ARTICLES

 

Portfolio liquidity-adjusted value-at-risk

 

 

Marius Botha

School of Management, University of the Free State

 

 

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ABSTRACT

An important, yet neglected, aspect of risk management is liquidity risk; changes in value due to reduced availability of traded financial instruments. This ubiquitous risk has emerged as one of the key drivers of the developing "credit crunch" with global financial liquidity plummeting since the crisis began. Despite massive cash injections by governments, the crisis continues. Contemporary research has focussed on the liquidity component of single instruments' value-at-risk. This work is extended in this article to measure portfolio value-at-risk, employing a technique which integrates individual instruments' liquidity-adjusted VaR into a portfolio environment without a commensurate increase of statistical assumptions.

JEL: C1, 2, 5, 13, 22

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References

1 ALEXANDER, C. (2001) Market Models: A Guide to Financial Data Analysis, Wiley: London.         [ Links ]

2 ALMGREN, R. & CHRISS, N. (1999) "Value under liquidation", Risk, December: 58-64.         [ Links ]

3 AMMAN, M. & REICH, C. (2001) "VaR for nonlinear financial instruments - linear approximation or full Monte Carlo?", Financial Markets and Portfolio Management, 15: 1-18.         [ Links ]

4 ANGELIDIS, T & BENOS, A. (2005) "Liquidity adjusted value-at-risk based on the components of the bid-ask spread", http://ssrn.com/abstract=661281 [Date accessed: 31 August 2007]        [ Links ]

5 BANGIA, A.; DIEBOLD, F.X.; SCHUERMANN, T & STROUGHAIR, J. (1998) "Modelling liquidity risk", http://www.ssc.upenn.edu/~fdiebold/papers/paper25/bds.pdf [Date accessed: 22September 2006]        [ Links ]

6 BANGIA, A.; DIEBOLD, F.X.; SCHUERMANN, T & STROUGHAIR, J. (1999) "Liquidity on the outside", Risk, 12: 68-73.         [ Links ]

7 BIS (1988) "International convergence of capital measurement and capital standards", http://www.bis.org/publ/bcbs04a.htm [Date accessed: 12 August 2006]        [ Links ]

8 BIS (2004) "International convergence of capital measurement and capital standards: A revised framework", http://www.bis.org/publ/bcbsca.htm [Date accessed: 17 December 2006]        [ Links ]

9 BIS (2005) "The application of Basel II to trading activities and the treatment of double default effects", http://www.bis.org/publ/bcbs111.htm [Date of access: 28 December 2006]        [ Links ]

10 BLAKE, D.; CAIRNS, A. & DOWD, K. (2000) "Extrapolating VaR by the square-root rule", Financial Engineering News, August, http://www.fenews.com/fen17/var.html [Date accessed: 14 November 2006]        [ Links ]

11 BOLLERSEV, T; CHOU, R.Y. & KRONER, K.F. (1992) "ARCH modelling in finance: a selective review of the theory and empirical evidence", Journal of Econometrics, 52: 5-59.         [ Links ]

12 BOUCHAUDY, J.P. & POTTERS, M. (1999) "Worst fluctuation method for fast Value-at-Risk estimates", Service de Physique de l'etat Condense, Centre d'etudes de Saclay, September. http://ssrn.com/abstract=181949 [Date of access: 11 September 2006]        [ Links ]

13 ÇETIN, U.; JARROW, R.A.; PROTTER, P. & WARACHKA, M. (2004) "Option pricing with liquidity risk", http://www.orie.cornell.edu/~protter/WebPapers/bspaper3.pdf [Date accessed: 2 October 2006]        [ Links ]

14 COSANDEY, D. (2001) "Adjusting value-at-risk or market liquidity", Risk, October: 115-118.         [ Links ]

15 DANIELSSON, J. & ZIGRAND, J-P. (2006) "On time-scaling of risk and the square-root-of-time rule", Journal of Banking & Finance, 30(10): 2701-2713.         [ Links ]

16 DIEBOLD, F.X. & LOPEZ, J. (1995) "Modelling volatility dynamics", in Horner, K. (ed.) Macroeconomics: Developments, Tensions and Prospects, Kluwer Academic Press: Boston, MA, pp. 427-472.         [ Links ]

