1cm Central Bank Driven Mispricing

Central Bank–Driven Mispricing

L. Pelizzon, M.G. Subrahmanyam, D. Tomio, J. UnoGoethe University, Stern School of Business, Darden School of Business, Waseda University

For presentation at the conference “Quantitative Easing and Financial (In)Stability”Frankfurt, Monday, April 1, 2019

Central Bank–Driven Mispricing

Central bank open-market interventions aim at affecting:I Level, slope, and curvature of the yield curve

I The equity risk premium

The side effects of such operations affect a continuum of quasi-arbitrage and arbitragerelationships:I Across securities with correlated cash flows (e.g., bonds and IRS)

I Across securities with partially overlapping cash flows (ECB-targeted bonds and the others)

I Across securities with identical cash flows (futures contract and underlying bonds).

L. Pelizzon, M.G. Subrahmanyam, J. Uno, D. Tomio Central Bank–Driven Mispricing 1 / 47

ECB Quantitative Easing

I Massive asset purchases by all major global central banks: FED, ECB, BoJ, BoE, etc.

I The ECB purchased between e 48 and e 80 billion of bonds a month under the AssetPurchase Program (APP) since March 2015 (currently, e 30bn from January 2018).

I First intervention targeting bonds issued by all countries.

I On average, e 9 billion spent on Italian and German sovereign bonds, for each month, foreach country, in the cash market, during 2015-2017.

I Significant potential disruptions? E.g., swap spreads, repo rates, central bank deposit rates,CCBSS, CDS-bond basis, futures-cash basis...

I The sizable intervention was accompanied by major changes in regulation of financialinstitutions, i.e., capital ratios (capital adequacy, leverage ratios, liquidity coverage ratio,NSFR), proprietary trading, etc.


Our Questions

On Market Neutrality

“One key principle [...] of the PSPP is the minimisation of unintended consequences. This can beensured by obeying the concept of market neutrality of our operations[, that is,] while we dowant to affect prices, we do not want to suppress the price discovery mechanism.”—Benoît Cœuré, Member of the Executive Board of the ECB

Can central bank interventions be market neutral?

What effect did QE have on bonds’ relative pricing?

To answer these questions, we choose the arbitrage between sovereign bond futures and the cashbond because:I It requires the least amount of assumptionsI It is the lowest cost arbitrage


Why should we care?

Price informativeness and market neutrality:I Prices should be informative. Dislocations in prices would indicate that they are not.I German and Italian debt account for 50% of the $10tr European sovereign debt.

Quantifying the transfer to financial institutionsI Bond purchases are transfers from tax payers to bondholders. In Europe, tax payers hold a

significant amount of bonds.I However, Central bank–driven mispricings are transfers from taxpayers to arbitrageurs.I ECB could have affected the rates all the same, but spending less. We propose a

market-neutral QE implementation strategy.Model-free analysis:I Any intervention detaches rates from their “natural level,” such a level is unknowable.I Relative pricing is measurable, needs no counterfactual and requires trivial assumptions.


Bond Purchases by the ECB

0

2.5

5

7.5

10

12.5

15

17.5

20

Euro

(Bn)

01/2013 01/2014 01/2015 01/2016 01/2017Date

ITDEQE

Monthly Central Bank Bond Purchases

I ECB purchases more German than Italian bonds, in absolute terms.


Bond Purchases by the ECB

0

2.5%

5%

7.5%

10%

12.5%

15%

17.5%

20%

% o

f Out

stan

ding

Am

ount

01/2013 01/2014 01/2015 01/2016 01/2017Date

ITDEQE

Cumulative Central Bank Bond Holdings

I Proportionally, ECB purchases more German than Italian bonds.I Bunds became scarcer than BTPs.I Main explanatory variable.


Futures-Bond Basis-.2

-.10

.1.2

.3.4

.5Eu

ro

01/2013 01/2014 01/2015 01/2016 01/2017Date

ITDEQE

Basis Between Cash and Futures

I Basis widens during the QE, more so for Germany.


