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On the elusive concept of liquidity. Liquidity can be seen from two different points of view: Asset-side liquidity: The transaction costs that an investor would suffer in the case of a forced sale. Liquidity Risk Liability-side liquidity : The refinancing costs of maturing debt. - PowerPoint PPT Presentation
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MONETARY AND FINANCIAL STUDIES DEPARTMENT
ON LIQUIDITY MEASURES
Ricardo Gimeno (Banco de España)
INTERNATIONAL COMPETITION IN BANKING: THEORY AND PRACTICE
Sumy, UkraineMay, 24-25 2012
This paper is the sole responsibility of the author and the point of view expressed on it do not necessarily reflect those of the Bank of Spain.
MONETARY AND FINANCIAL STUDIES DEPARTMENT
ON THE ELUSIVE CONCEPT OF LIQUIDITY
Liquidity can be seen from two different points of view:
Asset-side liquidity: The transaction costs that an investor would suffer in the case of a forced sale.
Liquidity Risk
Liability-side liquidity: The refinancing costs of maturing debt.
Funding Risk
2
The recent financial crisis provides an excellent sample for scientific analysis
MONETARY AND FINANCIAL STUDIES DEPARTMENT
ON THE ASSET-SIDE
Lack of liquidity on secondary markets obscure the information markets might provide on the underlying asset.
OTC derivatives vs. Organized Exchanges
Fixed-income markets vs. Stock markets
Sovereign markets and the “Flight To Liquidity” problem
3
MONETARY AND FINANCIAL STUDIES DEPARTMENT
ON THE LIABILITY SIDE
We have an unsolved challenge: to distinguish liquidity and credit risk: “inefficiency or Ponzi scheme”
Banks and the exit strategy
Public debt and the Central Banks support
The credit access to the private sector
4
MONETARY AND FINANCIAL STUDIES DEPARTMENT 5
MONETARY AND FINANCIAL STUDIES DEPARTMENT
GOAL
Present a model to explain the role played by liquidity in the deviations of sovereign bond quoted yields from a theoretical liquidity-free term structure of interest rates.
6
MONETARY AND FINANCIAL STUDIES DEPARTMENT
GOAL
7
0 2 4 6 8 10 12 14 16 180%
1%
2%
3%
4%
5%
6%
Duration (years)
Yie
lds
Spanish Government Bonds (11th May, 2010)
MONETARY AND FINANCIAL STUDIES DEPARTMENT
ESTIMATION OF THE TERM STRUCTURE
8
0 2 4 6 8 10 12 14 16 180%
1%
2%
3%
4%
5%
6%
Duration (years)
Yie
lds
Term structure function: ,ts
MONETARY AND FINANCIAL STUDIES DEPARTMENT
A BIT OF FINANCIAL MATHS
9
mmsn
j
ttsj eNeCP jj ·,
1
·,··
Bond Pricing:
Zero-coupon bonds (Letras del Tesoro)
Coupon-bearing bonds (Bonos y Obligaciones del Estado)
mmseNP ·,·
myn
j
tyj eNeCP j ·
1
···
myeNP ··
MONETARY AND FINANCIAL STUDIES DEPARTMENT
TERM STRUCTURE ESTIMATION
10
There are two options for the estimation of the term structure:Adjust bond PRICES
Adjust bond YIELDS
iPii PP ,ˆ
iyii yy ,ˆ
Since the paper of Vasicek and Fong (JoF, 1982), the error term is assumed to be homokedastic:
22ˆ ii yyE
myeNP ··
2
22·ˆ
dy
dPPPE i
MONETARY AND FINANCIAL STUDIES DEPARTMENT
YIELD CURVE ESTIMATION
11
The options for the estimation of the yield curve are basically two:
Minimizing errors in yields.Germany, Sweden, Switzerland, UK.
Minimizing weighted prices.Belgium, Canada, Finland, France, Italy, Spain.
k
i iii DPP
1
2 1·ˆminˆ
k
iii yy
1
2ˆminˆ
Bank for International Settlements (2005) “Zero-Coupon yield curves: technical documentation”
MONETARY AND FINANCIAL STUDIES DEPARTMENT
GOAL
Present a model to explain the role played by liquidity in the deviations of sovereign bond quoted yields from a theoretical liquidity-free term structure of interest rates.
Yields are cross-sectionally heteroskedastic. Liquidity-related variables are able to explain variance differences.
Liquidity constrains would produce wider movements for less liquid bonds, both in the upside and in the downside.
