Risky Proposition (Part 2)

I believe we should always be thinking about the likelihood of history to repeat before concluding too much from historical backtesting. Usually, the answer is “unlikely to repeat” and Monte Carlo simulation to randomize trade sequence seems like a logical solution. Studying only one historical equity curve introduces selection bias to the system development process.

Lines 4-6 in the last post suggested dividing initial equity by the maximum drawdown (DD) to best understand trading system risk. This prevents someone from inflating potential returns by advantageously changing the backtesting start date. Certainly when developing my own system I also want to avoid underestimating risk. In live trading if I lose much more than expected then the result could be catastrophic.

Lines 1-3 address accurate assessment of DD risk. I love to see an equity curve grow exponentially but the way to do that is by increasing position size along the way. DDs occurring later in the trade sequence will be proportional to position size and this can distort our understanding of risk. For example, which year has the worst DD for each system shown below?

Clearly the 2010 DD is twice that of 2008 for each system. Does the additional information shown below change your perception?

The 2010 DD is worse for system 1, the 2008 DD is worse for system 3, and the DDs are equivalent for system 2. I now can better understand how DD should be understood in terms of position size.

Using a constant position size during development of a trading system helps remove the bias produced by order-dependent testing results. We may already have a selection bias introduced by choosing an equity curve that is better than the mean. Do not compound that by adding artificial equity growth due to trade sequences not likely to be repeated.

Put in simpler terms, when analyzing DDs I need to keep position size constant to ensure apples-to-apples comparison.

A Brief Glimpse into Theoretical Physics

Last time I mentioned a concept arguably more suitable for a theoretical physics blog than a blog on option trading:

     > To say “calculate [drawdown] as if it happened on Day 1” is to
     > say any ordering of events is equally likely. A 2011-type
     > correction could have just as well happened in 2002 and a 9/11
     > could have just as well happened in 2008, etc.

Understanding our current reality as a cumulative result of historical events/decisions is a controversial interpretation amounting to fate and destiny. While many people do understand the world in these causal terms, cognitive psychology suggests the human brain works unconsciously to identify causation even where none actually exists. This is adaptive: living in a logical world is certainly less stressful than living in a world where utter chaos lurks around every corner.

How robust is our current reality? Is it like a sequence of dominoes where toppling of just one can affect everything that comes after? Is it more like Jenga where many previous decisions may be altered before the present is affected?

Trekkies will always remember the words of Jean-Luc Picard in “Yesterday’s Enterprise:” “Who is to say that this history is any less proper than the other?”

Another good description of the infinite realities concept is shown here from time index 07:00 to 09:45.

For all these reasons, I mentioned “overstated conclusion” in the final paragraph. I do not want to make the mistake of basing trading decisions on the shape of a backtested equity curve. People commonly ask to see these historical equity curves without realizing that these are just one possible path a trading system may follow through time. A slight alteration in the trade sequence may result in worse drawdowns, losing periods instead of profitable ones, etc.

Gaining that “broader perspective” by numerous Monte Carlo simulation runs can decrease the chance of falling prey to this sort of curve-fitting.

Risky Proposition (Part 1)

Continuing on with a previous discussion about normalizing risk:

     > Position sizing should be held constant throughout the   [1]
     > [duration of in-sample backtesting]… This allows for
     > an apples-to-apples comparison of PnL changes             [3]
     > throughout… A drawdown (DD) at any point should be
     > evaluated as if it occurred from Day 1; this is one          [5]
     > way of interpreting maximum risk.

I will start by describing the concept in lines 4-6 and then cover lines 1-3.

Risk tolerance may be used to determine position size. Suppose the max DD I can psychologically withstand is 10%. Based on the oft-quoted trading adage “the worst DD is always ahead of you,” I should select a smaller position size such as one corresponding to a max DD of 5%. If I now encounter something 2x worse in live trading, my psychology can [hopefully] tolerate it thereby avoiding the potentially catastrophic result of abandoning ship at the darkest moment.

Sticking with the conservative theme, I should also calculate DD as a percentage of initial equity because this will give a larger DD value and a smaller position size. For a backtest from 2001-2015, 2008 was horrific but as a percentage of total equity it might not look so bad if the system had doubled initial equity up to that point.

To say “calculate DD as if it happened on Day 1” is to say any ordering of events is equally likely. A 2011-type correction could have just as well happened in 2002 and a 9/11 could have just as well happened in 2008, etc. In case this is true, I prefer not to trade real money based on the overstated conclusion that a DD occurring later was destined to occur later. Monte Carlo simulation can randomize the trades to generate a large number of potential trade sequences for a trading system. I can then look at averages and standard deviations for things like net income and max DD to get a broader perspective of what to expect in live trading.