Futures-Bond Basis

0.0

5.1

.15

% o

f Out

stan

ding

Am

ount

0

0.5%

1%

1.5%

Pct

01/2013 01/2014 01/2015 01/2016 01/2017Date

Futures-Bond Basis % of bonds held by the ECB Quantitative Easing



Futures-Bond Basis

0.0

5.1

.15

.2%

of O

utst

andi

ng A

mou

nt

0

0.5%

1%

1.5%

2%

2.5%

Pct

01/2013 01/2014 01/2015 01/2016 01/2017Date

Futures-Bond Basis % of bonds held by the ECB Quantitative Easing



Findings

While the ECB’s quantitative easing (QE) interventions were aimed at, and succeeded in,lowering bond yields, they impeded the price discovery process:I QE drove a wedge between the sovereign cash bond and the corresponding futures contract,

directly, and indirectly through:1. Increased bond bid-ask spread2. Lower repo rates3. Increased dispersion in repo rates

I We estimate that 35% of the mispricing stems from the direct effect, and 4% from theliquidity, 57% from the repo rate, and 4% from the repo dispersion channels.

I Regulatory restrictions kept arbitrageurs from closing the mispricing.

I Central bank intervention cannot be market neutral unless either of two conditions is true:I All markets are targeted, i.e., the ECB takes arbitrage into considerationI Regulatory constraints are relaxed, allowing traders (mainly banks) to arbitrage the mispricing.

I A financial whack-a-mole problem!


Outline of the Presentation

I ECB Interventions

I The Arbitrage Mechanism

I Data

I Net Basis

I The Indirect Effects of the ECB Intervention on the Basis

I The Direct Effect of the ECB Intervention on the Basis

I The Arbitrage Opportunities

I Opportunity and Regulatory Costs

I Conclusions


Literature Review

I Pelizzon, Subrahmanyam, Tomio, and Uno (WP, 2014): Effect of SMP and LTRO on themispricing between BTP cash and futures and liquidity spillovers between markets.

I Buraschi, Menguturk, and Sener (RFS, 2014): Effect of FED interventions (TARP, TALF)on the basis between sovereign bonds in different currencies.

I Pelizzon, Subrahmanyam, Tomio, and Uno (JFE, 2016): ECB Intervention and marketliquidity.

I Corradin and Rodriguez-Moreno (ECB-WP, 2016): ECB mandated margin changesaffected the basis between sovereign bonds in different currencies.

I Corradin and Maddaloni (ECB-WP, 2017): ECB-purchased bonds had higher specialnessin the repo market and were more likely to be involved in failing-to-deliver.

I Pasquariello (RFS, 2017): Show theoretically that mispricing between assets (one of themtargeted by a central bank) arose from the uncertainty in the price the central bank targets.

I Song and Zhu (JFE, 2018): Fed purchases cheaper bonds, increasing efficient pricing



I ECB Interventions


I Data

I Net Basis





I Conclusions


ECB Intervention Characteristics

After 2010, an array of interventions were conducted.

SMPI Security Market

ProgrammeI Direct Bond PurchasesI Italy and SpainI Aug 2011 – Feb 2012

LTROI Long Term Refinancing

OperationsI Bank Liquidity ProvisionI All participating banksI Dec 2011 – Feb 2012

PSPPI Public Sector Purchase

ProgrammeI Direct Bond PurchasesI All European SovereignsI March 2015 – ...

SMP and PSPP intervened in the market directly. PSPP is the largest component of the AssetPurchase Programme (APP)

We focus on the PSPP, as its effects are not confounded by the market turmoil of 2011/2012.


ECB had mispricing on its mind

From the speech by Benoît Cœuré, Member of the Executive Board of the ECB, at the SecondInternational Conference on Sovereign Bond Markets, Frankfurt, 10 March 2015.

On Market Neutrality

One key principle underlying the implementation of the PSPP is the minimisation of unintendedconsequences. This can be ensured by obeying the concept of market neutrality of our operations[,that is,] while we do want to affect prices, we do not want to suppress the price discoverymechanism. Wewill operationalise this principle by ensuring a high degree of transparency aroundour interventions and by closely monitoring their impact on liquidity and collateral availability.

On the Future-Bond Basis

[...] We will take particular care to avoid exacerbating any existing market frictions. Morespecifically, we will try to avoid, to the extent possible, purchasing specific securities suchas current cheapest-to-deliver bonds underlying futures contracts, securities commanding“special” rates in the repo market as a sign of temporary scarcity, and other assets displayingsignificant liquidity shortages.

Did the ECB succeed in these objectives?



I ECB Interventions


I Data

I Net Basis





I Conclusions


Set up

Net Basis = Adjusted Forward Bond Price − Futures Equivalent Price

Tradeable Basis = Net Basis −Market Frictions ≥ Regulatory Costs

Market Frictions = Market Liquidity + Repo Cost (Overnight + Term Effects)

I Market frictions include transaction costs and cost of carry (repo rate).

