Turnover Liquidity and the Transmission of …...Endowments and production technology First...
Transcript of Turnover Liquidity and the Transmission of …...Endowments and production technology First...
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Turnover Liquidity and the Transmission ofMonetary Policy
Ricardo Lagos Shengxing Zhang
New York University London School of Economics
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Two questions
What is the effect of monetary policy on the stock market?
What is the mechanism?
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Two questions
What is the effect of monetary policy on the stock market?
What is the mechanism?
![Page 4: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/4.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
What we do
Theory
—Develop a model of monetary exchange in financial markets
—Study the effects of monetary policy on returns and financial liquidity
Evidence
Estimate the impact of monetary policy on returns and turnover:
—Marketwide
—Across stocks with different liquidity
Quantitative Theory
—Calibrate and simulate model to quantify the theoretical mechanism
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Theoretical results
Show how the quantity of money and market microstructure:
1 Determine asset prices and standard measures of financial liquidity
(trade volume, dealer supply of immediacy, spreads)
2 Activate the turnover-liquidity mechanism
tight money increases opportunity cost of holding nominal assetsroutinely used to settle financial transactions (money, bank reserves)
⇒ nominal assets become scarcer⇒ reduced resalability of stocks⇒ stock turnover falls⇒ stock price falls
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Theoretical results
Show how the quantity of money and market microstructure:
1 Determine asset prices and standard measures of financial liquidity
(trade volume, dealer supply of immediacy, spreads)
2 Activate the turnover-liquidity mechanism
tight money increases opportunity cost of holding nominal assetsroutinely used to settle financial transactions (money, bank reserves)
⇒ nominal assets become scarcer⇒ reduced resalability of stocks⇒ stock turnover falls⇒ stock price falls
![Page 7: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/7.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Theoretical results
Show how the quantity of money and market microstructure:
1 Determine asset prices and standard measures of financial liquidity
(trade volume, dealer supply of immediacy, spreads)
2 Activate the turnover-liquidity mechanism
tight money increases opportunity cost of holding nominal assetsroutinely used to settle financial transactions (money, bank reserves)
⇒ nominal assets become scarcer⇒ reduced resalability of stocks⇒ stock turnover falls⇒ stock price falls
![Page 8: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/8.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Theoretical results
Show how the quantity of money and market microstructure:
1 Determine asset prices and standard measures of financial liquidity
(trade volume, dealer supply of immediacy, spreads)
2 Activate the turnover-liquidity mechanism
tight money increases opportunity cost of holding nominal assetsroutinely used to settle financial transactions (money, bank reserves)
⇒ nominal assets become scarcer⇒ reduced resalability of stocks⇒ stock turnover falls⇒ stock price falls
![Page 9: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/9.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Theoretical results
Show how the quantity of money and market microstructure:
1 Determine asset prices and standard measures of financial liquidity
(trade volume, dealer supply of immediacy, spreads)
2 Activate the turnover-liquidity mechanism
tight money increases opportunity cost of holding nominal assetsroutinely used to settle financial transactions (money, bank reserves)
⇒ nominal assets become scarcer⇒ reduced resalability of stocks⇒ stock turnover falls⇒ stock price falls
![Page 10: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/10.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Empirical findings
1 25 bp surprise increase in policy rate ⇒ fall in marketwide...
Stock return (between 1% and 2%)
Turnover rate (between 17% and 30%)
2 Pattern of responses across stocks with different turnover liquidity
Return and turnover fall for all stock classes, but...
... relative to the class of stocks with median liquidity:
Return of top 5% most liquid falls 2 times more
Turnover of top 5% most liquid falls 2-3 times more
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Empirical findings
1 25 bp surprise increase in policy rate ⇒ fall in marketwide...
Stock return (between 1% and 2%)
Turnover rate (between 17% and 30%)
2 Pattern of responses across stocks with different turnover liquidity
Return and turnover fall for all stock classes, but...
... relative to the class of stocks with median liquidity:
Return of top 5% most liquid falls 2 times more
Turnover of top 5% most liquid falls 2-3 times more
![Page 12: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/12.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Empirical findings
1 25 bp surprise increase in policy rate ⇒ fall in marketwide...
Stock return (between 1% and 2%)
Turnover rate (between 17% and 30%)
2 Pattern of responses across stocks with different turnover liquidity
Return and turnover fall for all stock classes, but...
... relative to the class of stocks with median liquidity:
Return of top 5% most liquid falls 2 times more
Turnover of top 5% most liquid falls 2-3 times more
![Page 13: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/13.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Empirical findings
1 25 bp surprise increase in policy rate ⇒ fall in marketwide...
Stock return (between 1% and 2%)
Turnover rate (between 17% and 30%)
2 Pattern of responses across stocks with different turnover liquidity
Return and turnover fall for all stock classes, but...
... relative to the class of stocks with median liquidity:
Return of top 5% most liquid falls 2 times more
Turnover of top 5% most liquid falls 2-3 times more
![Page 14: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/14.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Empirical findings
1 25 bp surprise increase in policy rate ⇒ fall in marketwide...
Stock return (between 1% and 2%)
Turnover rate (between 17% and 30%)
2 Pattern of responses across stocks with different turnover liquidity
Return and turnover fall for all stock classes, but...
... relative to the class of stocks with median liquidity:
Return of top 5% most liquid falls 2 times more
Turnover of top 5% most liquid falls 2-3 times more
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Empirical findings
1 25 bp surprise increase in policy rate ⇒ fall in marketwide...
Stock return (between 1% and 2%)
Turnover rate (between 17% and 30%)
2 Pattern of responses across stocks with different turnover liquidity
Return and turnover fall for all stock classes, but...
... relative to the class of stocks with median liquidity:
Return of top 5% most liquid falls 2 times more
Turnover of top 5% most liquid falls 2-3 times more
![Page 16: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/16.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Empirical findings
1 25 bp surprise increase in policy rate ⇒ fall in marketwide...
