ETF Short Interest and Failures-to-Deliver: Naked …...ETF Short Interest and Failures-to-Deliver: Naked Short-Selling or Operational Shorting? Richard B. Evans Rabih Moussawi Michael

LeedsB U S I N E S S

ETF Short Interest and Failures-to-Deliver:Naked Short-Selling or Operational Shorting?

Richard B. Evans

Rabih Moussawi

Michael S. Pagano

John Sedunov

Discussant

Shaun Davies – University of Colorado, Boulder

CFIC 2018 Page 1

CFIC 2018

This Paper


Understanding the arbitrage mechanism in ETFs is important for

participants, regulators, and academics

CFIC 2018 Page 2

CFIC 2018

This Paper




Concept of “operational shorting” is intuitive and compelling

CFIC 2018 Page 2

CFIC 2018

This Paper





A basic understanding of option value suggests it is almost

certainly a common practice

CFIC 2018 Page 2

CFIC 2018

This Paper







My discussion is twofold:

CFIC 2018 Page 2

CFIC 2018

This Paper








(1) For the Authors: Provide a parsimonious model of the ETF

arbitrage mechanism to discipline the empirical work and

provide new testable predictions

CFIC 2018 Page 2

CFIC 2018

This Paper











(2) For the Audience: Build the model from pseudo first

principles to build greater appreciation for ETFs in general

CFIC 2018 Page 2

CFIC 2018

This Paper











(2) For the Audience: Build the model from pseudo first

principles to build greater appreciation for ETFs in general

My Big Point: Operational shorting substitutes for pure AP

activity ⇒ Can authors examine the extent? What

about relative price efficiency?

CFIC 2018 Page 2

CFIC 2018

The ETF Primary Market Mechanism


ETFs are designed to maintain relative price efficiency between

the ETF shares and the underlying assets

CFIC 2018 Page 3

CFIC 2018





The creation/redemption process enables arbitrageurs to earn

arbitrage profits. . .

CFIC 2018 Page 3

CFIC 2018







. . . the arbitrage profits are a means to restore relative price

efficiency between the ETF and the underlying

CFIC 2018 Page 3

CFIC 2018









Importantly, this implies that relative price efficiency is restored by

affecting the supply of shares outstanding

CFIC 2018 Page 3

CFIC 2018











Implicitly, the ETF mechanism assumes that ETF investors’

demand is downward sloping in the short-run

CFIC 2018 Page 3

CFIC 2018











Implicitly, the ETF mechanism assumes that ETF investors’

demand is downward sloping in the short-run and/or demand for

the underlying is downward sloping in the short-run

CFIC 2018 Page 3

CFIC 2018 Theoretical Model

Theoretic Model Building Blocks


Two period model

CFIC 2018 Page 4




Two period model

A passively managed equity ETF managed by a risk neutral,

competitive provider (e.g., BlackRock)

CFIC 2018 Page 4




Two period model



N Authorized Participants (APs)

CFIC 2018 Page 4




Two period model




APs can exploit mispricing via creating/redeeming shares

CFIC 2018 Page 4




Two period model





APs can exploit mispricing via operational shorting

• APs incur quadratic risk cost (e.g., unhedged price

movements)

CFIC 2018 Page 4




Two period model







movements)

The ETF mimics an underlying asset χ (e.g., the S&P 500 Index)

CFIC 2018 Page 4




Two period model







movements)


The initial number of ETF shares is of measure length q0

CFIC 2018 Page 4




Two period model







movements)



The ETF shares’ price pt and underlying asset’s tradable value

(i.e., NAV) πt are endogenously determined

CFIC 2018 Page 4




Two period model







movements)



