ETF Arbitrage under Liquidity Mismatch Kevin Pan Yao Zeng Discussant Shaun Davies – University of Colorado, Boulder

Leeds BUSINESS

Chapel Hill, NC

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This Paper I like this paper and I think it has potential in measuring a dimension of aggregate broker-dealer liquidity Yao is a great presenter, so I am not going to rehash the empirical results or restate the model The paper is pitched as if there is pseudo multi-task agency conflict (Holmstrom and Milgrom, 1991) APs have an ability to induce ETF price efficiency but may use that ability to manage their bond inventories Inventory management concerns may be so strong that APs abuse the ETF primary market and erode ETF price efficiency The current pitch is very tantalizing! But, while tantalizing, I don’t believe that is what is going on Yao and Kevin see Daisy Buchanan from the Great Gatsby, and I see an old woman Chapel Hill, NC

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Old Woman or Daisy Buchanan?

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Revisit the ETF Primary Market Mechanism ETFs are designed to maintain efficiency between the ETF price and the underlying assets’ value The creation/redemption process enables arbitrageurs to earn arbitrage profits. . . . . . the arbitrage profits are a means to restore relative price efficiency between the ETF and the underlying! IMPORTANTLY, this implies that relative price efficiency is restored by affecting the supply of shares outstanding Implicitly, the ETF mechanism assumes that ETF investors’ demand is downward sloping in the short-run Leeds BUSINESS

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The Model The paper’s existing model takes prices as exogenous And the model ignores the effect of competition It is important to consider the APs’ role in determining equilibrium prices via Cournot competition! In what follows, I provide and solve a model of ETF arbitrage with Cournot competition The model captures AP-level inventory imbalances Equilibrium share creation/redemptions quantities have important implications for how we interpret the empirical results! Leeds BUSINESS

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Theoretical Model

Theoretic Model Building Blocks Two period model A passively managed Corporate Bond ETF managed by a risk neutral, competitive provider (e.g., BlackRock) N Authorized Participants (APs) Each AP has a random (correlated?) initial bond inventory imbalance νi ∈ R The ETF mimics an underlying asset χ (e.g., the Barclays US Corporate High Yield Index) via full replication The initial number of ETF shares is of measure length q0 The ETF shares’ price pt is endogenously determined The underlying asset’s tradable value (i.e., NAV) per unit is πt (also endogenous) Leeds

ψt ≡ pt − πt ⇒ ETF premium Chapel Hill, NC

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Theoretical Model

Model Timing (1) The ETF and underlying asset are efficiently priced at t = 0 (a) AP Bond inventory imbalances are realized (b) Demand shock hits both ETF and underlying assets (but to different degrees), (c) APs step in and create (redeem) shares to exploit arbitrage (and manage inventory), (d) 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 Leeds BUSINESS

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Theoretical Model

ETF Share Pricing ETF investors’ collective demand is a downward-sloped curve, pt = −φqt + ǫt + α, φ ∈ R+ is the sensitivity of the ETF share price to changes in ETF 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. ǫt is a demand shock (ǫ0 = 0) α is an arbitrary constant that ensures initial share quantity is strictly positive Underlying asset NAV is π0 and p0 = π0 At t = 1, ǫ1 is drawn from g(ǫ1 ) on the support (−∞, ∞) Chapel Hill, NC

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Theoretical Model

Underlying Asset Pricing The N APs collectively create (redeem) ∆t shares to take advantage of the demand shift And APs trade to get closer to their bliss point inventory The tradable NAV price πt is a function of both ǫt and ∆t , πt = πt−1 + βǫt + λ∆t . β ∈ [0, 1] allows demand shocks to also affect the underlying assets λ relates buying (or selling) of underlying by arbitrageurs into price impact • For example, linear pricing rule in Kyle (1985) • Market makers that do not observe demand shock in ETF Leeds BUSINESS

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Theoretical Model

Arbitrage Activity Each AP’s optimal creation/redemption choice solves,
ϕ(νi − δi )2 maxδi ∈R δi p1 (δi + δ−i ) − π1 (δi + δ−i ) − , 2 | {z } | {z } Arbitrage Profits

Inventory Imbalance

AP’s choice partially internalizes effects on both the ETF and underlying asset prices AP’s choice fully internalizes effect on AP-specific inventory imbalances The equilibrium aggregate redemption/creation activity is, N P ϕ νi ǫN(1 − β) i=1 ∆= + (N + 1)(λ + φ) + ϕ (N + 1)(λ + φ) + ϕ | {z } | {z } Arbitrage Motive

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Inventory Motive

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Theoretical Model

Inventory Motive ϕ

N P

νi

i=1

(N + 1)(λ + φ) + ϕ This piece of the ETF arbitrage is the focal point of the paper The empirical results regarding this effect are solid Can the economic magnitudes of the empirical results be due to AP-level strategic actions? The average ETF in this sample has 44 APs and approximately half of them are active at any given time N  P Should E νi equal zero? i=1

When the realization is not equal to 0, what is going on?

Chapel Hill, NC

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Theoretical Model

Who Are the APs? State Street Global Advisors lists the following as their APs: Banca IMI Bluefin Europe LLP Citigroup Deutsche Bank AG Goldman Sachs Jane Street KCG Morgan Stanley Susquehanna Virtu Financial

BofA Merrill Lynch BNP Paribas Commerzbank Flow Traders HSBC Jefferies Kepler Cheuvreux Optiver UBS

Barclays Capital Cantor Fitzgerald Credit Suisse Goldenberg Hehmeyer LLP IMC JP Morgan Macquarie Société Générale Unicredit

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Theoretical Model

Bringing it Altogether & Concluding Thoughts The empirical results suggest that ETF arbitrage is affected by the ϕ

realization of

N P

νi

i=1

(N+1)(λ+φ)+ϕ

The authors pitch this as a pseudo multi-task agency conflict However, there are 20-44 APs (of which are the largest broker-dealers in the OTC space) trading this arbitrage There will only be an affect when inventory imbalances do not cancel out The effect seems to be driven by aggregate inventory imbalances Perhaps, the authors can use their results to think about a new measure of intermediary liquidity? Leeds BUSINESS

Chapel Hill, NC

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