictitious, randomized years Past Track Record 50th percentile 90th percentile 99th percentile 100th percentile -22% -16% -25% -39% -60%

The stats are eerily close to what has happened in real time for the APA Modified program, with the 99th percentile DD (we generally see future DDs come in between program’s 90th and 99th percentile DDs) coming in right at -39% (almost exactly the level the Modified program has drawn down).  The 50th percentile drawdown level was -16%, meaning that can and will happen with some regularity moving forward, while no DDs across 10,000 fictitious, randomized years was greater than -60%.

Expect a future DD equal to the 90th - 99th Percentile level:

While percentiles don’t necessarily correlate with the probability of those levels being hit, it doesn’t take a rocket scientist to ask the obvious question – why would you expect the 99th percentile DD level to be hit? Shouldn’t that level have something like a 1 in 100, or lower, chance of being hit?

The 99th percentile DD should have a very, very low probability of getting hit, if financial markets and investment returns followed a normal bell curve and had a normal distribution of returns. In such normally distributed data to see something happen which is 100 times the average is as close to impossible as you get.

But as anyone who lived through last year, 9/11, or October 1987 can attest to – financial markets and investment returns are anything but normally distributed. If they were, the worst case scenario for the stock market would be daily loss of -3% or so, not losses of -21% in a single day(1987) or -45% in a year (2008). To look at it from the other way, if people’s height were distributed like financial markets – you would see a one mile tall person walking down the street every few years (or as Nassim Taleb likes to say, a black swan)

This is a tough concept for people to grasp, if for no other reason than they don’t see 10 feet tall people walking around much less someone 1 mile tall (which is utterly incomprehensible to us). We are surrounded by normally distributed statistics – height, weight, population, floods, temperature, distances, etc.), making it that much harder to understand that in investing – the extraordinary is the ordinary.

Knowing that investment returns and financial markets are not normally distributed, we look to these extreme levels, the 90th and 99th percentile DDs as the best measuring stick for what COULD happen in the future, while keeping the 100th percentile number (a number which all drawdowns in the testing were below) in the back of our mind. While we rarely see the 100th percentile number get hit,  if the number were so large as to bankrupt you or the like – it is worth noting and avoiding that possibility.

We ran Monte Carlo simulations, doing 10,000 separate 240 day trials (like looking at 10,000 possible future years) on the following managed futures programs, who are kind enough to share their daily returns with us on a monthly basis.

Some investors may be surprised at some of the large numbers in the table below, with the 99th percentile Drawdowns 1.7 times the experienced historical Max Drawdown on average. But that is the point. We must expect the unexpected in financial markets, and not be blinded by was has happened while trying to understand what could happen

If some of these numbers are at risk of turning you off of managed futures – consider that the S&P 500 is only months removed from the bottom of a -52% DD, and the Nasdaq has a -78% DD in its history. And those DDs are with average annual returns of just 8% and 16% respectively. You’ll find much better risk adjusted returns than that on the list below, in our opinion.

But the table below should be taken with a grain of salt and the following caveats. One, these programs do not live in a vacuum and operate without human intervention. The Paskewitz program, for one, exits all trades at a drawdown of -35% and waits for another trade entry. The Monte Carlo simulation doesn’t know this, and could pile up a losing streak which goes right through Paskewitz’s -35% safety level.

Two, there is a problem inherent with using daily return data instead of trade results data (which we don’t have). It follows logically that different trade results could happen in any order in the future. But that isn’t necessarily the case with daily returns.  Consider a situation where a program like Clarke makes money a few days in a row being long Cotton, and then sees a sharp one day loss as Cotton reverses. The Monte Carlo simulation may take that one day loss and pile it up next to other losses, when in fact the Cotton loss was in part due to the gains from the previous days. Daily data is not so easily split and reshuffled, as it has a degree of correlation – where gains or losses one day are a result of positions taken on previous days.