The ETF shares’ price pt and underlying asset’s tradable value

(i.e., NAV) πt are endogenously determined

ψt ≡ pt − πt ⇒ ETF premium

CFIC 2018 Page 4


Model Timing


(1) The ETF and underlying asset are efficiently priced at t = 0

(a) Demand shock hits both ETF and underlying assets (but to

different degrees),

(b) APs step in and exploit mispricing

(i) Create (redeem) shares to exploit arbitrage,

(ii) and/or operational shorting to exploit arbitrage

(c) AP arbitrage activity affects price levels of both ETF and

underlying asset,

(2) The ETF’s price and underlying asset’s NAV are established at

t = 1,

(a) The ETF premium is finalized

CFIC 2018 Page 5


ETF Share Pricing


ETF investors’ collective demand is a downward-sloped curve,

pt = −φqt + ǫt + α,

CFIC 2018 Page 6


ETF Share Pricing




φ ∈ R+ is the sensitivity of the ETF share price to changes in ETF

share quantity

CFIC 2018 Page 6


ETF Share Pricing





share quantity

Lower values of φ relate to better liquidity in the ETF shares,

e.g., larger investor base and less price impact from share

creation/redemption.

CFIC 2018 Page 6


ETF Share Pricing





share quantity




ǫt is a demand shock (ǫ0 = 0)

CFIC 2018 Page 6


ETF Share Pricing





share quantity





α is an arbitrary constant that ensures initial share quantity is

strictly positive

CFIC 2018 Page 6


ETF Share Pricing





share quantity






strictly positive

Underlying asset NAV is π0 and p0 = π0

CFIC 2018 Page 6


ETF Share Pricing





share quantity






strictly positive

Underlying asset NAV is π0 and p0 = π0

t = 1: ǫ1 is drawn from g(ǫ1) on the support (−∞,∞)

CFIC 2018 Page 6


Underlying Asset Pricing


The APs collectively affect demand for shares and underlying

CFIC 2018 Page 7





Each AP i chooses δAPi shares to create/redeem and δOS

i to

operationally short

CFIC 2018 Page 7






i to

operationally short

Total quantity to affect ETF demand is

∆APt +∆OS

t ≡N∑

i=1

(δAP

i + δOSi

)

Total quantity to affect underlying demand is ∆APt ≡

N∑

i=1

δAPi

CFIC 2018 Page 7






i to

operationally short


∆APt +∆OS

t ≡N∑

i=1

(δAP

i + δOSi

)


N∑

i=1

δAPi

The tradable NAV price πt is a function of both ǫt and ∆APt ,

πt = πt−1 + βǫt + λ∆APt .

CFIC 2018 Page 7






i to

operationally short


∆APt +∆OS

t ≡N∑

i=1

(δAP

i + δOSi

)


N∑

i=1

δAPi



β ∈ [0,1] allows demand shocks to also affect the underlying

assets

CFIC 2018 Page 7






i to

operationally short


∆APt +∆OS

t ≡N∑

i=1

(δAP

i + δOSi

)


N∑

i=1

δAPi




assets

λ relates buying (or selling) of underlying by arbitrageurs intoprice impact

CFIC 2018 Page 7






i to

operationally short


∆APt +∆OS

t ≡N∑

i=1

(δAP

i + δOSi

)


N∑

i=1

δAPi




assets

λ relates buying (or selling) of underlying by arbitrageurs intoprice impact

• For example, linear pricing rule in Kyle (1985)CFIC 2018 Page 7


Arbitrage Activity


Each AP’s optimal creation/redemption choice solves,

maxδAP

i,δOS

i∈R

δAPi

(

p1(δAPi + δOS

i + δAP−i + δOS

−i )− π1(δAPi ++δAP

−i ))

︸︷︷︸

AP Activity Profits

+ δOSi

(

p1(δAPi + δOS

i + δAP−i + δOS


−i ))

︸︷︷︸

Operational Shorting Profits

− ωδOS

i

2

2︸︷︷︸

Operational Shorting Risk

CFIC 2018 Page 8


Arbitrage Activity


Each AP’s optimal creation/redemption choice solves,

maxδAP

i,δOS

i∈R

δAPi

(

p1(δAPi + δOS

i + δAP−i + δOS


−i ))

︸︷︷︸

AP Activity Profits

+ δOSi

(

p1(δAPi + δOS

i + δAP−i + δOS


−i ))

