On the elusive concept of liquidity

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.


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


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


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


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


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)


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


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 ··


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


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”


GOAL


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


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


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


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


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


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?


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:


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.



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



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.


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




GOAL



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


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


LIQUIDITY MODEL

23



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


LIQUIDITY MODEL

24



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


LIQUIDITY MODEL

25



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


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


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


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)



LIQUIDITY MODEL

29


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)



LIQUIDITY MODEL

30


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)



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


THANK YOU FOR YOUR ATTENTIONRICARDO GIMENO ([email protected])

mailto:[email protected]

Documents

On the elusive concept of liquidity