I Regulatory costs represent opportunity costs which are a function of the shadow price ofbalance sheet usage due to capital adequacy ratio, liquidity coverage ratio, NSFR, leverageratio, VaR considerations (present VaR and mark-to-market risk) and limits to portfolionotional.


The Futures Contract

I Fairly standardized contract, similar across all major countries, e.g., the US, Japan, India,the UK, Germany, France, and Italy.

I A bond futures contract is an exchange-traded instrument, whereby the futures seller agreesto deliver a bond to the futures buyer by the delivery date.

I The price the buyer pays is decided on the trade date.

I The traders’ positions are marked-to-market every day.

I Each contract requires delivery of bonds for a total of e 100,000 in face value.

I Bonds that are deliverable by investors who are short in the futures contract need to satisfya set of requirements. For the Italian bond futures contract, for example, bonds need to:I Have less than 16 years to maturity at issuanceI Have between 8.5 and 11 years to maturity at deliveryI Have an issue amount larger than e 5 billions.

I Similar requirements for German and French contracts.

I Prices of deliverable bonds differ, but are made comparable with conversion factors, whichare (currently) determined at a 6% yield.


The Arbitrage Trade

An arbitrageur would take advantage of mispricing as follow, if the cash bond is “rich”:

1. At trade date t: Go long the futures contract.2. At trade date t: “Borrow” the bond on the repo market.3. At trade date t: Sell the bond.4. At delivery date T : Receive the bond from the short side of the futures contract.5. At delivery date T : Close the repo transaction by delivering the bond.

I An arbitrageur who already owns the bond would simply sell it and buy the futures contract.I We consider the arbitrage trade with the highest trading cost, to be conservative, i.e., a

trader starting with no position, trading at (not inside) the spread.


The Arbitrage Profit

I Futures contract to deliver a bond.I Typically, the futures trade at a slight discount, due to many frictions (repo costs, funding

constraints, bid-ask spreads...). The reverse is less likely, due to lesser frictions.I Most often profitable: Sell a bond, buy futures contractI Details: Conversion factor, repo rate, CTD.I Basis:

Basist = (Bt + At+2)

(1 +

T − (t + 2)360

rt)− AT︸︷︷︸

Forward Bond Price

− Ft · CFb︸︷︷︸Futures

Equivalent

I At time t, B is bond price, At+2 is the accrued coupon at settlement date, AT is the accruedinterest at delivery date, rt the risk free rate, Ft the futures price, and CFb the conversionfactor for bond b.

I We calculate Basisi,t,m,b per country i, day t, trading minute m and (cheapest) deliverablebond b. We select the basis for the CTD bond, Basisi,t,m = mini

{Basisi,t,m,b

}and average

throughout the day. The dependent variable, for each day t, is

Basisit =1M

∑m

Basisi,t,m


CTD Identification

I For the average delivery, the bond we identify as CTD is the cheapest in 99% (96%) oftrading minutes for Germany (Italy)

Germany ITDelivery Bond % CTD Bond % CTD

201303 DE0001135465 99.938% IT0004848831 99.686%201306 DE0001135465 99.669% IT0004848831 67.326%201309 DE0001135473 99.901% IT0004848831 97.086%201312 DE0001135473 99.966% IT0004848831 89.498%201403 DE0001102309 99.926% IT0004848831 99.802%201406 DE0001102309 99.965% IT0004898034 99.866%201409 DE0001102325 86.357% IT0004898034 99.893%201412 DE0001102325 99.966% IT0004356843 99.747%201503 DE0001102333 99.654% IT0004953417 99.532%201506 DE0001102333 99.910% IT0004953417 99.399%201509 DE0001102358 99.816% IT0004513641 98.875%201512 DE0001102366 99.562% IT0004513641 76.382%201603 DE0001102374 99.808% IT0004513641 99.657%201606 DE0001102374 99.059% IT0004513641 99.872%201609 DE0001102382 98.648% IT0004644735 99.895%201612 DE0001102382 99.558% IT0004644735 99.981%201703 DE0001102390 99.991% IT0004644735 99.935%

Average 98.923% 95.672%Median 99.816% 99.686%


Arbitrage Costs

Basist = (Bt + At+2)

(1 +

T − (t + 2)360

rt)− AT︸︷︷︸

Forward Bond Price

− Ft · CFb︸︷︷︸Futures Equivalent

Standard definition of basis allows for a first-order effect:I Sheer buying pressure increases Bt

Is the net basis affected by the ECB bond purchases?

