Australian (ASX) Stock Market Forum

# Drawdown Monte Carlo Increase over time PROBLEM

#### Loop

after extensive testing using Monte Carlo mathematically correct for Drawdown analysis I see only bad news.

Using random selection with replacement to create 200 trades long series of cumulative return (More than 10 000 of them) and from this extracting the distribution for drawdowns it is very hard to come below very big drawdown with any system!!

As we know from Howard Bandy, Drawdown increase over time. This increase follow a diffusion equation. Square root over period.

This is really bad news because any test over longer periods will have DD of over 50% for ANY system. The only way to feel good and get it lower is to test shorter periods. (Much like peeing if its cold, keeps you warm a minute but then...)

The law of large numbers is a strong force!

Is there anyone who have seriously looked into this big problem for any and all system and can recommend solution, literature or other sources of information?

Kind regards

Loop

#### Quant

after extensive testing using Monte Carlo mathematically correct for Drawdown analysis I see only bad news.

Using random selection with replacement to create 200 trades long series of cumulative return (More than 10 000 of them) and from this extracting the distribution for drawdowns it is very hard to come below very big drawdown with any system!!

As we know from Howard Bandy, Drawdown increase over time. This increase follow a diffusion equation. Square root over period.

This is really bad news because any test over longer periods will have DD of over 50% for ANY system. The only way to feel good and get it lower is to test shorter periods. (Much like peeing if its cold, keeps you warm a minute but then...)

The law of large numbers is a strong force!

Is there anyone who have seriously looked into this big problem for any and all system and can recommend solution, literature or other sources of information?

Kind regards

Loop

The key lies in expectancy and the 2 sides of it , any system with expectancy in the lower boundaries is going to have large drawdowns comparitively . You can combat this with low position sizing but this makes the curve weak and uninspiring ( may as well invest in bonds ) . There is no easy answer really for the only true cure is elite expectancy and thats a steep and tall mountain , ive really only overcome this with intuitive systems , something beyond the realms of most i'm afraid . There is no easy answer

3 influences on Drawdown
R
position size

Without getting elite numbers in first 2 your position size has severe constraints and therefore the curve suffers accordingly .

#### CanOz

##### Home runs feel good, but base hits pay bills!
I think the key to smoother equity curves lies in dynamic portfolios.

#### Quant

I think the key to smoother equity curves lies in dynamic portfolios.

I think we are talking individual monte carlo simulations so im expressing my views in relation to that , i have no doubt diversification can lead to a smoother curve but certainly not a better potential return

#### Wyatt

I think we are talking individual monte carlo simulations so im expressing my views in relation to that , i have no doubt diversification can lead to a smoother curve but certainly not a better potential return

Below is a comparison between the same trend following system, with the one on the left being 16 x 6.25% position sizing and the one on the right being 25 x ATR based (equal volatility) position sizing. Results on XAO and use of an index filter, hence the flat spots. Both had similar win%. Interestingly the 16 x 6.25% is about 16% in front of the more conservative model since 1/1/2010

So theoretically over the long term this model performs better and more realistically tradeable over the longer term by having larger positions in less volatile stocks.

any system with expectancy in the lower boundaries is going to have large drawdowns comparitively

Gotta agree here. You can't polish a t*rd

#### CanOz

##### Home runs feel good, but base hits pay bills!
There is allot to be said for equalization of volatility through position sizing. In more volatility there is less need to trade bigger as returns can be magnified by volatility....in less volatility or lower vol regimes large position sizes can result in good returns provided trades are managed according to the potential that the regime provides.

I've not implemented at of this in my systems that are in functional tests, but it should only improve a good system.

I've yet to come to grips with how to apply this to discretionary trading....

Slightly off topic again....

#### howardbandy

Greetings --

In my opinion, the key is risk. The trader's personal risk tolerance and the risk of the trading system. Position size is very important -- it is adjusted trade-by-trade to keep the account gain as high as possible while keeping the risk within the trader's tolerance.

Monte Carlo analysis is very useful in estimating future risk and future profit potential. But, like any tool, use it correctly and wisely.

Be wary of choosing which of several alternative trading systems you might use based on the appearance of backtest equity curves.
1. In-sample backtests always overestimate profit and underestimate risk. In-sample results are the result of the model (logic, rules, indicators, and parameters) fitting to the training data. It is only by testing the model on data that is both more recent in time and never used in in-sample testing that we can determine whether the system "learned" or "memorized."
2. The equity curve is sequence-dependent. The equity curve that catches our eye is always in the optimistic tail of the distribution of results.
3. Rather than use the equity curve as the metric, analyze the distribution of trades. Compute the risk of drawdown and the estimate of profit.

The mantra of success is:
Hold a short period.

The sweet spot is accuracy greater than 65%, holding one or two days.

Terminal wealth, TWR (per Ralph Vince) is G ^ N, where G is geometric gain per trade (same as expectation), N is number of trades.

It is nearly impossible to generate high account gain at acceptable risk for systems that are less accurate than 65% or that hold longer than a few days. Much as we might wish it were different.

There are several problems applying any analysis to discretionary trading --
1. Subjective interpretation. We fool ourselves so easily. Read Daniel Kahneman, "Thinking, Fast and Slow."
2. Non-repeatability. Analysis of the same data by different people or even the same person at a different time results in different trades.

Monte Carlo analysis can be applied to any set of trades. To get reasonable forecasts of future performance, use only the "best estimate" of future trades.