Stock return (between 1% and 2%)
Turnover rate (between 17% and 30%)
2 Pattern of responses across stocks with different turnover liquidity
Return and turnover fall for all stock classes, but...
... relative to the class of stocks with median liquidity:
Return of top 5% most liquid falls 2 times more
Turnover of top 5% most liquid falls 2-3 times more
![Page 17: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/17.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Empirical findings
1 25 bp surprise increase in policy rate ⇒ fall in marketwide...
Stock return (between 1% and 2%)
Turnover rate (between 17% and 30%)
2 Pattern of responses across stocks with different turnover liquidity
Return and turnover fall for all stock classes, but...
... relative to the class of stocks with median liquidity:
Return of top 5% most liquid falls 2 times more
Turnover of top 5% most liquid falls 2-3 times more
![Page 18: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/18.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Empirical findings
1 25 bp surprise increase in policy rate ⇒ fall in marketwide...
Stock return (between 1% and 2%)
Turnover rate (between 17% and 30%)
2 Pattern of responses across stocks with different turnover liquidity
Return and turnover fall for all stock classes, but...
... relative to the class of stocks with median liquidity:
Return of top 5% most liquid falls 2 times more
Turnover of top 5% most liquid falls 2-3 times more
![Page 19: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/19.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Quantitative results
A calibrated version of the model accounts for:
1 Sign and 26% to 60% of the response of stock returns
2 Sign, persistence, modest part of initial response of turnover
3 Relative magnitude of responses of returns and turnoveracross liquidity classes
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Quantitative results
A calibrated version of the model accounts for:
1 Sign and 26% to 60% of the response of stock returns
2 Sign, persistence, modest part of initial response of turnover
3 Relative magnitude of responses of returns and turnoveracross liquidity classes
![Page 21: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/21.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Quantitative results
A calibrated version of the model accounts for:
1 Sign and 26% to 60% of the response of stock returns
2 Sign, persistence, modest part of initial response of turnover
3 Relative magnitude of responses of returns and turnoveracross liquidity classes
![Page 22: Turnover Liquidity and the Transmission of …...Endowments and production technology First subperiod As productive units (trees) Each unit yields y t dividend goods at the end of](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8f884968cbde3d37598ff0/html5/thumbnails/22.jpg)
Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Monetary policy and asset prices: related theoretical work
Inflation, liquidity, and asset prices
Lagos (2010, 2011), Lester, Postlewaite and Wright (2012), Nosal and
Rocheteau (2013), Piazzesi and Schneider (2016)
Money in OTC financial markets
Lagos and Zhang (2014), Geromichalos and Herrenbrueck (2016), Nosal and
Mattesini (2016), Trejos and Wright (2016)
Speculative bubbles
Harrison and Kreps (1978), Scheinkman and Xiong (2003)
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Monetary policy and asset prices: related empirical work
Event-study methodology
Cook and Hahn (1989), Thorbecke (1997), Kuttner (2001), Cochrane and
Piazzesi (2002), Bernanke and Kuttner (2005), Hanson and Stein (2015)
High-frequency identification
Gürkaynak, Sack and Swanson (2005), Gertler and Karadi (2015),
Gorodnichenko and Weber (2015), Nakamura and Steinsson (2015)
Heteroskedasticity-based identification
Rigobon and Sack (2004)
Role of firm characteristics
Ehrmann and Fratzscher (2004), Bernanke and Kuttner (2005), Gorodnichenko
and Weber (2015), Ippolito, Ozdagli and Perez (2013)
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Environment
Time. Discrete, infinite horizon, two subperiods per period
Population. [0, 1] investors (infinitely lived)
Commodities. Two divisible, nonstorable consumption goods:
dividend good
general good
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Preferences
E0
∞
∑t=0
βt (εtyt + ct − ht )
β ∈ (0, 1) : discount factor
ct : consumption of general good
ht : effort to produce general good
yt : consumption of dividend good
εt : valuation shock, i.i.d. over time, cdf G (·) on [εL, εH ]
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Endowments and production technology
First subperiod
As productive units (trees)
Each unit yields yt dividend goods at the end of the first subperiodyt = γtyt−1, where γt ∼ i.i.d. with E (γt ) = γ
Each unit permanently “fails”with probability 1− δat the beginning of the period
Failed units immediately replaced by new units(allocated uniformly to investors)
Second subperiod
Linear technology to transform effort into general goods
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Assets
Equity shares
As equity shares
At the beginning of period t:
(1− δ)As shares of failed trees disappear
(1− δ)As shares of new trees allocated uniformly to investors
Fiat money
Money supply: Amt dollars
Monetary policy: Amt+1 = µAmt , µ ∈ R++
(implemented with lump-sum injections/withdrawals)
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Market structure
First subperiod: OTC market
Money, equity (cum dividend)
Random access to a Walrasian market (with probability α)
Second subperiod: centralized market
Money, equity (ex dividend), general good
Walrasian trade between all agents
“Anonymity”⇒ quid pro quo ⇒ money used to pay for assets
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Timeline and marketstructure
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Value functions
W It (at ) = max
ct ,ht ,at+1
[ct − ht + β
∫V It+1
(at+1, ε′
)dG (ε′)
]at+1 = (amt+1, δa
st+1 + (1− δ)As )
ct +φt at+1 ≤ ht +φtat + Tt
φt = (φmt , φ
st ) : real prices of money and stock
V It (at , ε) = α{
εytast (at , ε) +WIt [at (at , ε)]
}+ (1− α)
[εytast +W
It (at )
]
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Value functions
W It (at ) = max
ct ,ht ,at+1
[ct − ht + β
∫V It+1
(at+1, ε′
)dG (ε′)
]at+1 = (amt+1, δa
st+1 + (1− δ)As )
ct +φt at+1 ≤ ht +φtat + Tt
φt = (φmt , φ
st ) : real prices of money and stock
V It (at , ε) = α{
εytast (at , ε) +WIt [at (at , ε)]
}+ (1− α)
[εytast +W
It (at )
]
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Portfolio problem in OTCM
Investor with portfolio at = (amt , ast ) and valuation ε solves
maxat
[εytast +W
It (at )
]amt + pta
st ≤ amt + ptast
pt : nominal equity price in the OTC interdealer market
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
OTCM post trade portfolio
ast =
{ast +
1ptamt if ε∗t < ε
0 if ε < ε∗t
amt =
{0 if ε∗t < εamt + pta
st if ε < ε∗t
where
ε∗t ≡ptφmt − φst
yt
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Euler equations
φmt ≥ βEt
[φmt+1 + αθ
∫ εH
ε∗t+1
(εyt+1 + φst+1
pt+1− φmt+1
)dG (ε)
]
φst ≥ βδEt
[εyt+1 + φst+1
+αθ∫ ε∗t+1
εL
[pt+1φmt+1 −
(εyt+1 + φst+1
)]dG (ε)
]
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Euler equations
φmt ≥ βEt
[φmt+1 + αθ
∫ εH
ε∗t+1
(εyt+1 + φst+1
pt+1− φmt+1
)dG (ε)
]
φst ≥ βδEt
[εyt+1 + φst+1
+αθ∫ ε∗t+1
εL
[pt+1φmt+1 −
(εyt+1 + φst+1
)]dG (ε)
]
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Friedman rule
Proposition
The allocation implemented by the stationary monetary equilibriumconverges to the symmetric effi cient allocation as µ→ β ≡ βγ.