Finally, not all programs lend themselves easily to a Monte Carlo analysis. Systematic programs are generally better suited to Monte Carlo analysis than discretionary programs, as their models will trigger a trade and take that trade no matter what (making it easier to assume those trades could happen in a random order in the future).  Discretionary traders, on the other hand, often let the performance on their last trade(s) affect their decision making/performance for the next trade (for better or worse). They may go to the sidelines or freeze like a deer in the headlights after a losing streak, making it less likely that one of the out of the ordinary losing streaks the random reshuffling of the Monte Carlo analysis will come to pass in the future.

Past Performance is Not Necessarily Indicative of Future Results

 Intramonth (Daily) Max Drawdowns for Various CTAs across 10,000 fictitious, randomized years Past Track Record 50th percentile 90th percentile 99th percentile 100th percentile Attain Portfolio Advisors - Strategic Diversificaiton Prog. -13.76% -8.26% -14.58% -22.79% -39.22% Clarke Capital Mgmt. - Millenium Prog. -39.38% -23.16% -43.54% -66.62% -100.57% Claughton Capital - Institutional Prog. -25.64% -16.94% -31.28% -48.52% -89.02% Dominion Capital Management - Sapphire Prog. -8.44% -3.97% -6.87% -10.46% -17.75% Emil Van Essen Spread Trading - High Minimum -43.82% -24.21% -46.87% -74.92% -105.78% Integrated Managed Futures - Global Invetsment Prog. -20.71% -11.43% -20.64% -32.48% -53.39% Mesirow - Absolute Return Strategy -3.04% -2.25% -3.65% -5.46% -10.53% Paskewitz Asset Management - Contrarian 3x Stock Index -23.54% -17.36% -33.33% -52.84% -99.14%

Most investors out there have probably run into a losing streak they couldn’t believe, or found themselves invested in a winning CTA who is suddenly in a drawdown double what happened in the past. These are errors of human logic, which doesn’t easily allow us to expect the unexpected, and which usually makes us put too much value on past performance.

The lesson is to use a tool like the Monte Carlo simulation to try and switch your thinking to a new regime – where you consider what COULD happen in an investment, not what DID happen. Armed with some Monte Carlo simulation percentiles, you can start to get a feel for what may really be in store for you in the future. No investment, unless run by Mr. Madoff or Stanford, makes money month after month, year after year. There will be losses, period. Once you are prepared for the inevitable drawdowns and have some data on just how far they are likely to go, it is easier to live through those losses, handle the future drawdowns, and achieve long term success when your programs go on to new equity highs.

Attain Capital is happy to run Monte Carlo simulations for you on any historical data, just email invest@attaincapital.com and we’ll get to work on looking over a few thousand possible years for you.

- Jeff Malec

Disclaimer: The tables in this article are intended to be an example and exhibit of the topic discussed herein. The profits/losses are for educational and illustrative purposes only, and do not represent trading in actual accounts.

IMPORTANT RISK DISCLOSURE

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# Feature | Week In Review: Sugar hits 10yr highs, stocks slow down

Overview

Domestic economic reports continued to be a bright spot for the Index futures and some sectors of commodity futures, but a midweek report from Asia about possible cutback in bank spending did give the marketplace an uneasy tone. The slowdown in price appreciation for many Commodities and Stock Indexes was also prompted by ideas of investors that the recent 6 month run-up in stock prices could abate and move into a correction phase especially if Asia, which has been the leader of the rally starts to have moderating economic conditions. These warning signs definitely had a bearing on price activity in other sectors as any slowdown in demand especially for energy could spark a heavy price correction with such large supplies on currently on hand worldwide. On the economic front most reports seemed to be near or better than market expectations, although a few were off of the mark which did seem to at least spark a pause to upside enthusiasm. The lineup for economic reports this week is heavier with the start of a new month highlights by the Monthly Jobs report scheduled to be released on Friday. The energy sector was again the most active last week with declines seen in all contracts except RBOB Gasoline that found light support ahead of the Labor Day holiday which is usual the peak driving time as summer ends. Natural Gas futures -6.42% led the fall followed by Heating Oil -2.26% and Crude Oil -1.39%. RBOB Gasoline futures ended the week +0.42%.

