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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.

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on the elusive concept of liquidity
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

The recent financial crisis provides an excellent sample for scientific analysis

on the asset side
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
on the liability side
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
slide6
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.

slide7
goal

Spanish Government Bonds (11th May, 2010)

estimation of the term structure
Estimation of thetermstructure

Term structure function:

a bit of financial maths
A bit of financialmaths

Bond Pricing:

  • Zero-coupon bonds (Letras del Tesoro)
  • Coupon-bearing bonds (Bonos y Obligaciones del Estado)
term structure estimation
Termstructureestimation

There are two options for the estimation of the term structure:

  • Adjust bond PRICES
  • Adjust bond YIELDS

Since the paper of Vasicek and Fong (JoF, 1982), the error term is assumed to be homokedastic:

yield curve estimation
Yield curve estimation
  • 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.

Bank for International Settlements (2005) “Zero-Coupon yield curves: technical documentation”

slide12
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-sectionallyheteroskedastic. 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.

trading book
Trading book

SPGB 5.85 01.31.22

Bloomberg, 2/12/2011,12:00

trading book1
Trading book

SGLT 01/20/12

Bloomberg, 2/12/2011,12:00

term structure estimation1
TERM STRUCTURE estimation

We have estimated the term structure, for the Spanish Sovereign Bond Market, using the Svensson (1994) model:

For each day between 1989 and 2010,

4,996 days

We estimate a yield curve for Spanish sovereign bonds, excluding one bond each time,

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)

the effect of liquidity on yield s variance
Theeffect of liquidityonyield’svariance

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.

the effect of liquidity on yield s variance1
Theeffect of liquidityonyield’svariance

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.

the effect of liquidity on yield s variance2
Theeffect of liquidityonyield’svariance

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.

the effect of liquidity on yield s variance3
Theeffect of liquidityonyield’svariance
  • Yields are cross-sectionally heteroskedastic. Liquidity-related variables are able to explain variance differences.

Model 1

Model 2

slide21
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-sectionallyheteroskedastic. 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).

liquidity model
Liquiditymodel

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

liquidity model1
Liquiditymodel

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 durations

liquidity model2
Liquiditymodel

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

liquidity model3
Liquiditymodel

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

liquidity model4
Liquiditymodel

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

liquidity model6
Liquiditymodel

We obtained similar results for other days:

20th April, 2010

liquidity model7
Liquiditymodel

We obtained similar results for other days:

20th April, 2010

11th May, 2010

liquidity model8
Liquiditymodel

We obtained similar results for other days:

20th April, 2010

11th May, 2010

7th July, 2010

conclusions
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.