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Nonmonetary equilibrium
Proposition
(i) A nonmonetary equilibrium exists for any parametrization.
(ii) In the nonmonetary equilibrium:
there is no trade in the OTC market
the equity price is:
φst =βδ
1− βδεyt .
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Monetary equilibrium
Proposition
(i) If µ ∈ (β, µ), there is one stationary monetary equilibrium.
(ii) For any µ ∈(
β, µ), there exists a unique ε∗ ∈ (εL, εH ).
(iv) As µ→ β, ε∗ → εH and φst →βδ
1−βδεHyt .
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Stationary monetary equilibrium: allocations
φst = φsyt
φs ≡ βδ
1− βδ
[ε+ αθ
∫ ε∗
εL(ε∗ − ε) dG (ε)
]
φmt Amt =
αG (ε∗)As
α [1− G (ε∗)] (ε∗ + φs ) yt
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Asset prices and the nominal interest rate
Proposition
In the stationary monetary equilibrium: ∂φs/∂µ < 0
The nominal interest rate is:
r =µ− β
β
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Trade volume and the nominal interest rate
V = αG (ε∗)As
Proposition
In the stationary monetary equilibrium: ∂V/∂µ < 0
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
The turnover-liquidity transmission mechanism
V = αG (ε∗)As
∂V∂µ
= V G′ (ε∗)
G (ε∗)∂ε∗
∂µ< 0
φs =βδ
1− βδ
[ε+ αθ
∫ ε∗
εL(ε∗ − ε) dG (ε)
]∂φs
∂µ= V βδθ(
1− βδ)As
∂ε∗
∂µ< 0
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
The turnover-liquidity transmission mechanism
V = αG (ε∗)As
∂V∂µ
= V G′ (ε∗)
G (ε∗)∂ε∗
∂µ< 0
φs =βδ
1− βδ
[ε+ αθ
∫ ε∗
εL(ε∗ − ε) dG (ε)
]∂φs
∂µ= V βδθ(
1− βδ)As
∂ε∗
∂µ< 0
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
The turnover-liquidity transmission mechanism
V = αG (ε∗)As
∂V∂µ
= V G′ (ε∗)
G (ε∗)∂ε∗
∂µ< 0
φs =βδ
1− βδ
[ε+ αθ
∫ ε∗
εL(ε∗ − ε) dG (ε)
]∂φs
∂µ= V βδθ(
1− βδ)As
∂ε∗
∂µ< 0
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Preview of empirical work
Aggregate announcement-day effects
Event-study regression
Estimation based on heteroskedasticity-based identification
High-frequency instrumental variable regression
Disaggregative announcement-day effects
Regressions on portfolios sorted on turnover liquidity
Regression with panel data on individual stocks
Regressions on portfolios sorted on liquidity betas
Dynamic effects(VAR identified with external high-frequency instrument)
VAR with aggregate data
VARs on portfolios sorted on turnover liquidity
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Data
Returns
stock s on day t: Rst =[(Pst +D
st ) /Pst−1 − 1
]× 100
aggregate: RIt = 1n ∑n
s=1Rst
Volume
turnover rate for stock s on day t: T st = V st /AstV st : # of shares traded; Ast : # of outstanding sharesaggregate: T It = 1
n ∑ns=1 T
st
Proxies for the policy rate
3-month Eurodollar futures rate (CME Group)tick-by-tick 30-day fed funds futures rate (CME Group)
Sample
all common stocks in NYSE (1300-1800 stocks, from CRSP)1994-2001, 2014 trading days, 73 FOMC announcement dates
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Event-study (Bernanke and Kuttner, 2005)
Yt = a+ b∆it + εt
∆it ≡ it − it−1 : proxy for unexpected change in policy rate
it : day-t nominal interest rate implied by 3-month Eurodollarfutures with closest expiration after day t
t ∈ S1 (sample of 73 FOMC policy announcement days)
Regression 1: Yt = RIt
Regression 2: Yt = T It − T It−1
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Heteroskedasticity-based (Rigobon and Sack, 2004)
Yt = α∆it + Xt + εt and ∆it = βYt + γXt + ηt
Two potential concerns with event-study approach:
Σε > 0 and β 6= 0 ⇒ simultaneity biasΣX > 0 and γ 6= 0 ⇒ omitted variable bias
Idea: consider two subsamples
S1 : subsample of FOMC-announcement daysS0 : subsample of non FOMC-announcement days
If Σ0η < Σ1η (variance of ηt is larger in S1 than in S0),α is identified from the difference between the covariance matrix ofYt and ∆it computed in S1 and in S0
Regression 1: Yt = RIt ; Regression 2: Yt = T It − T It−1
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Event study with high-frequency instrumental variable
Yt = a+ b∆it + εt
Event-study concerns:
Omitted variable biasEurodollar futures rate may respond to Yt on policy days
Instrument for ∆it with (unexpected) change in a narrow 30-minutewindow around the FOMC announcement
For each t ∈ S1 define zt ≡ it ,m∗t+20 − it ,m∗t−10it ,m : daily 30-day Fed Funds futures rate on minute m of day tm∗t : minute of day t when FOMC announcement is made
Estimate b on sample S1 using zt as HFIV for ∆it
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Impact of monetary policy on returns and turnover
E-based H-based HFIVEstimate Std dev Estimate Std dev Estimate Std dev
Return -3.77 1.02 -6.18 1.87 -8.57 1.69Turnover -.0025 .0007 -.0045 .0017 -.0043 .0009
