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# P2.T7.807. Estimating liquidity-adjusted value at risk (LVaR) (Dowd)

#### Nicole Seaman

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Learning objectives: Define liquidity risk and describe factors that influence liquidity, including the bid-ask spread. Differentiate between exogenous and endogenous liquidity. Describe the challenges of estimating liquidity-adjusted VaR (LVaR). Describe and calculate LVaR using the constant spread approach ...

Questions:

807.1. Foundations (Topic 1) in the Financial Risk Manager (FRM) syllabus contains an excellent reading by Markus K. Brunnermeier, "Deciphering the Liquidity and Credit Crunch 2007—2008." His article contains the following explanation of market liquidity: "Market liquidity is low when it is difficult to raise money by selling the asset (instead of by borrowing against it). In other words, market liquidity is low when selling the asset depresses the sale price and hence it becomes very costly to shrink the balance sheet. Market liquidity is equivalent to the relative ease of finding somebody who takes on the other side of the trade. The literature distinguishes between three sub-forms of market liquidity (Kyle, 1985): 1) the bid–ask spread, which measures how much traders lose if they sell one unit of an asset and then buy it back right away; 2) market depth, which shows how many units traders can sell or buy at the current bid or ask price without moving the price; and 3) market resiliency, which tells us how long it will take for prices that have temporarily fallen to bounce back. While a single trader might move the price a bit, large price swings occur when “crowded trades” are unwound—that is, when a number of traders attempt to exit from identical positions in unison."

Which of the following of Dowd's approaches BEST measures the "market depth" sub-form (the 2nd listed above) of market liquidity to which Brunnermeier refers?

a. Constant spread approach
b. Exogenous spread approach
c. Endogenous-price approach
d. Liquidity at Risk (LaR) approach

807.2. For a sub-portfolio with a market value of $1.0 million, Peter the analyst has calculated a liquidity cost (LC) of$10,000 under the constant spread approach. However, he observes that the spread is approximately normally distributed with a standard deviation of 44 basis points (0.440%). He read that Kevin Dowd advises, "A superior alternative [i.e., to the constant spread approach] is to assume that traders face random spreads. If our position is sufficiently small relative to the market, we can regard our spread risk as exogenous to us (i.e., independent of our own trading), for any given holding period." Therefore, he decides to employ the exogenous spread approach. If his confidence level is 95.0%, what is the portfolio liquidity cost (LC) under the exogenous spread approach?

a. $10,320 b.$13,619
c. $14,312 d.$27,238

807.3. An investment firm owns 10,000 shares in small cap, emerging market stock whose current price is $80.00 per share; i.e., an$800,000 long position. The stock's expected daily return, µ, is presumed to be zero. The stock's volatility, σ = 36.0% per annum. Under an assumption that the stock's geometric returns are normally distributed and a 250-day year, the stock position's 10-day 95.0% confident lognormal VaR is given by (10,000 * $80.00)*(1 - exp[0 - 0.360*1.645*sqrt(10/250)] =$89,356. If the stock's bid-ask spread is \$0.720 per share or 90 basis points (0.90%), then the "constant spread liquidity adjustment" is 1.040. Each of the following statements is true EXCEPT which is false?

a. If the LVaR horizon doubles to 20 days, the liquidity adjustment falls
b. If the LVaR horizon decreases to one day, the liquidity adjustment increases
c. If the LVaR confidence level increases to 99.0%, the liquidity adjustment increases
d. If the LVaR bid-ask spread increases to 120 basis points (1.20%), the liquidity adjustment increases

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