Marius Zoican
Finance professor at University of Toronto. Interested in securities exchanges, technology, and investments.
Michael Brolley and Marius Zoican
FMA 2020 October 22, 2020
Liquid speed:
a congestion fee for low-latency exchanges
Motivation
Who really needs to trade at warp speed?
- HFTs participate in markets at blistering speeds, providing price discovery as both makers and takers (Brogaard, Hendershott and Riordan, 2019).
- HFTs also race to capture latency arbitrage rents in zero-sum games (Budish,Cramton, & Shim, 2015).
- Speed inequality can adversely effect liquidity (Shkilko & Sokolov, 2020).
- Is this really welfare-enhancing? (Biais, Foucault, & Moinas, 2015).
- Should we tinker with or overhaul our market design? (Baldauf & Mollner 2020; Brolley & Cimon 2020; Haas,Khapko, & Zoican 2020).
How much speed do we really need?
Exchanges and micro-bursts: a love-hate relationship
HFT races drive up exchange costs...
- ~20% of transactions on Nasdaq and LSE occur in "micro-bursts'' that sum to 0.05s of average trading day
- Throughput on a random day is 3.21M msg/s; 25.2M msg/s during micro-bursts
- Excess capacity to service a small fraction of up time.
...but is that enough to stop them?
- Exchanges charge HFTs for "co-location": revenues between $874M-$1024M in 2018
- Co-location revenue on par with trading fees revenue.
Our paper
- Main idea: Surge pricing of speed (à la Uber).
- How? Implement a congestion fee on liquidity taking orders.
- Charge a uniform fee to each liquidity-taking order message whenever there are multiple take orders in a short time interval.
- Fee level the number of take orders, surging during micro-bursts.
- Latency arbitrage externalities are (partially) priced in.
- A system that is incentive-compatible for exchanges.
\uparrow
Status quo: Latency arbitrage rent-sharing
Ideal world: No latency arbitrage rents
Our idea: Incentive-compatible rent transfer from HFTs to investors
Model
Asset
- One risky asset, for which news arrive at Poisson rate . It pays off:
\eta
\tilde{v}=\begin{cases}
v+\sigma, & \text{if ``good news'' arrives} \\
v-\sigma, & \text{if ``bad news'' arrives} \\
v, & \text{if no news arrives}.
\end{cases}
Traders
- risk-neutral high-frequency traders (HFT) who submit market or limit orders.
- Liquidity investors (also risk neutral), arrive at the market with Poisson rate .
- Liquidity investors only submit market orders are equally likely to buy/sell.
H\geq 3
\mu
Congestion fee
If HFT "snipers'' submit a marketable order simultaneously, each is charged a fee
k\geq 2
f\left(k\right)=\begin{cases}
\phi \left(k-1\right) & \text{ if } k\geq 2 \\
0 & \text{ if } k=1.
\end{cases}
- Congestion fee number of liquidity-taking orders received by the exchange in a short time interval (100 s to 10 ms).
- Single marketable order arrives congestion fee is zero.
- Congestion fees are computed from intraday, but charged daily (or monthly, even).
- Unlikely that liquidity traders pay congestion fees. Estimated total duration of HFT races in FTSE100 stocks:
\propto
\mu
\Rightarrow
537 \text{ races/day} \times 81 \text{ $\mu$s/race} = 0.043 \text{ seconds/day}.
Model sequence of events
HFTs post quotes at t=0.
Afterwards, nothing happens until a "trigger event:''
- either news arrives, triggering a race between HFTs (probability ), or
- a liquidity trader arrives at the market (with probability ).
\delta=\frac{\eta}{\mu+\eta}
1-\delta=\frac{\mu}{\mu+\eta}
Finding an equilibrium
HFTs determine:
- Liquidity ( ): the half-spread posted by the HFM.
- Race intensity ( ): probability of an HFS to race on stale quotes.
s^\star
p
^\star
HFT expected profits (sum over random # of competitors in the race)
Impact of fee on liquidity and race intensity
- As the congestion fee increases ( ) liquidity improves. ( ).
- As the congestion fee increases ( ) sniping probability falls ( ).
- Similar dynamics for an increase in the number of HFTs ( ).
\phi\uparrow
\Rightarrow
\phi\uparrow
\Rightarrow
s^\star\downarrow
p^\star\downarrow
H\uparrow
Congestion fee revenue
What about fee revenues?
\text{Fee revenues}=\delta \sum_{j=2}^{H-1} \binom{H-1}{j} \left(p^{\star}\right)^j (1-p^\star)^{H-1-j} j \times \phi \left(j-1\right)
= \delta \phi \left(H-2\right)\left(H-1\right) \left(p^\star\right)^2
- Direct effect: implies higher revenues for each trade;
- Indirect effect: reduces HFT incentives to snipe less intense races.
\phi \nearrow
\phi \nearrow
\Longrightarrow
How would an exchange set ?
\phi
Congestion fees make exchanges better off
A regulator’s optimal fee choice
Conclusions
- Implement a "surge pricing of speed'' (a la Uber) on liquidity taking orders.
- Charge HFTs a fee whenever there are multiple liquidity-taking orders in a short time interval.
- Quick calibration indicates fee in the range of 15%-35% relative to the average arbitrage opportunity. (using Aquilina, Budish, and O'Neill, 2020).
- Latency arbitrage externalities are (partially) priced in.
- Incentive-compatible for exchanges (i.e., competition-proof vs. co-location fees).
Conclusions
Liquid Speed: A Congestion Fee for Low-Latency Exchanges
By Marius Zoican
Liquid Speed: A Congestion Fee for Low-Latency Exchanges
FMA conference presentation on October 22, 2020.
