On the elusive concept of liquidity

2. 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

3. 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

4. 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

6. 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.

7. goal Spanish Government Bonds (11th May, 2010)

8. Estimation of thetermstructure Term structure function:

9. A bit of financialmaths Bond Pricing: • Zero-coupon bonds (Letras del Tesoro) • Coupon-bearing bonds (Bonos y Obligaciones del Estado)

10. 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:

11. 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”

12. 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.

13. Trading book SPGB 5.85 01.31.22 Bloomberg, 2/12/2011,12:00

14. Trading book SGLT 01/20/12 Bloomberg, 2/12/2011,12:00

15. HOMOKEDASTICITY REALLY?

16. 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)

17. 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.

18. 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.

19. 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.

20. Theeffect of liquidityonyield’svariance • Yields are cross-sectionally heteroskedastic. Liquidity-related variables are able to explain variance differences. Model 1 Model 2

21. 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).

22. 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

23. 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

24. 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

25. 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

26. 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

27. Liquiditymodel

28. Liquiditymodel We obtained similar results for other days: 20th April, 2010

29. Liquiditymodel We obtained similar results for other days: 20th April, 2010 11th May, 2010

30. Liquiditymodel We obtained similar results for other days: 20th April, 2010 11th May, 2010 7th July, 2010

31. 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.