On the day of the announcement, a 25 bp increase in policy rate ⇒
stock return declines by .94%, 1.56%, or 2.14%
turnover rate decline in the range 17% to 30%(e.g., (.0025/4)/.0037≈.17)
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Impact of monetary policy on returns and turnover
E-based H-based HFIVEstimate Std dev Estimate Std dev Estimate Std dev
Return -3.77 1.02 -6.18 1.87 -8.57 1.69Turnover -.0025 .0007 -.0045 .0017 -.0043 .0009
On the day of the announcement, a 25 bp increase in policy rate ⇒
stock return declines by .94%, 1.56%, or 2.14%
turnover rate decline in the range 17% to 30%(e.g., (.0025/4)/.0037≈.17)
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Announcement-day effects across liquidity portfolios
1 For each policy date, t, calculate T st as the average turnoverrate of an individual stock, s, over all trading days during thefour weeks prior to the policy date
2 Stocks with T st between [5 (i − 1)]th percentile and (5i)th
percentile are sorted into the i th portfolio, i = 1, ..., 20
3 Estimate announcement-day effects for each portfolio
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Announcement-day effects across liquidity portfolios
E-based H-based HFIVPortfolio Turnover Return Turnover Return Turnover Return Turnover
1 .11 -2.03*** -.0003 -3.40*** -.0008 -5.80*** -.0008**
2 .19 -1.83** -.0008** -3.77*** -.0014** -5.95*** -.0011**
3 .25 -1.57* -.0007 -3.02* -.0012* -4.54*** -.0014**
4 .31 -1.05 .0002 -2.69 .0005 -4.29*** -.0031***
5 .37 -2.54** -.0011** -5.21** -.0020 ** -5.89*** -.0017***
6 .42 -2.67*** -.0021** -4.58** -.0039*** -3.43** -.00167 .47 -3.33*** -.0016** -6.11** -.0031*** -6.38*** -.0022***
8 .53 -2.55** -.0011 -4.81** -.0024** -6.14*** -.0024***
9 .58 -2.65** -.0023*** -5.00** -.0034** -8.02*** -.0025***
10 .65 -4.33*** -.0027*** -7.25*** -.0065** -8.19*** -.0029***
11 .71 -3.88*** -.0023*** -6.20*** -.0039*** -6.63*** -.0036***
12 .78 -3.76*** -.0030*** -5.98*** -.0059*** -8.84*** -.0048***
13 .86 -3.98*** -.0028* -6.62*** -.0050 *** -11.15*** -.0036***
14 .95 -4.73*** -.0034*** -7.71*** -.0061** -9.13*** -.00341*
15 1.06 -4.69*** -.0035*** -7.61*** -.0068** -9.35*** -.0052***
16 1.19 -5.37*** -.0037*** -9.10*** -.0066** -12.66*** -.0047***
17 1.36 -6.02*** -.0078*** -10.50*** -.0136 *** -12.15*** -.0078***
18 1.61 -5.21*** -.0001 -8.82*** -.0001 -13.90*** -.0098***
19 2.02 -5.93*** -.0083*** -10.57*** -.0153*** -13.37*** -.0098***
20 3.11 -6.27*** -.0088*** -12.01*** -.0172** -15.70*** -.0125***
NYSE .94 -3.77*** -.0025*** -6.18*** -.0045** -8.57*** -.0043***
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Liquidity portfolios: returns and turnover (E-based)
Portfol io0 2 4 6 8 10 12 14 16 18 20
Bas
is P
oint
s (p
er 1
bp
incr
ease
in p
olic
y ra
te)
10
8
6
4
2
0
Response of Stock Return to Policy Rate: Data
Portfol io0 2 4 6 8 10 12 14 16 18 20
Nor
mal
ized
Res
pons
e(a
s pr
opor
tion
of a
vera
ge r
espo
nse)
6
5
4
3
2
1
0
1Response of Turnov er Rate to Policy Rate: Data
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Liquidity portfolios: returns and turnover (H-based)
Portfol io0 2 4 6 8 10 12 14 16 18 20
Bas
is P
oint
s (p
er 1
bp
incr
ease
in p
olic
y ra
te)
20
18
16
14
12
10
8
6
4
2
0
Response of Stock Return to Policy Rate: Data
Portfol io0 2 4 6 8 10 12 14 16 18 20
Nor
mal
ized
Res
pons
e(a
s pr
opor
tion
of a
vera
ge r
espo
nse)
7
6
5
4
3
2
1
0
1Response of Turnov er Rate to Policy Rate: Data
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Liquidity portfolios: returns and turnover (HFIV)
Portfol io0 2 4 6 8 10 12 14 16 18 20
Bas
is P
oint
s (p
er 1
bp
incr
ease
in p
olic
y ra
te)
20
15
10
5
0
Response of Stock Return to Policy Rate: Data
Portfol io0 2 4 6 8 10 12 14 16 18 20
Nor
mal
ized
Res
pons
e(a
s pr
opor
tion
of a
vera
ge re
spon
se)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0.5Response of Turnov er Rate to Policy Rate: Data
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Announcement-day effects for individual stocks (E-based)
Rst = β0 + β1∆it + β2T st + β3T st × ∆it+Ds +Dt + β4 (∆it )
2 + β5 (T st )2 + εst
∆it : announcement-day change in 3-month Eurodollar futures rate
T st : average turnover rate of individual stock s over all tradingdays during the four weeks prior to policy date
T st ≡ (T st − T ) and ∆it ≡ (∆it − ∆i)
Ds : stock fixed effect; Dt : quarterly time dummy
εst : error term for stock s on policy announcement day t
Theory suggests β3 < 0
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Announcement-day effects for individual stocks (E-based)
Rst = β0 + β1∆it + β2T st + β3T st × ∆it+Ds +Dt + β4 (∆it )
2 + β5 (T st )2 + εst
∆it : announcement-day change in 3-month Eurodollar futures rate