︸︷︷︸

Operational Shorting Profits

− ωδOS

i

2

2︸︷︷︸

Operational Shorting Risk

AP’s choice partially internalizes effects on both the ETF and

underlying asset prices

CFIC 2018 Page 8


Equilibrium AP Trades


Assume ω ≥ λ for tractability

CFIC 2018 Page 9





The equilibrium AP-level redemption/creation and aggregate

redemption/creation activity are,

δAPi =

(1 − β)(ω − λ)ǫ

(N + 1)ω(λ+ φ)− Nλ2, ∆AP =

N(1 − β)(ω − λ)ǫ

(N + 1)ω(λ+ φ)− Nλ2

δOSi =

(1 − β)λǫ

(N + 1)ω(λ+ φ)− Nλ2, ∆OS =

N(1 − β)λǫ

(N + 1)ω(λ+ φ)− Nλ2

CFIC 2018 Page 9





The equilibrium AP-level redemption/creation and aggregate

redemption/creation activity are,

δAPi =

(1 − β)(ω − λ)ǫ

(N + 1)ω(λ+ φ)− Nλ2, ∆AP =

N(1 − β)(ω − λ)ǫ

(N + 1)ω(λ+ φ)− Nλ2

δOSi =

(1 − β)λǫ

(N + 1)ω(λ+ φ)− Nλ2, ∆OS =

N(1 − β)λǫ

(N + 1)ω(λ+ φ)− Nλ2

Equilibrium premium is given by:

ψt ≡ pt − πt =(1 − β)ω(λ+ φ)ǫ

(N + 1)ω(λ+ φ)− Nλ2

CFIC 2018 Page 9


Comparative Statics of AP and OS Activity


(1) ↑ λ⇒ ↑ ∆OS and ↓ ∆AP

CFIC 2018 Page 10




(1) ↑ λ⇒ ↑ ∆OS and ↓ ∆AP

More price impact in underlying, more operational shorting

and less AP activity

EP: Less liquid underlying should be characterized by more

operational shorting and less AP activity (substitution effect)

CFIC 2018 Page 10




(1) ↑ λ⇒ ↑ ∆OS and ↓ ∆AP





(2) ↑ ω ⇒ ↓ ∆OS and ↑ ∆AP

CFIC 2018 Page 10




(1) ↑ λ⇒ ↑ ∆OS and ↓ ∆AP





(2) ↑ ω ⇒ ↓ ∆OS and ↑ ∆AP

Larger cost to operational shorting, less operational shorting

and more AP activity

EP: Hard to hedge underlying should be characterized by less

operational shorting and more AP activity (substitution effect)

CFIC 2018 Page 10




(1) ↑ λ⇒ ↑ ∆OS and ↓ ∆AP





(2) ↑ ω ⇒ ↓ ∆OS and ↑ ∆AP





(3) ↑ φ⇒ ↓ ∆OS and ↓ ∆AP

CFIC 2018 Page 10




(1) ↑ λ⇒ ↑ ∆OS and ↓ ∆AP





(2) ↑ ω ⇒ ↓ ∆OS and ↑ ∆AP





(3) ↑ φ⇒ ↓ ∆OS and ↓ ∆AP

More inelastic demand for ETF shares, less operational

shorting and less AP activity

EP: Liquid ETFs with diverse clienteles should have

more operational shorting and more AP activity

CFIC 2018 Page 10


Comp. Statics of AP and OS Activity (cont)


(1) ↑ β ⇒ ↓ ∆OS and ↓ ∆AP

CFIC 2018 Page 11




(1) ↑ β ⇒ ↓ ∆OS and ↓ ∆AP

More similar clienteles for ETF shares and underlying, less

operational shorting and less AP activity

EP: More similar ownership, e.g., institutional ownership of

underlying relative to institutional ownership of ETF shares,

should have relatively less operational shorting and less AP

activity

CFIC 2018 Page 11




(1) ↑ β ⇒ ↓ ∆OS and ↓ ∆AP






activity

(2) ↑ N ⇒ ↑ ∆OS and ↑ ∆AP

CFIC 2018 Page 11




(1) ↑ β ⇒ ↓ ∆OS and ↓ ∆AP






activity

(2) ↑ N ⇒ ↑ ∆OS and ↑ ∆AP

More APs, internalize a smaller fraction of AP and OS activity

and trade more

EP: ETFs with more APs should have relatively more

operational shorting and more AP activity

Model is generally consistent with paper!