12
MONETARY AND FINANCIAL STUDIES DEPARTMENT
TRADING BOOK
13
Dealer Px Yld Sz(mm)
Ask
Sabadell 103,062 5,451 1Citigroup 102,983 5,466 10Santander 102,805 5,484 1HVB 102,803 5,480 10RBC CM 102,681 5,508 5Commerzbank 102,660 5,502 1Bankinter 102,615 5,509 5Danske BK 102,613 5,509 5BNP Paribas 102,575 5,514 10RBS 102,493 5,525 5Nomura 102,482 5,531 2,5DZ Bank 102,453 5,533 10ING 102,167 5,566 3
Dealer Px Yld Sz(mm)
Bid
Sabadell 102,062 5,581 1Danske BK 101,713 5,626 5Bankinter 101,680 5,631 5DZ Bank 101,653 5,637 10Santander 101,605 5,639 1BNP Paribas 101,475 5,657 10RBS 101,440 5,662 5ING 101,367 5,671 3Nomura 101,357 5,677 2,5RBC CM 101,281 5,691 5Citigroup 100,884 5,740 10HVB 100,803 5,741 10Commerzbank 100,660 5,764 1
0 10 20 30 40 50 60 70 8099.0
99.5
100.0
100.5
101.0
101.5
102.0
102.5
103.0
103.5
mm€
Pri
ce
SPGB 5.85 01.31.22
Bloomberg, 2/12/2011,12:00
0 10 20 30 40 50 60 70 805.20
5.30
5.40
5.50
5.60
5.70
5.80
mm€
Yie
ld
MONETARY AND FINANCIAL STUDIES DEPARTMENT
TRADING BOOK
14
SGLT 01/20/12
Bloomberg, 2/12/2011,12:00
Dealer Px YldSz(mm
)
Ask
RBC CM 99,829 1,403 10RBS 99,761 1,959 10CommerzBank 99,760 1,970 10Bankinter 99,756 2,000 10ING 99,752 2,036 5Natixis 99,720 2,300 25Danske BK 99,714 2,347 5
Dealer Px Yld Sz(mm)
Bid
CommerzBank 99,648 2,890 10Natixis 99,647 2,900 25Danske BK 99,641 2,947 5RBC CM 99,586 3,403 10RBS 99,579 3,459 10ING 99,575 3,496 5Bankinter 99,513 4,000 10
0 10 20 30 40 50 60 70 8099.35
99.40
99.45
99.50
99.55
99.60
99.65
99.70
99.75
99.80
99.85
99.90
mm€
Pri
ce
0 10 20 30 40 50 60 70 800.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
mm€
Yie
ld
MONETARY AND FINANCIAL STUDIES DEPARTMENT 15
0 10 20 30 40 50 60 70 805
6
6
SPLT 01.20.12 SPGB 5.85 01.31.22
mm€
Yie
ld
HOMOKEDASTICITY
REALLY?
MONETARY AND FINANCIAL STUDIES DEPARTMENT 16
For each day between 1989 and 2010,
We estimate a yield curve for Spanish sovereign bonds, excluding one bond each time,
4,996 days
121,758 term structures
For each expected term structure, we have tried 30 genetic algorithms (Gimeno and Nave, 2009) to get the best fitting.
3,652,740 G.A.
So, we get out-of-sample yield errors,
121,758 yield errors (it)
TERM STRUCTURE ESTIMATION
6655 ·1···1··, 46
435
321
tttt
eet
eet
ts
We have estimated the term structure, for the Spanish Sovereign Bond Market, using the Svensson (1994) model:
MONETARY AND FINANCIAL STUDIES DEPARTMENT 17
THE EFFECT OF LIQUIDITY ON YIELD’S VARIANCE
Turnover (Tit). If the bond is rarely traded, a matching operation would be difficult to reach, and the willing seller (buyer) would have to accept a lower (higher) price in order to complete the transaction.
Elton and Green (1998) signaled that trading volume was a more robust measure of asset liquidity than other proxies used in other studies such as type of security.
MONETARY AND FINANCIAL STUDIES DEPARTMENT 18
THE EFFECT OF LIQUIDITY ON YIELD’S VARIANCE
Tick size. Bond pricing implies that the same price changes has a different effect on a bond depending on their time to maturity (Dit), so those close to maturity will experience higher return swings than the rest.
mreP ·
mreP ·P
P
mrr
·ln
1
0 10 20 30 40 50 60 70 80-0.2
0.0
0.2
0.4
SGLT 01 20 12 SPGB 5.85 01.31.22
mm€
Yie
ld
0 10 20 30 40 50 60 70 8097
98
99
100
101
102
SPLT 01.20.12 SPGB 5.85 01.31.22
mm€
Pri
ce
MONETARY AND FINANCIAL STUDIES DEPARTMENT 19
THE EFFECT OF LIQUIDITY ON YIELD’S VARIANCE
Tick size. Bond pricing implies that the same price changes has a different effect on a bond depending on their time to maturity (Dit), so those close to maturity will experience higher return swings than the rest.
