Marius Zoican PRO
I am an Associate Professor of Finance and Canada Research Chair in Financial Technology at the University of Calgary’s Haskayne School of Business. My research sits at the intersection of technology and finance.
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.