The standard definition of basis ignores significant costs:I Selling the bond does not take place at the bond midquote, but at the bid.I Borrowing the bond does not result in a gain of rf .I The term repo rate is generally increasing in the repo term. If a term repo is not available,

the arbitrageur faces a roll-over risk, i.e., uncertainty about continued viability of the trade.

Are these costs directly affected by the ECB intervention?What are the QE direct and indirect effects on the basis?



I ECB Interventions


I Data

I Net Basis





I Conclusions


Data

MTS, Mercato dei Titoli di Stato, is an Electronic, Inter-Dealer market.I Dealer to Retail client (Bondvision): not covered.I Primary Dealers and Price takers

We observe:I Trade-by-Trade data.I Order-by-Order data, uniquely linked to the trades.I Every quote, every update, un-netted.

Eurex is an Electronic, limit order market for futuresI Only one designated market maker but many competitive traders.I High frequency data for best bid- and ask-prices.

Special repo rates are obtained from the MTS repo platform.

We cover from the March ’13 delivery to the June ’17 delivery.



I ECB Interventions


I Data

I Net Basis





I Conclusions


Net Basis

-.2-.1

0.1

.2.3

.4.5

Euro

01/2013 01/2014 01/2015 01/2016 01/2017Date

ITDEQE


I The basis does not take any cost/friction into account (bonds are borrowed at overnightEONIA).

I The basis is, on average, positive, more so during the QE (e 0.051 vs. e0.003).I The basis in 2016/2017 is very similar across the two markets, despite the differences in

underlying bonds (Bund, BTP).I Consistent with an arbitrageur allocating trades, equalizing the bases, at the margin.


Net Basis

-.2-.1

0.1

.2.3

.4.5

Euro

01/2013 01/2014 01/2015 01/2016 01/2017Date

ITDEQE


All DE IT

Before QE 0.007 0.031 −0.017During QE 0.073 0.095 0.051Difference 0.066∗∗∗ 0.064∗∗∗ 0.067∗∗∗

I This calculation represents arbitrage profits that should be zero or negative. They aremostly positive because we have not taken costs into considerations.


Net Basis: Results

(1) (2) (3) (4)Basisit Basisit TradeBasisit Arbitrageit

ECB%it 0.817∗∗∗ 0.283∗∗ 0.188∗∗∗ 0.319∗∗∗

(10.781) (1.996) (5.014) (4.249)DEi 0.036∗∗∗ 0.036∗∗∗ 0.043∗∗∗ 0.027∗∗∗

(4.935) (5.125) (8.264) (2.894)DtDit 0.001∗∗∗ 0.001∗∗∗ 0.001∗∗∗ 0.001∗∗∗

(4.923) (5.367) (4.669) (3.645)BAB

it 0.169(1.311)

CTDRepoit −0.070∗∗∗(−3.083)

CTDRepoRangeit 0.048(1.516)

Adj. R2 0.619 0.661 0.392 TobitObs 2116 2116 2116 2116Country FE Yes Yes Yes YesCluster DC DC DC DC

I Before taking trading costs into account, the mispricing between futures and cash bonds ise0.8 cent larger, every 1% increase in ECB holding.

I Including ECB%it to Specification (1) increases Adj. R2 by 33.5%, from 28.5%.


Identifying the ECB’s effect

I It is the coincidence of 1) lack of regulatory capital and 2) a central bank intervention thatgives rise to the mispricing we observe.

I We can look at the same market interested by the intervention, but consider a trade withsubstantially lower regulatory capital: arbitraging the put-call parity of bund futures.

I We can control for the availability of arbitrage capital directly in the regressions.I We can repeat the analysis for the same trade, but in a market not affected by the

intervention (US Treasury notes futures, in progress).

-.2-.1

0.1

.2.3

.4.5

Euro

01/2013 01/2014 01/2015 01/2016 01/2017Date

Futures-Bond Basis (DE) Put-Call Parity (DE) Quantitative Easing

Futures-Bond Basis and Put-Call Parity Deviations


Identifying the ECB’s effect

I It is the coincidence of 1) lack of regulatory capital and 2) a central bank intervention thatgives rise to the mispricing we observe.

I We can look at the same market interested by the intervention, but consider a trade withsubstantially lower regulatory capital: arbitraging the put-call parity of bund futures.