Best regards, Howard

#### howardbandy

Greetings --

Loop asks specifically about drawdown increasing as the forecast horizon increases. He correctly states that drawdown expands in accord with the diffusion equation -- like smoke rising from a single source is a narrow column at the base and expands as distance increases.

Whenever a forecast is made, it is with respect to a time horizon. I recommend setting the time horizon at some period that is reasonable relative to your life and your trading. I use two years in my examples, and my own work. If I will be trading for four more years, I will re-run a second two-year estimate when that time comes.

If you have not already, consider changing from impulse-based signals to state-based signals. Also change from trade-by-trade accounting and trade management to mark-to-market-daily accounting and trade management. When analyzing results for a given period of time, only those trades that are completely within the period can be used. State-signals and M-T-M accounting give every system 252 data points in every year.

Best regards, Howard

#### rb250660

Try reinvesting the square root of your profits. Follow the diffusion equation with profits too in other words.

#### jjbinks

hi howard and others.

you mention use period relative to life/trading plans

So if you plan to trade for 40 years. Would it not make sense to test over at least a decade?

#### systematic

The mantra of success is:
Hold a short period.

The sweet spot is accuracy greater than 65%, holding one or two days.

Following this path of success, what CAGR% should be aimed for?

#### howardbandy

Try reinvesting the square root of your profits. Follow the diffusion equation with profits too in other words.

Greetings --

Having position sizing a function of trading management gives an opportunity to monitor the health of the system and adjust position size trade by trade to manage risk. The dynamic position sizing technique I describe gives the best combination of account growth with risk control.

Having the position size be a function of system profit increases profit when the model is in sync with the data, but does not include a management tool. Work through some simulations using trades that represent a system being considered. See what happens during periods of drawdown.

Best regards, Howard

#### howardbandy

hi howard and others.

you mention use period relative to life/trading plans

So if you plan to trade for 40 years. Would it not make sense to test over at least a decade?

The analysis begins with a statement of personal risk tolerance. For example:
I am trading a \$100,000 account, forecasting two years, desiring to hold the chance of a drawdown in excess of 20% to 5%.

This is a subjective statement. Each analyst / developer / trader will adjust it to reflect his or her own conditions.

There are four parameters. I discuss the sensitivity of each, including length of forecast horizon, in my "Quantitative Technical Analysis" book, beginning on page 406.

I recommend using a forecast horizon that is realistic relative to the business, and that allows reasonable modeling and simulation. If the system uses impulse signals and accounts for complete trades (compare with using state signals and accounting using mark-to-market daily), there will be few trades in any given period. Shorter periods and fewer trades cause increase in variability of results. Longer periods allow more trades and will result in higher drawdowns, lower safe position size, and lower compound annual rate of return.

I highly recommend using state signals and mark-to-market daily management and accounting. As I describe in the QTA book (also in the "Foundations" book), the two are equivalent in terms of accounting. But having a state signal for each and every day creates 252 data points for every year, which is a big advantage in simulation and trade management.

Using the data from the book, a system that has safe-f and CAR25 of 1.14 and 48%, respectively, for a one year horizon, has safe-f and CAR25 of 0.85 and 42% for a four year horizon. Safe position size is lower in anticipation of higher drawdown over a four year horizon, resulting in lower rate of return.

If the dynamic position sizing technique is followed, the two year horizon (or whatever forecast horizon is chosen) is not static, but is a rolling window. The risk and profit potential are recomputed frequently -- as frequently as the system is marked to market, or as infrequently as about weekly. The less frequently the safe-f is computed, the higher the risk of a drawdown that exceeds the tolerance. By the time the initial two years has passed, the system is probably different than it was at first trade.

Given two components of the trade management system --
...the statement of personal risk tolerance.
then everything else follows from the mathematics. Including trade-by-trade position size, drawdown, account growth, etc. What will happen in real time is unknowable in advance, but the technique provides the tools for adapting to whatever does happen.

Be certain to keep position sizing as a function of trading management and out of the trading system model. The only purpose of the trading system model is to identify patterns that precede profitable trades.

Best regards, Howard

#### howardbandy

Following this path of success, what CAGR% should be aimed for?

As high as possible, in keeping with your risk tolerance.

Begin with a statement of risk tolerance, a data series to trade, and a set of rules that include all trading decisions. Everything follows from there.

Use the risk-normalized CAR25 computed using the best estimate of future performance to decide which of the alternative uses of funds is best. Then do that one thing.

The "Foundations of Trading" book outlines the process. The "Quantitative Technical Analysis" book gives details and executable code that can be used as templates to get started.

Best regards, Howard

#### rb250660

Greetings --
Having the position size be a function of system profit increases profit when the model is in sync with the data, but does not include a management tool. Work through some simulations using trades that represent a system being considered. See what happens during periods of drawdown.
Best regards, Howard

I understand. And my proposed approach was perhaps too simple in negating the issue at hand.

To add to the conversation, I am a "real-world" example of the implementation of Howard's dynamic position sizing. It works very well with the finger always on the pulse of system health. I recalculate position size after each trade is closed (I personally don't use MTM). It has saved me from big drawdowns and during good performance it quickly adds profit. The way I have tuned my management parameters has resulted in:
- Quick response to changes in performance (good and bad),
- Halved my drawdowns so far when compared to no dynamic position sizing (back tested), and
- Reduced downside volatility in my returns.

As a side note I trade a basket of ASX stocks, not a single ETF. I highly recommend you put in the work to implement Howard's method. "Bet the run of the table" come to mind here, in my experience trading short term is very much like that. Dennis Gartman puts it very nicely.

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