T st : average turnover rate of individual stock s over all tradingdays during the four weeks prior to policy date
T st ≡ (T st − T ) and ∆it ≡ (∆it − ∆i)
Ds : stock fixed effect; Dt : quarterly time dummy
εst : error term for stock s on policy announcement day t
Theory suggests β3 < 0
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Announcement-day effects for individual stocks (E-based)
Variable (I) (II) (III) (IV) (V) (VI) (VII) (VIII) (IX)
∆it -2.52 -2.40 -2.46 -2.37 -2.44 -3.36 -3.37 -3.62 -3.63(.086) (.090) (.091) (.097) (.098) (.099) (.100) (.110) (.110)
T st 25.93 25.36 17.54 22.37 13.93 45.29 42.58 39.09 33.13(2.26) (2.26) (3.08) (2.29) (3.16) (5.71) (7.55) (5.72) (7.71)
T st × ∆it -109.43 -121.14 -100.43 -111.09 -403.98 -415.17 -398.96 -410.15(25.36) (25.76) (25.28) (25.68) (28.22) (28.71) (28.06) (28.55)
Ds yes yes yes yes
Dt yes yes yes yes
(∆it )2 .947 .947 1.00 1.00
(.041) (.042) (.042) (.043)
(T st )2 -1696.88 -1921.29 -1378.21 -1418.23
(392.48) (465.31) (389.33) (466.21)
R2 .0084 .0086 .0085 .0314 .0316 .0132 .0132 .0363 .0364
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Dynamic responses of aggregate returns and turnover
Yt =10
∑j=1BjYt−j + ut
Yt =(it ,RIt , T It
)′for every day in the sample
it : 3-month Eurodollar rate on day t
RIt : average stock-market return on day t
T It : average stock-market turnover rate on day t
External high-frequency instrument to identify money shocks
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Dynamic responses of aggregate returns and turnover
Days0 5 10 15 20 25 30
Bas
is p
oint
s
9
8
7
6
5
4
3
2
1
0
1Stock return
Days0 5 10 15 20 25 30
Tim
es p
er d
ay
105
5
4
3
2
1
0
1Daily turnover rate
Days0 20 40 60 80 100 120
Bas
is p
oint
s
9
8
7
6
5
4
3
2
1
0
1Stock return
Days0 20 40 60 80 100 120
Tim
es p
er d
ay
105
5
4
3
2
1
0
1Daily turnover rate
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Liquidity portfolios: dynamic responses
Day s0 5 10 15 20 25 30
Perc
enta
ge p
oint
s
25
20
15
10
5
0
5Stock return
portfolio 1portfolio 5portfolio 10portfolio 15portfolio 20
Day s0 5 10 15 20 25 30
Tim
es p
er d
ay
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0.005Daily turnover rate
portfolio 1portfolio 5portfolio 10portfolio 15portfolio 20
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Liquidity portfolios: dynamic responses
Day s0 5 10 15
Perc
enta
ge p
oint
s
20
15
10
5
0
5Stock return
portfolio 1portfolio 5portfolio 10portfolio 15portfolio 20
Day s0 5 10 15
Tim
es p
er d
ay
0.03
0.025
0.02
0.015
0.01
0.005
0Daily turnover rate
portfolio 1portfolio 5portfolio 10portfolio 15portfolio 20
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Theory: monetary policy shocks and multiple assets
µt ∼ M-state Markov chain [σij ] | Amt+1 = µtAmt
N asset classes | segmented OTC markets | different αs
Investors choose{ast+1, a
mst+1
}Ns=1
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Equilibrium conditions
φsi = βδ ∑j∈M
σij
[ε+ φsj + αsθ
∫ εs∗j
εL(εs∗j − ε)dG (ε)
]
Zi =β
µi∑j∈M
σij
[Zj + αsθ
∫ εH
εs∗j
(ε− εs∗j )dG (ε)Zj
εs∗j + φsj
]
Z si =G (εs∗i )A
s
1− G (εs∗i )(εs∗i + φsi )
Zi = ∑s∈N
Z si
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Calibration
dividend processyt+1 = ext+1yt
xt+1 ∼ N(γ− 1,Σ2
) γ = 1+ .04/365
Σ = .12/√365
number of asset classes N 20
asset supply As 1
distribution of asset liquidity {αs}20s=1 estimated
monetary policy shocks {µi}7i=1 , [σij ] estimated
discount factor β (0.97)1/365
bargaining power θ 1
idiosyncratic shocks ε ∼ U [0, 1]
asset destruction δ (0.7)1/365
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
The quantitative exercises
Compute equilibrium price functions
Feed into the model the actual path of the policy rate(3-month Eurodollar futures)
Simulate 1000 dividend samples of equal length as data sample andcompute equilibrium path for each sample
Exercise 1: run aggregate event-study regression on each sample
Exercise 2: for each asset class, run event-study on each sample
Exercise 3: estimate VAR impulse responses on each sample(same specification and identification procedure as empirical work)
For each exercise, report distribution of estimates across simulations
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Announcement-day effects on returns and turnover
Model E-based H-based HFIVReturn -2.23 -3.77 -6.18 -8.57Turnover -.0001 -.0025 -.0045 -.0043
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Announcement-day effects on returns (E-based)
Basis Points (per 1 bp increase in policy rate)7 6 5 4 3 2 1 0 1 2
Freq
uenc
y
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16Estimates of Response of Stock Return to Policy Rate
Model Distribution Data Estimate 595 percentiles