I We can control for the availability of arbitrage capital directly in the regressions.I We can repeat the analysis for the same trade, but in a market not affected by the

intervention (US Treasury notes futures, in progress).

(1) (2)Basist Basist

ECB%t 0.798∗∗∗ 0.660∗∗∗

(8.530) (14.360)DtDt 0.002∗∗∗ 0.002∗∗∗

(4.499) (5.268)Put − Callt 0.022

(0.253)Noiset 201.636

(1.323)

Adj. R2 0.678 0.692Obs 907 1057



I ECB Interventions


I Data

I Net Basis





I Conclusions


Set up

The net basis does not represent potential arbitrage opportunities, as it does not account for costs:

Tradeable Basis = Net Basis −Market Frictions ≥ Opportunity Cost + Regulatory Costs

Market Frictions = Market Liquidity + Repo Cost (Overnight + Term Effects)

We need to take into account the effect of QE on the market frictions included in the basis:I Transaction costs.I Repo rates.I Repo term effects.

And regulatory costs:I Opportunity costs, as determined by the shadow price of balance sheet usage due to capital

adequacy ratio, liquidity coverage ratio, NSFR, leverage ratio.I Regulatory costs, e.g., VaR considerations and limits to portfolio notional.


The Indirect Effects of ECB InterventionBond Market IlliquidityI The net basis shown in previous slides assumes traders buy the futures and sell the bond at

the midprice. The tradeable basis in a few slides corrects for this.I We want to test whether the bond purchases affected arbitrage costs.I ECB intervention increases the scarcity of bonds and reduces their liquidity.I Larger bid-ask spread allows the midpoints to diverge even further away.

Bid-Ask Spread for CTD Bond

0.0

5.1

.15

.2.2

5Eu

ro

01/2013 01/2014 01/2015 01/2016 01/2017Date

Italy Germany Quantitative Easing


The Indirect Effects of ECB InterventionBond Market IlliquidityI The net basis shown in previous slides assumes traders buy the futures and sell the bond at

the midprice. The tradeable basis in a few slides corrects for this.I We want to test whether the bond purchases affected arbitrage costs.I ECB intervention increases the scarcity of bonds and reduces their liquidity.I Larger bid-ask spread allows the midpoints to diverge even further away.

(1) (2) (3) (4) (5) (6) (7)BAB

it BABit BAB

it BABit LogBAB

it BADelit BAB

it

ECB%it 0.189∗∗∗ 0.139∗∗ 0.146∗∗ 0.188∗∗∗ 2.134∗∗ 0.164∗∗∗ 0.077∗

DEi −0.044∗∗∗ −0.034∗∗∗ −0.034∗∗∗ −0.033∗∗∗ −0.472∗∗∗ −0.052∗∗∗ −0.003TtMit 0.012 −0.001 0.001 0.043 −0.002Longi 0.009 0.013∗∗ 0.014∗∗ 0.126 0.019∗∗∗AmtIssuei 0.001 0.000 0.000 0.009 0.000σB

it 0.031∗∗∗ 0.031∗∗∗ 0.324∗∗∗ 0.005∗∗VolumeB

it −0.102∗∗∗ −0.102∗∗∗ −1.048∗∗∗ −0.075∗∗∗CCBSSt 0.000 −0.002 0.000∗∗BADel

it 0.673∗∗∗

Adj. R2 0.426 0.444 0.574 0.576 0.603 0.495 0.728Obs 2116 2116 2116 2116 2116 2116 2116Country FE Yes Yes Yes Yes Yes Yes Yes

I 10% of ECB holding translates into e 2 cent larger bid ask spread (30% over 0.06).I Alternatively, a 1% (5%) increase in holdings increases the bid-ask spread by 2% (10%)


The Indirect Effects of ECB InterventionThe Repo RateShorting the bond requires the arbitrageur to acquire it by reverse repoI The “cost of carry” of actually financing the position (the reverse repo rate) will be affected

by the supply of bonds available for borrowing.I Relationship of general collateral (GC) vs special repo rate unclear.I Bond scarcity due to ECB purchases makes borrowing them less profitableI Consistent with borrowing to sell to ECB (Corradin and Maddaloni, 2017)I ECB interventions lower special repo rates, decreasing the mispricing→ net effect of

higher cash bond prices vs. lower special repo rates on basis?

