Advertisement

Using Value-at-Risk (VaR) to Measure Market Risk of the Equity Inventory of a Market Maker

  • Argyn Kuketayev
  • James Beatty
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 135)

Abstract

We propose a simple approach to using value-at-risk (VaR) to measure market risk within the equity inventory of a market making entity, a task which presents several challenges specific to the market making function. Market makers constantly stand ready to buy and sell shares to market participants. In doing so, they inevitably maintain the inventory of shares, a portfolio of sorts, subject to market risk. VaR is a standard tool for measuring the market risk in investment portfolios, so a variety of calculation techniques have been developed over the years. However, the application of VaR to market making inventories requires a few adjustments, for unlike the typical investment portfolio these inventories change rapidly, as if they were rebalanced intra-day. Moreover, the number of unique tickers in the inventory for a given day may routinely list thousands of securities. As a result, at any moment in an inventory there could be hundreds of items with missing historical price data, which makes challenging the application of even the simplest VaR methods. The approach proposed in this paper deals with the rapidly rebalancing portfolio and missing data issues inherent in market making equity portfolios by rescaling portfolio weight to allow for the application of well-known VaR techniques to very large inventories.

Keywords

Value-at-risk Market making Equity Portfolio rebalancing 

References

  1. 1.
    Schwartz, R.A., Francioni, R.: Equity Markets in Action. Wiley, Hoboken (2004)Google Scholar
  2. 2.
    Harris, L.: Trading and Exchanges: Market Microstructure for Practitioners. Oxford University Press, New York (2002)Google Scholar
  3. 3.
    Schwartz, R.A., Peng, L.: Market makers. In: Lee, C., Lee, A.C. (eds.) Encyclopedia of Finance. Springer, New York (2006)Google Scholar
  4. 4.
    Grossman, S.J., Miller, M.H.: Liquidity and market structure. J. Financ. 43(3), 617–633 (1988). doi: 10.1111/j.1540-6261.1988.tb04594.x CrossRefGoogle Scholar
  5. 5.
    Glosten, L.R., Milgrom, P.R.: Bid, ask and transaction prices in a specialist market with heterogenously informed traders. J. Financ. Econ. 14(1), 71–100 (1985). doi: 10.1016/0304-405X(85)90044-3
  6. 6.
    O’Hara, M., Oldfield, G.S.: The microeconomics of market making. J. Financ. Quant. Anal. 21(04), 361–376 (1986). doi: 10.2307/2330686 CrossRefGoogle Scholar
  7. 7.
    Hasbrouck, J., Sofianos, G.: The trades of market makers: an empirical analysis of NYSE specialists. J. Financ. 48(5), 1565–1593 (1993). doi: 10.1111/j.1540-6261.1993.tb05121.x CrossRefGoogle Scholar
  8. 8.
    Linsmeier, T.J., Pearson, N.D.: Value at risk. Financ. Analysts. J. 56(2), 47–67 (2000). doi: 10.2469/faj.v56.n2.2343 CrossRefGoogle Scholar
  9. 9.
    Yamai, Y., Yoshiba, T.: On the validity of value-at-risk: comparative analysis with expected shortfall. Monet. Econ. Stud. 20(1), 57–85 (2002)Google Scholar
  10. 10.
    Riskmetrics (1996) Technical Document. Morgan Guaranty Trust Company of New YorkGoogle Scholar
  11. 11.
    Jorion, P.: Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill Companies, Inc., New York (2006)Google Scholar
  12. 12.
    Alexander, C.: Market Risk Analysis, Value at Risk Models. Wiley, Chichester (2008)Google Scholar
  13. 13.
    Little, R.J.A. Rubin, D.B.: Statistical Analysis with Missing Data. Wiley, New York (1987)zbMATHGoogle Scholar
  14. 14.
    Sharpe, W.F.: A simplified model for portfolio analysis. Manag. Sci. 9(2), 277–293 (1963). doi: 10.1287/mnsc.9.2.277 CrossRefGoogle Scholar
  15. 15.
    Björk, T.: Arbitrage Theory in Continuous Time. Oxford University Press, Oxford (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.E*TRADE Financial CorporationViennaUSA
  2. 2.KPMGNew YorkUSA

Personalised recommendations