Amihud and Mendelson (1991) found evidence that there was a liquidity premia that was decreasing and convex function of the time to maturity.
MONETARY AND FINANCIAL STUDIES DEPARTMENT 20
Model 1
Model 2
Model 1
Model 2
Level Equation
Intercept -0,989
-0.240
log(hit)
0.184 ***
Variance Equation
Intercept 3,373
3.290
log (Turnoverit) -0,133 ***
-0.129 ***
1/Durationit 0,139 ***
0.142 ***
# of observations
121758
# of days
4996
# of bonds
662
ititit h ·0 1,0~ Nit
itititit hh ··log10 1,0~ Nit
ititit DTch
1··loglog 21
ititit DTch
1··loglog 21
THE EFFECT OF LIQUIDITY ON YIELD’S VARIANCE
Yields are cross-sectionally heteroskedastic. Liquidity-related variables are able to explain variance differences.
MONETARY AND FINANCIAL STUDIES DEPARTMENT
GOAL
Present a model to explain the role played by liquidity in the deviations of sovereign bond quoted yields from a theoretical liquidity-free term structure of interest rates.
Yields are cross-sectionally heteroskedastic. Liquidity-related variables are able to explain variance differences.
Liquidity constrains would produce wider movements for less liquid bonds, both in the upside and in the downside.
Define a term structure model that includes liquidity factors both in the level and variance of the yield.
Liquidity should be included in the variance equation (liquidity risk) and in the level equation (liquidity premium).
21
MONETARY AND FINANCIAL STUDIES DEPARTMENT
LIQUIDITY MODEL
22
The first consequence of previous models is that term structure estimations are not efficient.
Errors should be weighted by the estimated variance
i.e.: 11th May, 2010
0
0,01
0,02
0,03
0,04
0,05
0,06
0 2 4 6 8 10 12 14 16 18
Term (years)
Yields
MONETARY AND FINANCIAL STUDIES DEPARTMENT
LIQUIDITY MODEL
23
The first consequence of previous models is that term structure estimations are not efficient.
Errors should be weighted by the estimated variance
i.e.: 11th May, 2010
0
0,01
0,02
0,03
0,04
0,05
0,06
0 2 4 6 8 10 12 14 16 18
Term (years)
Duration-weightedYields
k
i iii DPP
1
2 1·ˆminˆ
Svensson model weighted by
durations
j1 j2 j3 j4 j5 j6Duration-weighted 0.046 -0.041 -0.002 0.067 2.337 51.435
MONETARY AND FINANCIAL STUDIES DEPARTMENT
LIQUIDITY MODEL
24
The first consequence of previous models is that term structure estimations are not efficient.
Errors should be weighted by the estimated variance
i.e.: 11th May, 2010
Svensson model weighted by estimated
variance
k
i ititititt
hDPP
t 1
2
·
1·ˆminˆ
0
0,01
0,02
0,03
0,04
0,05
0,06
0 2 4 6 8 10 12 14 16 18
Term (years)
YieldsDuration-weightedLiquidity-weighted
j1 j2 j3 j4 j5 j6Duration-weighted 0.046 -0.041 -0.002 0.067 2.337 51.435Liquidity-weighted 0.031 -0.031 0.000 0.084 1.754 16.800
MONETARY AND FINANCIAL STUDIES DEPARTMENT
LIQUIDITY MODEL
25
The first consequence of previous models is that term structure estimations are not efficient.