-2-1

.5-1

-.50

.51

Pct

01/2013 01/2014 01/2015 01/2016 01/2017Date

ITDEQE

Reverse Special Repo Rate


The Indirect Effects of ECB InterventionThe Repo RateShorting the bond requires the arbitrageur to acquire it by reverse repoI The “cost of carry” of actually financing the position (the reverse repo rate) will be affected

by the supply of bonds available for borrowing.I Relationship of general collateral (GC) vs special repo rate unclear.I Bond scarcity due to ECB purchases makes borrowing them less profitableI Consistent with borrowing to sell to ECB (Corradin and Maddaloni, 2017)I ECB interventions lower special repo rates, decreasing the mispricing→ net effect of

higher cash bond prices vs. lower special repo rates on basis?

-2.5

-2-1

.5-1

-.50

.51

Pct

01/2013 01/2014 01/2015 01/2016 01/2017Date

Italy CTD Germany CTD EoniaItaly Index Germany Index Quantitative Easing


The Indirect Effects of ECB InterventionThe Repo Rate

(1) (2) (3) (4) (5)CTDRepoit RFRit R̂FRit CTDRepo − RFRit CTDRepo − R̂FRit

ECB%it −6.759∗∗∗ −4.644∗∗∗ −5.239∗∗∗ −2.107∗∗∗ −1.449∗∗∗

DEi −0.108∗∗∗ −0.072∗∗ −0.114∗∗∗ −0.046 −0.021σB

it −0.003 0.012AmtIssuei 0.001 0.006BAB

it −0.225 −0.362∗TtMit −0.019 −0.018Longi 0.008 −0.038

Adj. R2 0.808 0.818 0.811 0.420 0.274Obs 2116 2116 2116 2116 2116Country FE Yes Yes Yes Yes YesCluster Bond Bond Country Bond Bond

I The scarcer bonds are, the lower are their repo rates. 1% increase in ECB bond holdingstranslates into an average repo rate that is 5bp smaller.

I CTD bonds are “more special” than the whole set of bonds. 1% increase in ECB bondholdings translates into a repo rate that is 7bp smaller for the CTD bond.

I No bond-specific characteristics have additional explanatory power.



We can identify the effect of the ECB by comparing the repo rate of the CTD to bonds that werenot purchased by the ECB:I We can compare the repo rates of long-term bonds to their short-term counterparts

-.75

-.25

.25

.75

Pct

01/2013 01/2014 01/2015 01/2016 01/2017Date

Long-Term Bonds (IT) ZCB (IT) Short-term Bonds (IT) QE

Long vs Short-term Bonds / ZCB: Repo Rates




-.05

.05

.15

Pct

01/2013 01/2014 01/2015 01/2016 01/2017Date

Short-term Bonds (IT) ZCB (IT) QE





-.5-.4

-.3-.2

-.10

.1Pc

t

01/2013 01/2014 01/2015 01/2016 01/2017Date

ZCB (IT) QE





(1) (2) (3) (4)RepoZCB

it − RepoLongit RepoZCB

it − RepoLongit RepoShort

it − RepoLongit RepoShort

it − RepoLongit

ECB%t 0.441∗∗∗ 0.619∗∗∗ 0.221∗∗∗ 0.373∗∗∗

(8.813) (3.426) (3.690) (3.871)DummyDec14it −0.108∗∗∗ −0.105∗∗∗

(−28.342) (−18.857)RFRit 0.033 0.029∗∗∗

(1.193) (2.834)

Adj. R2 0.304 0.311 0.277 0.315Obs 1000 1000 1000 1000


The Indirect Effects of ECB InterventionThe Uncertainty in the Repo Rate

Rolling over an overnight repo for, e.g., 30 days is not the same as entering a 1-month term repo:I The difference between overnight and term repo rates depends on the volatility of the

overnight rate, the term, and the duration of the underlying bondI Similar concept to determining a swap rate when swapping a fixed- for a floating-rateI Gupta and Subrahmanyam (JFE, 2000) calculate the difference based on different interest

rate modelsI E.g., for the Vasicek model, the difference in price between a forward and a futures contract

is: 12σ

2mT , where σ2 is the interest rate volatility, m is the maturity of the futurescontract, and T is the duration of the bond.


The Indirect Effects of ECB InterventionThe Uncertainty in the Repo RateI The term structure of repo rates is increasing in the term. Term repos are not easily

available, arbitrageurs need to account for the rollover risk, which will be a function ofinterest rate volatility.

