Ian Thorpe vs. Eddie the Eel or Federer vs. Djokovic?

TLDR

The vast majority of contested trades could go either way for a given set of participants involved. There is sufficient noise in the system (on the side of the exchange and/or on the side of the participants so that participants have reasonable win rates against many other participants

Introduction

The outcome of a tennis match between Roger Federer and myself would be pretty certain whereas a match between Federer and Novak Djokovic can go either way.

This is a follow-up on my post from last week where we found that only a minority of all trades are contested, i.e., have a winner and at least one loser. Here we only consider these contested trades. Given that participant A and participant B both go for the same opportunity, for all possible A's and B's, what is the distribution of win rates (where "win" means that the order reaches the exchange first)?

Consider the following limiting cases:

1. All participants have a fixed and distinct latency - there is a linear hierarchy. Then the outcome of each race between a given set of participants is certain. One participant would have a win rate of 100% against the other participant, the other would have a win rate of 0%. The distribution of the win rates of all possible pairings is bimodal with 0 and 100% being the only values.
2. All participants have exactly the same latency and the outcome of the race is only due to random effects. All possible pairings would then have a 50% win rate.
3. There are two groups of participants with different latencies between the groups but identical latencies within each group. If the groups have the same number of participants, then 50% of all pairings have a 100% (or 0%) win rate and half have a 50% win rate. The distribution of win rates would be trimodal with values at 25%, 50%, and 75%.

Methodology

We extract a list of all trades on Xetra and Eurex including any subsequent IOC misses within 1 ms which targeted any of the traded levels by the winner. Misses by the winner are ignored as are duplicate misses by the same participant.

From all trades, we then only look at events where

• the trade was initiated by an IOC order
• the event had at least one IOC miss

We then decompose each event into a series of dyadic interactions. Assume an event had a winner and multiple losers, e.g. W/L1/L2/L3. We also count the pairings between the losers as interactions. This single event then gives us the following samples (winner, loser): (W, L1), (W, L2), (W, L3), (L1, L2), (L1, L3), (L2, L3).

For each pair of distinct participants we can then compute the win rate. Win rates which are based on less than 100 interactions are ignored.

Why do we only consider events that were initiated by an IOC order? Because also allowing non-IOC orders would introduce a bias. Consider a participant who never sends IOCs. He then would never lose. His orders either win or enter the book, but never miss.

And finally we need to consider that not all participants are equally active. So, A & B might have 10,000 interactions but X & Y only competed 100 times against each other. Should we weight both equally or weigh them by the number of occurrences?

Results

Fig. 1 below shows the distribution of win rates. Eurex and Xetra are is shown in dark and light blue, respectively. Win rates are weighed by the number of interactions for the dashed lines. So, given there is a race, they represent the distribution of win rates. The solid lines, on the other hand, are appropriate when given a pair of participants.

We see that most races are pretty close. Very high and low win rates are uncommon mostly because there are much fewer interactions between very disparate participants (just like in tennis where Federer yet has to play against me but had plenty of matches against Djokovic).

The mostly flat equally-weighted solid curve is inconsistent with any of the three limiting cases described earlier. It is consistent with a scenario of a fuzzy linear ranking (not a technical term) where the win rate is close to 50% against participants just ahead or behind in the ranking, but tends to 0 and 100% with increasing rank difference.

PS: I never thought I would consult the journal Animal Behavior for terminology - "linear hierarchy", "dyadic interaction", "dominance matrix", ...

#eurex #xetra #hft #fpga #lowlatency #quantitativeresearch #microstructure #equitytrading #derivativestrading #animalbehavior