Rationally Irrational

Ideas from behavioral economics such as prospect theory have enlightened us to our reactions to gains and losses over varying time periods, but I have yet to come across research discussing what I am calling ‘rationally irrational’ decisions. Let me attempt to explain.

Our decisions are influenced by rewards, potential or actual. These rewards can create habits that lead to the continuation of a specific behaviour. But since rewards are felt by chemicals in our brains, something that is unhealthy for our minds and bodies – getting high on hard drugs, smoking cigarettes, or drinking excessive amounts of alcohol – may be felt of as a reward which could lead to future cravings.

Often it is the case that the individual knows fully well the impacts of his or her decision, and sometimes in fact craves these effects. Think of the masochist who gets off on the pain, or the dieter who wants to improve their body image yet craves unhealthy foods. Most people want the fitness physique, yet also want to eat all the cakes.

In terms of finance this could translate to a rogue trader gambling deeper and deeper into the red, or an institution plotting to cheat and steal from clients. Of course, there have been many cases of both.

As I am planning to create a basic model of a complex economical system, I am looking to model one of the most important aspect of the system, the participants. And of course, I need to include their irrationality. If anybody has any research that I may have overlooked in regards to reward mechanisms, please let me know.

The Elements of Risk

Let’s start with some basic assumptions to come to further conclusions regarding risk.

Assumption 1. Increased time exposure increases risk.

With the knowledge that asset returns are fat tailed, we can make the basic assumption that the longer you are exposed to the market, the greater the chances of catching a negative outlier event.


But as the time and risk exposure extends, so too should exposure to a positive outlier. This leads us to our second basic assumption.

Assumption 2. Increased risk means increased potential profit.

This assumption generally stands true, but there are many cases where it’s not quite the case. For example, under this basic assumption, going long a stock at 10 is clearly less risky than shorting the same stock at 10 (long max risk = -10, short max risk = unlimited).

Another example is in strategy and asset diversification of the portfolio. The risk of individual transactions will remain the same, but spreading this risk across multiple and lightly correlated risks will decrease the volatility of portfolio returns.

Leverage is obviously another example. And as we have seen with the previous post, increasing position sizing at higher frequencies to have the same risk: reward as the lower timeframes simply increased your left end tail risk. A sudden spread-spike of 120 pips when you have a 100 pip stop loss at 1% of capital will hurt you less than if you have a 10 pip stop loss at 1% of capital.


These assumptions are not measuring the probability of an event occurring. Going long the previously mentioned imaginary stock at 10 may be lesser risky than shorting the same stock on paper, but if the stock is never going above 10 then the risks are clearly not equally weighted.

There are other risks involved with individual transactions. These include liquidity and regulatory risks, as well as completely unforeseen game-changers that could stem from anywhere.

It is arguable whether attempting to quantify probabilities of risk in such an unpredictable environment is worthwhile, but it seems to be productive as long as it is measured without getting too caught up in individual biases.

Left Tail Liquidity Risk

The foreign exchange market is quoted as being one of the most efficient and liquid financial markets. Yet the recent Swiss Franc unpegging from the Euro has shown what sort of movements can be caused by central bank intervention. Some were surprised to learn that many trend following hedge funds in fact lost out during the move, despite usually being mostly structured to limit the skewness of the left and eat the asymmetry of the right tails. Most trend followers survived the day due to their immense diversification, and some still even profited from also being short the Euro versus the Swiss Franc. Still, the risks can be highly destructive. This is the left-tail risk caused by a swift liquidity pull.

There is much research showing that asset returns and bid-ask spreads are fat-tailed (Koedijk et al., 1990; Hols and De Vries, 1991; Müller and Sgier, 1992; Loretan and Phillips, 1994; Ghose and Kroner, 1995, amongst the earliest) But for very high frequency data, the price uncertainty within the bid-ask spread becomes very important (Ramazan Gençay, Michel Dacorogna, Ulrich A. Muller, Olivier Pictet, and Richard Olsen, 2001).

Witness the foreign exchange market’s most liquid currency pair bid-ask spread sizes across the sample month of April 2015.

Exhibit 1. EURUSD
Exhibit 1. EURUSD

As can be observed, there are many extreme deviations from the bid-ask spread mean, with one instance in particular recording a spread of over 130 pips.

Using a tight stop loss with large leverage will not protect a high frequency strategy from the hidden liquidity risks, specifically since stop order slippage is all about the (lack of) liquidity.

Fortunately, most of these extreme deviations occur during large news releases such as NFP (Non-Farm Payrolls) or central bank decisions, but bear in mind that this will not always be the case. Therefore, decreasing position sizing around these times in particular and generally being careful of overall leverage can mitigate the risks. We will be exploring these factors for potential alpha extraction in the near future.

musings on edge seeking