Stock Index futures held their upside momentum for the most part, although the advance was somewhat muted by the light late summer trading activity. Jitters from the most recent consumer confidence report adding a fourth month of weaker readings also seemed to keep market participants from initiating large bets in the marketplace. For the week Mid-Cap 400 futures +0.55% led the way followed by Dow futures +0.50%, NASDAQ futures +0.43% and S&P 500 futures +0.21%. Russell 2000 Futures -0.24% ended the week slightly lower.

Commodity and Food sectors posted mixed results last week as weather was a key concern for many markets. The grains were led higher by market participants need to add weather premium into the price structure as worries of an early frost in the U.S. and dry conditions in Australia help spark a sector wide rally. The Soft arena was again mostly weaker during the past week as another round of profit taking and news of possible record harvests in some Cocoa and Coffee growing regions help aid selling pressure. The Livestock arena was mixed although weaker demand and heavier supplies did keep the overall down bias in check. Sugar +7.69% was a lone beacon as continued rain delays in Brazil have aided ideas that yield reductions could be steeper than earlier estimated. Other price rallies were seen in Soybeans +3.91%, Wheat +1.64%, Corn +0.73% and Lean Hogs +0.46%. Decliners were led by Cocoa -5.44% followed by OJ -4.21%, Coffee -2.20%, Live Cattle -2.14% and Cotton -0.49%.

The metals complex was mostly firm as investors seem to flock back into this complex based on hard asset purchasing on worries of an economic slowdown in Asia.  Strong industrial activity domestically was also seen as a supporting factor for most sectors. For the week Silver closed +4.34% followed by Palladium +2.71% Copper +1.95% and Gold +0.43%. Platinum -0.83% was a bit weaker.

Currency activity was again fairly subdued, although the British Pound -1.46% did find pressure from a couple of weak economic releases which also led to pressure in the Swiss Franc -0.17% and Euro -0.13%. The Japanese Yen +0.79% and U.S. Dollar index futures +0.36% benefitted from the negative bias in Europe. The rate sector was again supported by favorable auction results and news of a possible slowdown in Asian economic conditions. 30-year Bond futures ended +1.58% and 10-year Notes futures were +0.88%.

Managed Futures

Heading into the last day of trading August appears to be a mixed bag of results for multi-market managers.   The official stats through the end of the month will be updated on our site tomorrow, so please make sure to check back and see the final results tomorrow night at www.attaincapital.com !

Integrated Managed Futures Global Concentrated continues to thrive in August and is up approximately +10.84% for the month heading into today.   Most likely Integrated will be the leader tomorrow as the next closest manager is Dominion Capital Management at an estimated +2.62%, who despite being so far behind, still had a nice month of trading.   Other impressive managers include Robinson Langley Capital Management +1.97% est. and Futures Truth MS4 +1.09% est.

Managers who just made it into positive territory include Dighton Capital USA Aggressive Futures Trading +0.53% est., Lone Wolf Investments LLC Diversified +0.21% est., Attain Portfolio Advisors Strategic Diversification +0.15% est., Mesirow Financial Commodities Low Volatility +0.13% est., while Mesirow Financial Commodities Absolute Return was at breakeven.

August was a bumpy month for some managers however.   Programs that were in the red heading into the last day of trading included DMH Futures Management LLC -0.38% est., Futures Truth SAM 101 -2.67% est., Hoffman Asset Management -2.67% est., APA Modified -2.80% est., Clarke Global Magnum -9.39% est. and Clarke Global Basic -12.87% est.

Short term index traders were also mixed with Paskewitz Asset Management 3X Stock Index Contrarian +1.36% est. gaining ground while MSLO -2.28% est. continues to struggle.