17 DIEBOLD, F.X.; HICKMAN, A.; INOUE, A. & SCHUERMANN, T (1996) "ConvertingJ-day volatility to h-day volatility: scaling by h is worse than you think", http://www.ssc.upenn.edu/~diebold/ [Date accessed: 18 October 2006].         [ Links ]

18 DOWD, K.; BLAKE, D. & CAIRNS, A. (2003) "Long term value-at-risk", http://www.lse.ac.uk/ubs/pdf/dp17.pdf [Date accessed: 7 November 2006].         [ Links ]

19 ERWAN, L. (2002) "Incorporating liquidity risk in VaR models", June. http://www.gloriamundi.org/picsresources/els.pdf [Date accessed: 17 December 2006].         [ Links ]

20 FERNANDEZ, F.A. (1999) "Liquidity risk: new approaches to measurement and monitoring", http://www.sia.com/research/pdf/workingpaper.pdf [Date accessed: 21 November 2006].         [ Links ]

21 HAUSMAN, J.; LO, A. & MACKINLAY, A.C. (1992) "An ordered probit analysis of transaction stock prices", Journal of Financial Economics, 31: 319-379.         [ Links ]

22 HFRX indices. (2006) http://www.hedgefundresearch.com/hfrx_reg/index.php?fuse=login&1162138035 [Date accessed: 12 December 2006].         [ Links ]

23 HISATA, Y. & YAMAI, Y. (2000) "Research toward the practical application of liquidity risk evaluation methods", Monetary and Economic Studies, December: 83-128.         [ Links ]

24 HOLTON, G. (2003) Value-at-Risk: Theory and Practice, Academic Press: New York.         [ Links ]

25 JARROW, R.A. & PROTTER, P. (2005) "Liquidity risk and risk neasure computation", Review of Futures Markets, 14(1): 2-17.         [ Links ]

26 JARROW, R. & SUBRAMANIAN, A. (1997) "Mopping up liquidity", Risk, December: 170-173.         [ Links ]

27 JARROW, R. & SUBRAMANIAN, A. (2001) "The liquidity discount", Mathematical Finance, 11(4): 447-474.         [ Links ]

28 JP MORGAN. (1996) "Riskmetrics technical document", http://www.riskmetrics.com [Date accessed: 12 January 2007].         [ Links ]

29 L'HABITANT, F.S. (2000) "Hedge funds and investment partnerships: a primer", Discussion Paper, Thunderbird, The American Graduate School of International Management: 1-35.         [ Links ]

30 LHABITANT, F.S. (2001) "Assessing market risk for hedge funds and hedge fund portfolios", The Journal of Risk Finance, 2(4): 16-32.         [ Links ]

31 LAWRENCE, C. & ROBINSON, G. (1995) "Liquidity, dynamic hedging and value-at-risk", Risk Management for Financial Institutions: 63-72.         [ Links ]

32 LE SAOUT, E. (2002) "Incorporating liquidity risk in VaR models", http://www.site.voila.fr/erwanlesaout/eng/rech/abstract.htm#artc01 [Date accessed: 19 September 2006].         [ Links ]

33 LOWENSTEIN, R. (2002) "When genius failed: The rise and fall of long term capital management", Fourth Estate, January, New York.         [ Links ]

34 MADHAVAN, A.; RICHARDSON, M. & ROOMANS, M. (1997) "Why do security prices change? A transaction-level analysis of NYSE stocks", Review of Financial Studies, 10: 1035-1064.         [ Links ]

35 MCNEIL, A.J. (1996) "Estimating the tails of loss severity distributions using extreme value theory", Mimeo: 117-137.         [ Links ]

36 MULVEY, J. (2003) "The role of hedge funds for long-term investors", Journal of financial transformation: 23-28.         [ Links ]

37 RISK MAGAZINE JOURNALISTS (2004) Private communication.         [ Links ]

38 SHARPE, W.F. (1988) "Determining a fund's effective asset mix", Investment Management Review, 2(6), December: 59-69.         [ Links ]

39 UMUT, C.; JARROW, R.A. & PROTTER, P. (2004) "Liquidity risk and arbitrage pricing theory", Finance and Stochastics, 8: 311-341.         [ Links ]

40 YAMAI, Y. & YOSHIBA, T. (2002) "Comparative analyses of expected shortfall and value-at-risk: their validity under market stress", IMES Discussion Paper #2002-E-2, Bank of Japan: 216-270.         [ Links ]