I Uncertainty about ECB intervention increases this dispersion of repo rates, as measured bytheir daily interquartile difference.

Special repo rate dispersion

0.2

5.5

.75

1Pc

t

01/2013 01/2014 01/2015 01/2016 01/2017Date

Italy Germany Quantitative Easing


The Indirect Effects of ECB InterventionThe Uncertainty in the Repo RateI The term structure of repo rates is increasing in the term. Term repos are not easily

available, arbitrageurs need to account for the rollover risk, which will be a function ofinterest rate volatility.

I Uncertainty about ECB intervention increases this dispersion of repo rates, as measured bytheir daily interquartile difference.

(1) (2) (3)CTDRepoRangeit CTDRepoRangeit CTDRepoσit

ECB%it 0.678∗∗∗ 0.685∗∗∗ 0.563∗∗∗

DEi −0.003 −0.004 −0.003σB

it −0.002 −0.007AmtIssuei 0.000 0.000BAB

it 0.028 0.087TtMit 0.007 0.015Longi −0.005 −0.017

Adj. R2 0.161 0.160 0.174Obs 2116 2116 2116Country FE Yes Yes YesCluster Bond Bond Bond

I Higher bond repo rate volatility during ECB bond purchases. Therefore, the ECBpurchases increases the difference between rolling over overnight repos and term repos.



I ECB Interventions


I Data

I Net Basis





I Conclusions


Net Basis: Results


ECB%it 0.817∗∗∗ 0.283∗∗ 0.188∗∗∗ 0.319∗∗∗

(10.781) (1.996) (5.014) (4.249)DEi 0.036∗∗∗ 0.036∗∗∗ 0.043∗∗∗ 0.027∗∗∗

(4.935) (5.125) (8.264) (2.894)DtDit 0.001∗∗∗ 0.001∗∗∗ 0.001∗∗∗ 0.001∗∗∗

(4.923) (5.367) (4.669) (3.645)BAB

it 0.169(1.311)

CTDRepoit −0.070∗∗∗(−3.083)


Adj. R2 0.619 0.661 0.392Obs 2116 2116 2116 2116Country FE Yes Yes Yes YesCluster DC DC DC DC

I After taking trading costs into account, the mispricing between futures and cash bonds ise0.3 cent larger, every 1% increase in ECB holding.

I 0.2830.817 = 35% of the effect is direct through bond prices, 65% indirect through frictions.

I BABit ,

0.189·0.1690.871 = 4%, Repoit,

(−6.759)·(−0.074)0.871 = 57%, Rangeit,

0.678·0.0480.871 = 4%,


Net Basis: Results

(1) (2) (3) (4)∆90Basisit ∆90Basisit ∆90TradeBasisit ∆90Arbitrageit

ECBit 0.019∗∗∗ 0.006∗∗∗ 0.006∗∗∗ 0.003∗∗∗(10.187) (3.539) (3.738) (4.998)

DEi 0.001∗ −0.002∗∗∗ −0.001∗ 0.002∗∗∗(1.695) (−3.471) (−1.752) (3.888)

∆90BABit 0.147∗∗∗

(4.079)∆90CTDRepoit −0.097∗∗∗

(−11.944)∆90CTDRepoRangeit 0.027∗∗

(1.985)

Adj. R2 0.032 0.273 0.003 0.008Obs 1936 1936 1936 1936Country FE Yes Yes Yes YesCluster DC DC DC DC

I Results are not spurious effects of non-stationarityI We account for pull-to-parity by repeating the analysis using xi,t − xi,t−90 instead of levels.I During the ECB’s QE, the basis increased e2 cents every contract.



I ECB Interventions


I Data

I Net Basis





I Conclusions


Net Basis: Results


ECB%it 0.817∗∗∗ 0.283∗∗ 0.188∗∗∗ 0.319∗∗∗

(10.781) (1.996) (5.014) (4.249)DEi 0.036∗∗∗ 0.036∗∗∗ 0.043∗∗∗ 0.027∗∗∗

(4.935) (5.125) (8.264) (2.894)DtDit 0.001∗∗∗ 0.001∗∗∗ 0.001∗∗∗ 0.001∗∗∗

(4.923) (5.367) (4.669) (3.645)BAB

it 0.169(1.311)

CTDRepoit −0.070∗∗∗(−3.083)


Adj. R2 0.619 0.661 0.392 TobitObs 2116 2116 2116 2116Country FE Yes Yes Yes YesCluster DC DC DC DC

I Whether frictions are accounted for directly (3) or indirectly (2), ECB increases mispricing.I We identify foregone arbitrage profits by calculating Arbitrageit = max(TradeBasisit, 0)I Arbitrage is present. Effect of QE is smaller for Arbitrageit than for TradeBasisit , but the

parameter for the Tobit in Specification 4 compounds the probability of seeing arbitrageand its magnitude.