Heading into the last day of the month, option trading results are mixed.  Index option traders are mostly ahead while the diversified managers have been playing catch up most of the month after having been stumped on several currency and sugar positions in the first week of August.  The current estimates are as follows: ACE Investment Strategist +1.70%, Cervino Diversified -0.42%, Cervino Diversified 2x -0.92%, Crescent Bay PSI +1.1%, FCI OSS -2.49%, FCI CPP -0.90%, Raithel Investments +1.12%, and Zephyr Investment Group -5.15%.  We will be looking forward to see how each of the above managers handle the expected rise in market volume and volatility, that typically is associated with September and October…In other words, what did they learn from 2008?

On the whole, it has been a slightly down month for Specialty Managers involved in spread trading and agriculture markets as they have limited their activity to a small number of new positions.  Emil Van Essen’s Spread Trading program is down -0.10% threatening to break it’s string of 2 winning months in a row – the program is up an estimated +18.92% for 2009 with only one losing month in May.  NDX Capital’s Abednego and Shadrach programs are also down slightly (-0.17%and -0.38% respectively) yet remain positive for the YTD (+0.66% and +3.03% respectively).  Rosetta Capital is also down for August (-1.12%) and, of the Specialty Managers we track, is the only one in the red for the year (-4.19%).  Both NDX and Rosetta head into September with open positions where they’ll be looking to capitalize on a down trending livestock market.

Trading system performance was mixed last week with swing systems finishing mostly higher while day trading systems took a hit across the board.  On several occasions last week, U.S. stock indices appeared to be faltering only to come roaring back towards the end of the day, which is a recipe for disaster for day trading systems that jumped on board with the sellers.

Beginning with the swing systems, newcomer BAM 90 ES continues to shine and tacked on +\$4,265 last week. The program is unique in that it can enter into multiple contracts either at the same time or by scaling into the position. For example, last week the system was in at least two contracts at all times throughout the week and up to as many as six contracts.  In the 30 Yr Bond market, both Jaws US Daily and US 60 finished ahead by +\$563.99 and +\$485.62 respectively after entering in line with the bullish trend mid-week.  AG Mechwarrior ES was quiet with just one trade that it closed out on Monday for +\$220. On the losing side, Strategic SP and ES finished the week down -\$2,475 and -\$427.50.

Transitioning to the day trading systems, the only program that was able to stay above water was ATB TrendyBalance v2 Dax +170€ on three trades. Other results were as follows: ATB Welcome v2 Dax -1,295€, BetaCon 4/1 ESX -310€, Clipper ERL -\$140, Compass SP -\$465.27, PSI! -\$260, Rayo Plus Dax -3,605€, Upper Hand ES -\$610 and Waugh ERL -\$17.06.

IMPORTANT RISK DISCLOSURE
Futures based investments are often complex and can carry the risk of substantial losses. They are intended for sophisticated investors and are not suitable for everyone. The ability to withstand losses and to adhere to a particular trading program in spite of trading losses are material points which can adversely affect investor returns.

Past performance is not necessarily indicative of future results. The performance data for the various Commodity Trading Advisor ("CTA") and Managed Forex programs listed above are compiled from various sources, including Barclay Hedge, Attain Capital Management, LLC's ("Attain") own estimates of performance based on account managed by advisors on its books, and reports directly from the advisors. These performance figures should not be relied on independent of the individual advisor's disclosure document, which has important information regarding the method of calculation used, whether or not the performance includes proprietary results, and other important footnotes on the advisor's track record.

The dollar based performance data for the various trading systems listed above represent the actual profits and losses achieved on a single contract basis in client accounts, and are inclusive of a \$50 per round turn commission (\$30 per e-mini contracts). Except where noted, the gains/losses are for closed out trades. The actual percentage gains/losses experienced by investors will vary depending on many factors, including, but not limited to: starting account balances, market behavior, the duration and extent of investor's participation (whether or not all signals are taken) in the specified system and money management techniques. Because of this, actual percentage gains/losses experienced by investors may be materially different than the percentage gains/losses as presented on this website.