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Liquidity portfolios: returns and turnover (E-based)
Portfol io0 2 4 6 8 10 12 14 16 18 20
Bas
is P
oint
s (p
er 1
bp
incr
ease
in p
olic
y ra
te)
10
8
6
4
2
0
Response of Stock Return to Policy Rate: Model
Portfol io0 2 4 6 8 10 12 14 16 18 20
Nor
mal
ized
Res
pons
e(a
s pr
opor
tion
of a
vera
ge re
spon
se)
6
5
4
3
2
1
0
1Response of Turnov er Rate to Policy Rate: Model
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Liquidity portfolios: returns and turnover (E-based)
Portfol io0 2 4 6 8 10 12 14 16 18 20
Bas
is P
oint
s (p
er 1
bp
incr
ease
in p
olic
y ra
te)
10
8
6
4
2
0
Response of Stock Return to Policy Rate: Model and Data
Model Data
Portfol io0 2 4 6 8 10 12 14 16 18 20
Nor
mal
ized
Res
pons
e(a
s pr
opor
tion
of a
vera
ge re
spon
se)
6
5
4
3
2
1
0
1Response of Turnov er Rate to Policy Rate: Model and Data
Model Data
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Dynamic responses of aggregate returns and turnover
Days0 5 10 15 20 25 30
Bas
is p
oint
s
10
8
6
4
2
0
2
4Stock return
Days0 5 10 15 20 25 30
Tim
es p
er d
ay
105
5
4
3
2
1
0
1Daily turnover rate
Days0 20 40 60 80 100 120
Bas
is p
oint
s
10
8
6
4
2
0
2
4Stock return
Days0 20 40 60 80 100 120
Tim
es p
er d
ay
105
5
4
3
2
1
0
1Daily turnover rate
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Summary
What are the effects of monetary policy on the stock market?
Unanticipated tightening causes sizeable declines in returns and turnover.
These effects are larger for more liquid stocks.
What is the mechanism?
We documented, modeled, and quantified a new mechanism:
the turnover-liquidity transmission mechanism of monetary policy.
tight money ⇒ scarcer means of payment ⇒ turnover falls ⇒ price falls
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Summary
What are the effects of monetary policy on the stock market?
Unanticipated tightening causes sizeable declines in returns and turnover.
These effects are larger for more liquid stocks.
What is the mechanism?
We documented, modeled, and quantified a new mechanism:
the turnover-liquidity transmission mechanism of monetary policy.
tight money ⇒ scarcer means of payment ⇒ turnover falls ⇒ price falls
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Summary
What are the effects of monetary policy on the stock market?
Unanticipated tightening causes sizeable declines in returns and turnover.
These effects are larger for more liquid stocks.
What is the mechanism?
We documented, modeled, and quantified a new mechanism:
the turnover-liquidity transmission mechanism of monetary policy.
tight money ⇒ scarcer means of payment ⇒ turnover falls ⇒ price falls
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Summary
What are the effects of monetary policy on the stock market?
Unanticipated tightening causes sizeable declines in returns and turnover.
These effects are larger for more liquid stocks.
What is the mechanism?
We documented, modeled, and quantified a new mechanism:
the turnover-liquidity transmission mechanism of monetary policy.
tight money ⇒ scarcer means of payment ⇒ turnover falls ⇒ price falls
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Summary
What are the effects of monetary policy on the stock market?
Unanticipated tightening causes sizeable declines in returns and turnover.
These effects are larger for more liquid stocks.
What is the mechanism?
We documented, modeled, and quantified a new mechanism:
the turnover-liquidity transmission mechanism of monetary policy.
tight money ⇒ scarcer means of payment ⇒ turnover falls ⇒ price falls
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Summary
What are the effects of monetary policy on the stock market?
Unanticipated tightening causes sizeable declines in returns and turnover.
These effects are larger for more liquid stocks.
What is the mechanism?
We documented, modeled, and quantified a new mechanism:
the turnover-liquidity transmission mechanism of monetary policy.
tight money ⇒ scarcer means of payment ⇒ turnover falls ⇒ price falls
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Summary
What are the effects of monetary policy on the stock market?
Unanticipated tightening causes sizeable declines in returns and turnover.
These effects are larger for more liquid stocks.
What is the mechanism?
We documented, modeled, and quantified a new mechanism:
the turnover-liquidity transmission mechanism of monetary policy.
tight money ⇒ scarcer means of payment ⇒ turnover falls ⇒ price falls
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
To do ...
Study other assets
Endogenize αs
Incorporate leverage (realistic, likely to improve model fit)
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
end.