Errors should be weighted by the estimated variance
i.e.: 11th May, 2010
Joint estimation of variance equation and
Svensson model
k
i itititittt
hDPP
tt 1
2
, ·
1·ˆminˆ,ˆ
j1 j2 j3 j4 j5 j6 g0 g1 g2
Duration-weighted 0.046 -0.041 -0.002 0.067 2.337 51.435Liquidity-weighted 0.031 -0.031 0.000 0.084 1.754 16.800Joint estimation 0.026 -0.026 0.000 0.105 0.967 22.228 -0.012 0.000 1.906
0
0,01
0,02
0,03
0,04
0,05
0,06
0 2 4 6 8 10 12 14 16 18
Term (years)
YieldsDuration-weightedLiquidity-weightedJoint estimation
MONETARY AND FINANCIAL STUDIES DEPARTMENT
LIQUIDITY MODEL
26
Liquidity risk could be priced in the level equation a la Elton and Greene (1998) or Alonso et al. (2004)
i.e.: 11th May, 2010
Liquidity model
k
i ititititttt
hDPP
ttt 1
2
,, )(·
1·,ˆminˆ,ˆ,ˆ
hmmsn
j
httsj eNeCP jj ··,
1
··,··ˆ
mmsn
j
ttsj eNeCP jj ·,
1
·,··ˆ
0
0,01
0,02
0,03
0,04
0,05
0,06
0 2 4 6 8 10 12 14 16 18
Term (years)
YieldsDuration-weightedLiquidity-weightedJoint estimationLiquidity model
j1 j2 j3 j4 j5 j6 g0 g1 g2 aDuration-weighted 0.046 -0.041 -0.002 0.067 2.337 51.435Liquidity-weighted 0.031 -0.031 0.000 0.084 1.754 16.800Joint estimation 0.026 -0.026 0.000 0.105 0.967 22.228 -0.012 0.000 1.906Liquidity model 0.024 -0.024 0.000 0.110 0.888 21.716 0.000 -0.043 2.034 0.001
MONETARY AND FINANCIAL STUDIES DEPARTMENT
LIQUIDITY MODEL
27
j1 j2 j3 j4 j5 j6 g0 g1 g2 aDuration-weighted 0.046 -0.041 -0.002 0.067 2.337 51.435Liquidity model 0.024 -0.024 0.000 0.110 0.888 21.716 0.000 -0.043 2.034 0.001
0 2 4 6 8 10 12 14 16 180
0.01
0.02
0.03
0.04
0.05
0.06
Yields
Duration-weighted
Liquidity model
Term (years)
hmmsn
j
httsj eNeCP jj ··,
1
··,··ˆ
MONETARY AND FINANCIAL STUDIES DEPARTMENT
LIQUIDITY MODEL
28
We obtained similar results for other days:
20th April, 2010j1 j2 j3 j4 j5 j6 g0 g1 g2 a
20/04/2010 0.023 -0.023 0.031 0.092 4.142 19.303 10.869 -0.313 1.179 0.00012
0
0,01
0,02
0,03
0,04
0,05
0,06
0 2 4 6 8 10 12 14 16 18
Term (years)
YieldsDuration-weightedLiquidity-weightedJoint estimationLiquidity model
MONETARY AND FINANCIAL STUDIES DEPARTMENT
LIQUIDITY MODEL
29
We obtained similar results for other days:
20th April, 2010
11th May, 2010j1 j2 j3 j4 j5 j6 g0 g1 g2 a
11/05/2010 0.024 -0.024 0.000 0.110 0.888 21.716 0.000 -0.043 2.034 0.00060
j1 j2 j3 j4 j5 j6 g0 g1 g2 a20/04/2010 0.023 -0.023 0.031 0.092 4.142 19.303 10.869 -0.313 1.179 0.00012
0
0,01
0,02
0,03
0,04
0,05
0,06
0 2 4 6 8 10 12 14 16 18
Term (years)
YieldsDuration-weightedLiquidity-weightedJoint estimationLiquidity model
MONETARY AND FINANCIAL STUDIES DEPARTMENT
LIQUIDITY MODEL
30
We obtained similar results for other days:
20th April, 2010
11th May, 2010
7th July, 2010
j1 j2 j3 j4 j5 j6 g0 g1 g2 a11/05/2010 0.024 -0.024 0.000 0.110 0.888 21.716 0.000 -0.043 2.034 0.00060
j1 j2 j3 j4 j5 j6 g0 g1 g2 a20/04/2010 0.023 -0.023 0.031 0.092 4.142 19.303 10.869 -0.313 1.179 0.00012
j1 j2 j3 j4 j5 j6 g0 g1 g2 a07/07/2010 0.029 -0.029 0.003 0.101 0.374 16.115 0.000 -0.122 0.803 0.00000
0
0,01
0,02
0,03
0,04
0,05
0,06
0 2 4 6 8 10 12 14 16 18
Term (years)
YieldsDuration-weightedLiquidity-weightedJoint estimationLiquidity model
MONETARY AND FINANCIAL STUDIES DEPARTMENT
CONCLUSIONS
Liquidity differences among bonds from the same issuer can produce heteroskedasticity.
Cross-sectional models for the term structure should be corrected for liquidity differences
We propose a Svensson model modified by liquidity risk.
31
MONETARY AND FINANCIAL STUDIES DEPARTMENT
THANK YOU FOR YOUR ATTENTIONRICARDO GIMENO ([email protected])