I ECB Interventions


I Data

I Net Basis





I Conclusions


Arbitrage CostsRegulatory Frictions: Capital Ratios

Banks need to attain leverage ratio of 3%, 5% if they are systemically important financialinstitutions, and 6% if they had past deficiencies. Banks, however, would aim at a higher rate,e.g., 8%, to be conservative.I Capital needs to be available to trade the basis.I VaR restrictions keep traders from taking advantage of the arbitrage.I Arbitrageurs would not trade an arbitrage unless the profit, net of all costs, is larger than the

required of return on the amount of capital employed.I E.g., the return on the futures-bond arbitrage should be higher than

Threshold = 5%︸︷︷︸Target

Leverage Ratio

· 10%︸︷︷︸Required Rateof Return

= 50bps

I 50 bps of yearly return on this strategy corresponds to roughly 12.5 bps per contract, or e0.125 per e 100 of face value.



-.25

0.2

5.5

Euro

01/2013 01/2014 01/2015 01/2016 01/2017Date

ITDEQE

Basis Between Cash and Futures and Required Arbitrage Profits



0

1%

2%

3%

4%

5%

6%

Leve

rage

Rat

io

01/2013 01/2014 01/2015 01/2016 01/2017Date

Ratio

Average Leverage Ratio for 18 Large Banks

I Annualized returns of the arbitrage strategyI Actual leverage ratios from Datastream, Eikon and Bloomberg for a set of 18 large players

in the sovereign space (JPMorgan, Morgan Stanley, Goldman Sachs, Barclays...)L. Pelizzon, M.G. Subrahmanyam, J. Uno, D. Tomio Central Bank–Driven Mispricing 43 / 47


0

0.25%

0.50%

0.75%

1.00%

1.25%

Year

ly R

etur

n

01/2013 01/2014 01/2015 01/2016 01/2017Date

ITDEReqRetQE

Basis Between Cash and Futures and Required Annualized Returns

I Annualized returns of the arbitrage strategyI Actual leverage ratios from Datastream, Eikon and Bloomberg for a set of 18 large players

in the sovereign space (JPMorgan, Morgan Stanley, Goldman Sachs, Barclays...)L. Pelizzon, M.G. Subrahmanyam, J. Uno, D. Tomio Central Bank–Driven Mispricing 43 / 47

Final Considerations

The intervention did not minimize costs:I We assume that ECB could have purchased based on mid-point and that the basis we

observe is common to all bonds bought.I An average basis of e7.3 cents for e100 of bonds would translate in overpaying e1.46

billions the e2 trillions of bonds that were bought.I A direct transfer to financial institutions.I Not a welfare cost, but a symptom of lack of market efficiency which could, in turn,

decrease welfare.

Arbitrage opportunities stem from bond purchases AND regulatory requirements:I Without capital requirements, arbitrage would be taken advantage of, despite the ECB.I Without ECB’s purchases, there would be nothing to perturb the futures-bond basis.I Capital requirements were there before March 2015.I Would help if intervention targeted both bonds and futures.


A Market Neutral QE

I The ECB’s QE dislocated the market for cash bonds vis-a-vis their futures contracts.

I We propose an alternative implementation of the intervention.

I If the ECB bought both cash bonds and futures contract depending on what is cheaper atthe time, it could lower the cost of the intervention.

I They could minimize the market dislocation and keep the market arbitrage-free, even in thepresence of capital regulation.



I ECB Interventions


I Data

I Net Basis





I Conclusions


Conclusions

The ECB’s QE interventions were aimed and succeeded at lowering bond yields but:

I Contributed to dislocating the price of futures contract vis-a-vis its underlying bond.

I Increased the market illiquidity of the cash bond market.

I By increasing the scarcity of bonds, they lowered repo rates.

I Increased the volatility of the cash bond market, increasing the cost of repo terms.Regulatory restrictions and shortness of capital restrained the capacity of arbitrageurs to closethe mispricing.


Thank you

1cm Central Bank Driven Mispricing

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