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Monetary policy, OTC frictions, and asset prices
0 10 20 30 40 50 60 70 80 90 1000
2
4
6
8
10
12x 10 5
t (years)
Equity prices (cum dividend, daily)
t (years)0 10 20 30 40 50 60 70 80 90 100
10 7
0
1
2
3
4
5
6
7
8
9
10Real balances
t (years)0 10 20 30 40 50 60 70 80 90 100
10 3
0
0.5
1
1.5
2
2.5Nominal price level
t (years)0 10 20 30 40 50 60 70 80 90 100
10 5
0
1
2
3
4
5
6
7Equity prices (ex dividend, daily)
t (years)0 10 20 30 40 50 60 70 80 90 100
10 6
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2Real balances
t (years)0 10 20 30 40 50 60 70 80 90 100
10 5
0
1
2
3
4
5
6
7
8Nominal price level
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
VAR identification with high-frequency external instrument
KY t = ∑Jj=1 CjYt−j+εt (SVAR)
Yt = ∑Jj=1
(K−1Cj
)Yt−j + ut (VAR)
ut = K−1εt (RFR)
E(utu′t
)= K−1K−1′ (IC1)
K , Cj : n× n matrices
εt ∈ Rn , E (εt ) = 0, E (εt ε′t ) = I , E (εt ε′s ) = 0 for s 6= t
The identification problem:
want to find n2 elements of K−1
condition (IC1) provides n (n+ 1) /2 independent conditionsneed n (n− 1) /2 additional conditions
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
VAR identification with high-frequency external instrument
Yt =(it ,RIt , T It
)′, εt =
(εit , ε
Rt , ε
Tt
)′, ut =
(uit , u
Rt , u
Tt
)′ut = K−1εt (RFR)
K−1 =
k ii kRi kTik iR kRR kTRk iT kRT kTT
⇒
uituRtuTt
= k iik iRk iT
εit +
kRikRRkRT
εRt +
kTikTRkTT
εTt
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
VAR identification with high-frequency external instrument
Find instrument zt for εit , i.e.,
E(zt εRt ) = E(zt εTt ) = 0 < E(zt εit ) ≡ v for all t⇒
Λ ≡ E(ztut ) = K−1E(zt εt ) =(k ii , k
iR, k
iT)′v
Since Λ = (Λ1,Λ2,Λ3)′ is a known (3×1) vector,
vk ii = Λ1
vk iR = Λ2
vk iT = Λ3
⇒ k iRk ii=
Λ2
Λ1and
k iTk ii=
Λ3
Λ1
Λ2Λ1= E(ztuRt )
E(ztu it ): slope of regression of uRt on uit proxied with zt
Λ3Λ1= E(ztuTt )
E(ztu it ): slope of regression of uTt on uit proxied with zt
Our instrument: zt = it ,m∗t+20 − it ,m∗t−10 (on subsmaple S1)
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
VAR: choice of number of lags
Akaike information criterion: 10 lags
Schwarz’s Bayesian information criterion: 5 lags
Hannan and Quinn information criterion: 5 lags
Check how well these specifications estimate the true theoreticalimpulse responses (simulations of length equal to data sample)
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
VAR: choice of number of lags
Compute equilibrium functions for calibrated model
Set policy rate to follow the AR(1) process estimated from data
Compute true theoretical IR to a 1bp increase in the policy rate
Simulate 1000 samples of the dividend and the policy rate
For each sample:
compute equilibrium paths for{RIt}and
{T It}
estimate baseline VAR with 5 and 10 lags. Compute IR to 1bpincrease in policy rate (with HFIV identification scheme)
For version with 5 and 10 lags, report median IR and 95%confidence intervals (from distribution of estimates). Compare withtrue theoretical IR
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
VAR: choice of number of lags
Day s0 5 10 15 20 25 30
Bas
is p
oint
s
7
6
5
4
3
2
1
0
1
2
3Stock return
Day s0 5 10 15 20 25 30
Tim
es p
er d
ay
10 6
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9Daily turnover rate
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
VAR: confidence intervals for impulse responses
Recursive wild bootstrap to compute 95% confidence intervals forestimated IR coeffi cients (Gonçalves and Kilian, 2004)
Given VAR estimates, {Bj}Jj=1 and {ut}, generate bootstrapdraws,
{Y bt}, by Y bt = ∑J
j=1 BjYt−j + ebt ut
ebt : the realization of a scalar random variable taking values of −1or 1, each with probability 1/2
HFIV identification procedure requires bootstrap draws for proxyvariable,
{zbt}. Generate random draws for the proxy variable via
zbt = ebt zt (Mertens and Ravn, 2013)
Use the bootstrap samples{Y bt}and
{zbt}to reestimate the VAR
coeffi cients and compute the associated impulse responses. Theconfidence intervals are the percentile intervals of the distribution of10,000 bootstrap estimates for the impulse response coeffi cients
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Impulse responses to a 1pp increase in the policy rate
Days0 5 10 15 20 25 30
Bas
is p
oint
s
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3Policy rate
DataModel
Days0 5 10 15 20 25 30
Bas
is p
oint
s10
8
6
4
2
0
2
4Stock return
Days0 5 10 15 20 25 30
Tim
es p
er d
ay
105
5
4
3
2
1
0
1Daily turnover rate
Days0 20 40 60 80 100 120
Bas
is p
oint
s
0.4
0.6
0.8
1
1.2
1.4
1.6Policy rate
DataModel
Days0 20 40 60 80 100 120
Bas
is p
oint
s
10
8
6
4
2
0
2
4Stock return
Days0 20 40 60 80 100 120
Tim
es p
er d
ay
105
5
4
3
2
1
0
1Daily turnover rate
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Impulse responses to 1pp increase in policy rate (data)
Days0 200 400 600 800 1000
Bas
is p
oint
s
0.5
0
0.5
1
1.5
2Policy rate
Days0 200 400 600 800 1000
Bas
is p
oint
s
9
8
7
6
5
4
3
2
1
0
1Stock return
Days0 200 400 600 800 1000
Tim
es p
er d
ay
105
5
4
3
2
1
0
1Daily turnover rate
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Results for portfolios sorted on liquidity betas
Rst= αs+βs0T It +βs1MKT t+βs2HMLt+βs3SMB t+εst
For each stock s , run it 73 times, once for each policy day tk , usingsample of all trading days between day tk−1 and day tk
