Liquidity Stress Tests

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Joined: Mon Sep 29, 2008 9:21 am

Liquidity Stress Tests

Postby daniel » Mon Sep 29, 2008 9:34 am

On stress testing I am looking for something practical. Given the recent market events, I am keen to find out the practicalities of how one can stress test different portfolios i.e private equity holdings, equity and bond portfolios against different market events to find out how liquidity squeezes and jumps in interest rates and credit spreads can affect you. Also, how one can measure how each bank strategy you have i.e private equity holdings, bond and equity portfolios for example are correlated and the impact of market events on the correlation of each strategy and how you can lose money on one market (equities) driving other markets.
Would you have any spreadsheet based material?

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Joined: Sun Sep 28, 2008 10:30 pm

Re: Liquidity Stress Tests

Postby coalexander » Mon Sep 29, 2008 9:56 am

You need to represent the portfolio P&L as a function of the risk factors, then use scenarios on your risk drivers to induce changes in these risk factors. This will all be explained in detail in Chapter IV.7. Meanwhile, you may like to look at Chapter III.5, which describes how we map the P&L to risk factors, for each different type of portfolio.

Market liquidity risk is the risk associated with an inability to perform market transactions at the current mark-to-market value. It is commonly measured by an exogenous factor, i.e. the relative size of the bid–ask spread, and by an endogenous factor, i.e. market impact. Market impact relates to market depth, i.e. the ability to trade a substantial amount without seriously impacting the mid price. Exogenous liquidity is usually minor compared with endogenous liquidity, so the main liquidity effect you need to capture in stress tests is in the mid price itself as it comes under pressure in a one-way market.

I attach an example (preview from Volume IV, chapter 7) with an Excel spreadsheet for you to play around with. Hope this helps! C[attachment=1:1rf8dwmj]Adjusting VaR for Endogenous Liquidity.pdf[/attachment:1rf8dwmj][attachment=0:1rf8dwmj]Liquidity Adjusted VaR.xls[/attachment:1rf8dwmj]

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Joined: Tue Oct 21, 2008 12:18 am

Re: Liquidity Stress Tests

Postby purbani » Tue Oct 21, 2008 1:04 am

Dear Prof. Alexander

Congratulations on your new four volume set which looks set to become just as critical a reference set as ‘Market Models’.

Attached please find a spreadsheet on the impact of longer liquidity horizons on both the ‘normal’ or Gaussian VaR and CVaR and on the Cornish Fisher (1937) ‘modified’ VaR and CVaR. This is based on simple rather than log returns and is based on the methodology outlined in “The Analytics of the Intervaling Effect on Skewness and Kurtosis of Stock Returns.” By Wingender and Lau.

The use of the Cornish Fisher or ‘modified’ VaR in particular allows one to take account of the excess skewness and kurtosis of returns in your time series. I should warn, however, that the Cornish Fisher expansion to the normal distribution can only handle smallish departures from ‘normality’ and these topics are well covered in Kevin Dowd’s ‘Measuring Market Risk’ and Stefan Jaschke’s and Mina and Ulmer’s papers (“The Cornish-Fisher expansion in the context of Delta-Gamma-Normal approximation” and “Delta Gamma Four Ways” ). The spreadsheet contains a small test that warns if the skewness and kurtosis parameters are causing the Cornish-Fisher expansion to break down in the tail. Obviously simply replacing the ‘normal’ distribution with another assumption is no less egregious and for best results a proper ‘best-fit’ KS or Anderson darling test should be performed to determine what distribution to use.

As there are a number of newer papers relating to the time-scaling problem (More recent papers include: Christoffersen, Diebold and Schuermann’s "Horizon Problems and Extreme Events in Financial Risk Management" and Danielsson and Zigrand’s "On time-scaling of risk”) I would appreciate any feedback from you or the forum on this methodology. The impact of liquidity or the lack-thereof is currently very germane to Hedge Funds and Funds of Funds in particular due to their often inherent liquidity mismatch in terms of their weighted average underlying liquidity profile ( typically 90 to 180 days ) and what they often offer investors ( 30 – 60 days ).

Kind regards,

Peter Urbani

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