CFIC 2018 Page 11


Comp. Stats ETF Premium - Relative Efficiency


(1) ↑ λ⇒ ↑ ψt

CFIC 2018 Page 12




(1) ↑ λ⇒ ↑ ψt

(a) More price impact in underlying, AP activity is substituted for,

but not fully

CFIC 2018 Page 12




(1) ↑ λ⇒ ↑ ψt


but not fully

(2) ↑ ω ⇒ ↓ ψt

CFIC 2018 Page 12




(1) ↑ λ⇒ ↑ ψt


but not fully

(2) ↑ ω ⇒ ↓ ψt

(a) Larger cost to operational shorting, greater resulting AP

activity is more effective in restoring relative price efficiency

(b) Price impact on both the underlying and the ETF shares

CFIC 2018 Page 12




(1) ↑ λ⇒ ↑ ψt


but not fully

(2) ↑ ω ⇒ ↓ ψt




(3) ↑ φ⇒ ↓ ψt

CFIC 2018 Page 12




(1) ↑ λ⇒ ↑ ψt


but not fully

(2) ↑ ω ⇒ ↓ ψt




(3) ↑ φ⇒ ↓ ψt

(a) More inelastic demand for ETF shares ⇒ bigger price impact

on ETF shares, better relative price efficiency

CFIC 2018 Page 12




(1) ↑ λ⇒ ↑ ψt


but not fully

(2) ↑ ω ⇒ ↓ ψt




(3) ↑ φ⇒ ↓ ψt



(4) ↑ β ⇒ ↓ ψt

CFIC 2018 Page 12




(1) ↑ λ⇒ ↑ ψt


but not fully

(2) ↑ ω ⇒ ↓ ψt




(3) ↑ φ⇒ ↓ ψt



(4) ↑ β ⇒ ↓ ψt

(a) More similar clienteles, better relative price efficiency

CFIC 2018 Page 12




(1) ↑ λ⇒ ↑ ψt


but not fully

(2) ↑ ω ⇒ ↓ ψt




(3) ↑ φ⇒ ↓ ψt



(4) ↑ β ⇒ ↓ ψt


(5) ↑ N ⇒ ↓ ψt

CFIC 2018 Page 12




(1) ↑ λ⇒ ↑ ψt


but not fully

(2) ↑ ω ⇒ ↓ ψt




(3) ↑ φ⇒ ↓ ψt



(4) ↑ β ⇒ ↓ ψt


(5) ↑ N ⇒ ↓ ψt

(a) More APs, better relative price efficiency

CFIC 2018 Page 12


Bringing it Altogether & Concluding Thoughts


Operational shorting substitutes for traditional AP

creation/redemption activity

CFIC 2018 Page 13






Operational shorting is not as effective in restoring price efficiency

CFIC 2018 Page 13







Creation/redemption activity puts price pressure on both the

underlying assets and the ETF shares

CFIC 2018 Page 13









Caveat: requires that price impact on underlying assets viahedging is not equal to outright purchase of underlying

CFIC 2018 Page 13










• Derivative-based ETFs’ price efficiency may be the same with

operational shorting versus without (because the underlyingasset is the same/or similar to the hedging instrument)

CFIC 2018 Page 13










• Derivative-based ETFs’ price efficiency may be the same with

operational shorting versus without (because the underlyingasset is the same/or similar to the hedging instrument)

Authors may find interesting results looking at the composition of

arbitrage activity (fraction that is operational shorting and fraction

that is traditional AP creation/redemption activity)

CFIC 2018 Page 13

ETF Short Interest and Failures-to-Deliver: Naked …...ETF Short Interest and Failures-to-Deliver: Naked Short-Selling or Operational Shorting? Richard B. Evans Rabih Moussawi Michael

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