292 betas estimated for each stock s , i.e., {{βsj (k)}3j=0}73k=1,where βsj (k) is for sample (tk−1, tk ]
For each policy day tk , stocks with βs0 (k) between [5 (i − 1)]th
percentile and (5i)th percentile are sorted into the i th portfolio,i = 1, ..., 20
Compute daily Rit and T it − T it−1 for each portfolio
Run event-study regressions portfolio-by-portfolio
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Results for portfolios sorted on liquidity betas
Return TurnoverPortfolio Estimate Std dev Estimate Std dev
1 -.85 1.89 -.0033 .00212 -2.11 1.41 -.0052*** .00193 -1.22 1.23 -.0052*** .00134 -3.38*** 1.19 -.0048*** .00155 -2.69** 1.20 -.0036** .00146 -2.68** 1.10 -.0040*** .00137 -2.64*** .99 -.0032** .00148 -2.39** 1.06 -.0037*** .00149 -3.59*** 1.02 -.0028* .001510 -3.17*** 1.03 -.0028* .001311 -3.92*** 1.09 -.0053*** .001612 -4.71*** 1.05 -.0006 .001513 -4.41*** 1.17 -.0034** .001314 -6.12*** 1.28 -.0025* .001415 -6.53*** 1.43 -.0047*** .001416 -6.63*** 1.50 -.0032* .001717 -7.25*** 1.57 -.0044*** .001518 -6.66*** 1.78 -.0055*** .001719 -10.16*** 2.42 -.0080*** .001920 -13.17*** 3.02 -.0082*** .0023
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Liquidity-beta portfolios: exposure to Fama-French risk factors
Rst= αs+βs0T It +βs1MKT t+βs2HMLt+βs3SMB t+εst
Construct the series of monthly return for each of the 20portfolios for 1994-2001, {
(Rit)20i=1}
Run above regression to estimate {{βij}20i=1}3j=0
For each factor j , plot (i , βij )20i=1
(normalize {βi0}20i=1 by dividing it by∣∣β10∣∣)
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Liquidity-beta portfolios: exposure to Fama-French risk factors
Portfolio0 2 4 6 8 10 12 14 16 18 20
s i
2
1.5
1
0.5
0
0.5
1
1.5
2
2.5Exposure to risk factors
Exposure to market turnoverExposure to market riskExposure to SMB factorExposure of HML factor
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Response of returns: simple CAPM vs. liquidity-beta portfolios
Portfolio0 2 4 6 8 10 12 14 16 18 20
Bas
is p
oint
s (p
er 1
bp
incr
ease
in p
olic
y ra
te)
20
15
10
5
0
5Response of stock return to policy rate
Actual responseResponse according to CAPM
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
3-month Eurodollar futures rate
dateJan94 Jan95 Jan96 Jan97 Jan98 Jan99 Jan00 Jan01 Jan02
Pol
icy
Rat
e in
Bas
is P
oint
s
100
200
300
400
500
600
700
800Time Series of Policy Rate
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Rates: 3-month Eurodollar, effective Fed Funds, target0
200
400
600
800
1/1/92 1/1/94 1/1/96 1/1/98 1/1/00 1/1/02 1/1/04 1/1/06 1/1/08date
Threemonth Eurodollar futures rate Effective Fed Funds rateFed Funds target rate
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Rates: 3-month Eurodollar futures, Fed Funds target0
200
400
600
800
1/1/92 1/1/94 1/1/96 1/1/98 1/1/00 1/1/02 1/1/04 1/1/06 1/1/08date
Threemonth Eurodollar futures rate Fed Funds target rate
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Rates: 3-month Eurodollar futures, effective Fed Funds0
200
400
600
800
1/1/93 7/1/97 1/1/02 7/1/06 1/1/11 7/1/15date
Threemonth Eurodollar futures rate Effective Fed Funds rate
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Rates: effective Fed Funds, Fed Funds target
020
040
060
080
0
1/1/92 1/1/94 1/1/96 1/1/98 1/1/00 1/1/02 1/1/04 1/1/06 1/1/08date
Effective Fed Funds rate Fed Funds target rate
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Estimated monetary policy process
it : 3-month Eurodollar futures rate on day t (in bps)
Estimate (1994-2001): ln it = (1− ξ) ln i0 + ξ ln it−1 + εt
E (it ) = 346 bps SD (it ) = 172 bps ξ = .9997652
Approximate AR(1) with 7-state Markov chain, {ri , σij}7i ,j=1(Rouwenhorst method, Galindev and Lkhagvasuren, 2010)
Mapping between {ri , σij}7i ,j=1 and {µi , σij}7i ,j=1 given by
ri ≈µi − β
β
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Intro Model Theoretical implications Empirical evidence Quantitative theory Conclusion Appx.
Announcement effects for liquidity portfolios: 1994-2007
E-based H-based HFIVPortfolio Turnover Return Turnover Return Turnover Return Turnover
1 .18 -3.85*** -.0004 -9.75*** -.0015** -6.25*** -.0009***
2 .35 -4.26*** -.0006 -12.13*** -.0017 -6.84*** -.0012**
3 .45 -3.60*** -.0008 -9.46*** -.0015 -5.69*** -.0022**
4 .54 -3.22*** -.0002 -11.40*** -.0012 -5.49*** -.0029***
5 .62 -4.83*** -.0010 -14.28*** -.0025 -7.23*** -.00196 .69 -3.65*** -.0009 -12.79*** -.0009 -5.16*** -.00187 .76 -4.88*** -.0008 -15.21*** -.0014 -7.33*** -.0029*
8 .84 -4.34*** -.0011 -21.28*** -.0019 -7.244*** -.0026**
9 .91 -5.10*** -.0013 -14.78*** -.0009 -8.79*** -.0030*
10 .97 -5.60*** -.0016 -16.57*** -.0040 -9.08*** -.0036*
11 1.06 -5.12*** -.0016 -14.48*** -.0025 -8.02*** -.003412 1.15 -5.73*** -.0022* -17.27*** -.0047 -9.46*** -.0049***
13 1.26 -6.87*** -.0020 -18.10*** -.0038 -11.40*** -.0042***
14 1.37 -5.95*** -.0026 -18.36*** -.0026 -9.84*** -.0049**
15 1.49 -6.48*** -.0039** -18.97*** -.0080* -10.00*** -.0059***
16 1.66 -7.60*** -.0035* -22.26*** -.0050 -13.25*** -.0069***
17 1.85 -7.46*** -.0035*** -21.64*** -.0042 -13.03*** -.0093***
18 2.13 -8.35*** -.0041* -23.26*** -.0076 -14.31*** -.0096***
19 2.57 -8.33*** -.0061** -23.74*** -.0115 -13.85*** -.0123***
20 3.63 -9.28*** -.0062 -27.55*** -.0061 -16.40*** -.0189***
NYSE 1.23 -5.73*** -.0022* -16.79*** -.0037 -9.43*** -.0053**