Sep 03

Liquidity risk: Liquidity-adjusted Value at Risk (LVaR)(2007 FRM)

by David Harper, CFA, FRM, CIPM

FRM | Risk |

liquidityIntroLVAR

Learning Outcome

  • LO 20.5: Calculate liquidity-adjusted VAR.

Liquidity-adjusted value at risk (VaR)

Previously we defined liquidity and itemized factors that exacerbate liquidity risk. One way to adjust value at risk (VaR) to account for liquidity risk is to simply tweak up the VaR. The 'constant spread' approach achieves this by adding one-half of the asset's bid-ask spread to increase the VaR (here are some weaknesses of the bid-ask spread).

For FRM candidates, the Culp reading gives liquidity-adjusted VaR as: 

culplvar2

However, this formula creates confusion if you are not careful. For example, I recently read an application of this formula where the author used an expected return of 5% and a standard deviation of 2%. As plugged into the above, they computed a VaR (before the spread term) of 1.7% because 5% - (2%)(1.645) = 1.7%. Then the spread term increases the LVaR. But this is wrong because a higher return would make for an even higher LVaR! That's because the above formula is an absolute VaR not a relative VaR (see this thread for explanation of absolute vs. relative VaR) and so you have to pay attention to the signs.

It is better to use use Kevin Dowd's version:

dowdlvar

This is just VaR increased by one-half the spread. The EditGrid spreadsheet below illustrates with an example.  If you would like to try the spreadsheet, this link will open a new copy (and File > Save As... will upload to Excel or another format). The inputs are colored yellow. Only the following inputs are required:

  • Confidence level [e.g., =NORMSINV(95%) gives 1.645]
  • Initial portfolio value
  • Time horizon (e.g., 1 day)
  • Spread (e.g., 2%)
  • Expected annual return
  • Annual standard deviation

Given those assumptions, the spreadsheet first calculates "plain old" VaR on a percentage and dollar basis. Right below that, with a green background, are the liquidity-adjusted LVaRs. They are higher directly as a function of the spread.

Finally, the ratio between LVaR/VaR is given to illustrate the dramatic impact that a small spread can have on VaR. For our initial assumptions, a 2% spread translates into a +39% increase from VaR to LVaR!.

EditGrid Spreadsheet by bt/frm2007.

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