Contracting for Financial Execution

Discussion by Andreas Park

Paper by Markus Baldauf, Christoph Frei, and Joshua Mollner

Problem

investors want to trade a large order with the help of a broker

Research Question

What is the optimal contract that the investor should offer?

Answer

investor should offer to pay the volume weighted average price

How do they get there?

t=0
t=0t=0
t=1
t=1t=1
t=2
t=2t=2
t=T
t=Tt=T
\ldots
\ldots
\ldots
\ldots

How do they get there?

t=0
t=0t=0
t=1
t=1t=1
t=2
t=2t=2
t=T
t=Tt=T
\ldots
\ldots
\ldots
\ldots

Contract offer

price

volume

p_1
p1p_1
V_1
V1V_1
p_2
p2p_2
V_2
V2V_2
p_T
pTp_T
V_T
VTV_T

How do they get there?

t=0
t=0t=0
t=1
t=1t=1
t=2
t=2t=2
t=T
t=Tt=T
\ldots
\ldots
\ldots
\ldots

Contract offer

price

volume

p_1
p1p_1
V_1
V1V_1
p_2
p2p_2
V_2
V2V_2
p_T
pTp_T
V_T
VTV_T
\textit{payment}=
payment=\textit{payment}=
\textit{function}(p_1,\ldots,p_T; V_1,\ldots,V_T)
function(p1,,pT;V1,,VT)\textit{function}(p_1,\ldots,p_T; V_1,\ldots,V_T)

Key components

V_t=\text{exogenous volume}+\text{broker volume}=v_t+x_t
Vt=exogenous volume+broker volume=vt+xtV_t=\text{exogenous volume}+\text{broker volume}=v_t+x_t
p_t=\text{concave function}(v_t,x_t)=\left(\frac{x_t}{v_t}\right)^\alpha+\text{noise}_t
pt=concave function(vt,xt)=(xtvt)α+noisetp_t=\text{concave function}(v_t,x_t)=\left(\frac{x_t}{v_t}\right)^\alpha+\text{noise}_t

Key components of time-line

t=0
t=0t=0
t=1
t=1t=1
t=T
t=Tt=T

Contract offer

broker learns all exogenous volume v1,...,vT

investor pays broker

trades occur with temporary price impact

Objective functions

Broker

observe volume and then choose order size to maximize expected utility

accept contract if expected utility > reservation utility

\text{at }t=0~~~~~~~~~~~~~~~
at t=0               \text{at }t=0~~~~~~~~~~~~~~~
\text{at }t\in\{1,\ldots,T\}
at t{1,,T}\text{at }t\in\{1,\ldots,T\}

Investor

propose contract that minimizes trading cost

\text{at }t=0~~~~~~~~~~~~~~~
at t=0               \text{at }t=0~~~~~~~~~~~~~~~

payment occurs at T

Main Results

Lemma 1

If the investor could trade itself, it would follow the VWAP relative to the exogenous volume.

Theorem 1

The VWAP contract is optimal, and under reasonable conditions uniquely so.

Key Model Features

broker assumes the risk when it accepts the contract*

*except in a "degenerate" case

orders have only transitory price impact 

no sense of urgency or time preferences

Four ways to trade

pure agency => broker decides

direct market access

broker internalizes and takes risk

broker matches customer orders

The model covers

pure agency => broker decides

direct market access

broker internalizes and takes risk

broker matches customer orders

The model covers

Source: Nomura Research Institute, “Asset Management Companies’ Evaluation of Brokers” April 2014 (cited by the authors); for Japanese data

Canada: 10-15% of daily $-volume

Pricing

pure agency => broker decides

direct market access

broker internalizes and takes risk

broker matches customer orders

common: single ex ante price

common:

  • "give me the VWAP"
  • "small IS, please"

Bottom Line

  • Setup doesn't yet quite match institutions

    • subtle: in reality, we often see "give me the VWAP" as instructions for agency trades

    • But paper's premise is an incentive contract, not "instructions"

    • In paper, "the first-best trading policy [...] fully insulates the broker from risk" is an outcome, in reality risk is not part of the discussion.
    • => cannot say that the model explains why VWAP is used for agency.

    • And risk trades commonly have fixed prices

  • This matters in terms of the applicability and interpretation of the results as the paper develops. 

  • Way forward: decide what kind of paper to write => several options...

Option 1:

focus on risk trades

  • write a normative paper:

    • show that paper's setup is welfare maximal for "risk trades"

    • how that and how frictions (e.g., regulation) interfere with optimality

Option 2:
focus on agency trades

  • expand to match institutions

    • true agency trades (broker executes but takes no risk)

    • competing brokers

    • repeated interactions

  • show conditions such that VWAP is optimal iff trade has no price impact
    • e.g., timing no concern 

  • show conditions such that implementation shortfall is optimal
    • e.g., timing & impact are concerns

@financeUTM

andreas.park@utoronto.ca

slides.com/ap248

sites.google.com/site/parkandreas/

Discussion of "Contracting for Financial Execution"

By Andreas Park

Discussion of "Contracting for Financial Execution"

This is a deck that I used at the 2018 Bank of Canada -Laurier workshop on market microstructure in May 2018.

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