# LO 52.7: Describe approaches to estimate liquidity risk during crisis situations and

LO 52.7: Describe approaches to estimate liquidity risk during crisis situations and challenges which can arise during this process.
In a crisis, assumptions concerning the level of liquidity and other properties that are reasonable in a normal market may not hold. Such crises have occurred in 1987, 1992, 1998, and 20072009. Some event usually precipitates the crisis, such as a large fall in some asset prices, which leads to lower demand and wider bid-ask spreads. The time needed for selling orders to be executed increases. Market liquidity falls at the very time the market needs it.
Many things change during the course of a crisis, and a researcher needs a model that takes into account the distinctive features of a crisis (e.g., large losses, high bid-ask spreads). CrashMetrics may be one way to address this. As an example, the following is the profit/loss on a derivative position based on a delta-gamma approximation:
II = 6 AS +(AS)2
2
where: AS = change in the stock price
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Topic 52 Cross Reference to GARP Assigned Reading – Dowd, Chapter 14
Taking the derivative of this measure with respect to AS and solving for AS gives the change that produces the maximum loss: AS = 8/^, and that maximum loss in absolute value terms is:
max(loss) =
For a derivative position that requires margin and mark-to-market, letting m equal the margin requirement, the worst-case cash outflow is simply m times this amount: m x 82/(2~f). This approximation can be more precise with the inclusion of the effects of other Greeks (e.g., thetas), counterparty risk, and other factors.
Another method for examining the liquidity consequences associated with worst-case scenarios is to apply the basic procedure above to an extreme-value method estimated with expected shortfall (ES). The cash flow would then be m x ES.
These two variations of estimating the worst-case cash flow do not address many real-world complications. A researcher might also wish to address the complications with simulations designed for specific complications. Those complications include: The discreteness of credit events. The interdependency of credit events. The interaction of credit and market risk factors. Complications arising from the use of credit-enhancement methods, such as netting
arrangements, periodic settlement, credit derivatives, credit guarantees, and credit triggers.
Crisis-scenario analysis is an alternative to the probabilistic approaches described previously. This would involve analyzing the potential problems of a particular event (e.g., the failure of a major institution) and working through the specific details of how this might occur. This has the advantage of working through scenarios at a chosen level of detail and accounting for complications and interactions. The problem is that there will be a lot of subjectivity, and the results will depend heavily on the assumptions used.
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Topic 52 Cross Reference to GARP Assigned Reading – Dowd, Chapter 14
K e y C o n c e p t s
LO 52.1 Liquidity risk is the degree to which a trader cannot trade a position without excess cost, risk, or inconvenience. Liquidity depends on factors such as the number of traders in the market, the frequency and size of trades, the time it takes to carry out a trade, the cost, and the risk of the transaction not being completed. It also depends on the type of asset and the degree to which the asset is standardized.
A wider (narrower) bid-ask spread indicates lower (higher) liquidity. If an asset becomes less liquid, the spread increases, and the costs of trading the asset increase.
LO 52.2 Exogenous liquidity refers to the bid-ask spread not being affected by the individual trades made by investors. This is more likely to be the case when the trades are relatively small.
Endogenous liquidity refers to when a given trade can influence the liquidity risk of the trade (i.e., a trader submitting a buy or sell order that increases the spread).
LO 52.3 The main challenge in estimating liquidity is finding the best method. One approach is finding adjustments to add on to the basic VaR. The researcher must understand how the inputs affect the add-ons and, if there are more than one, how the add-ons interact.
LO 52.4 The constant spread approach assumes the bid-ask spread is constant and the liquidity cost is simply, LC = 0.5 x spread x V, which can be added into the VaR formula.
VaR = [1 exp(p a x z )] x V
LVaR = VaR + LC = [1 exp(p a x za) + 0.5 x spread] x V
LO 52.5 To account for endogeneity, a trader may estimate the elasticity of the price to the proportion of the market in a given large trade, denoted E, the proportion itself, denoted AN/N, and adjust the VaR formula.
LVaR = VaR x
1
AP] = VaRx p Ex 1 Ex
AN) N
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Topic 52 Cross Reference to GARP Assigned Reading – Dowd, Chapter 14
LO 52.6 Liquidity at risk (LaR) is also known as cash flow at risk (CFaR) and is the maximum likely cash outflow over the horizon period at a specified confidence level.
LaR can be very different from the VaR of the same position. For example, a bond hedged with a futures contract has low VaR but high LaR from the possible margin call on the futures contract.
Factors that affect future cash flows are: borrowing or lending, margin requirements, collateral obligations, options positions, and changes in risk management policy
LO 52.7 Many things change during the course of a crisis, and a researcher needs a model that takes into account the distinctive features of a crisis (e.g., large losses, high bid-ask spreads).
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Topic 52 Cross Reference to GARP Assigned Reading – Dowd, Chapter 14
C o n c e p t C h e c k e r s
1.
2.
3.
4.
5.
Suppose that portfolio XYZ has a \$1,000,000 portfolio invested in a stock that has a daily standard deviation of 2%. The current bid-ask spread of that stock is 1%. Assuming a constant spread, what is the liquidity-adjusted VaR (normal VaR) at the 95% confidence level? A. \$5,000. B. \$38,000. C. \$44,200. D. \$43,000.
Which of the following actions would most likely increase liquidity risk? A. A rapid execution of orders. B. A higher level of standardization of the asset. C. An increase in the number of traders and a decrease in the size of those trades. D. A decrease in the number of traders and an increase in the size of those trades.
When a given trade can influence the liquidity risk of a trade, this type of liquidity is known as: A. exogenous liquidity. B. undefined liquidity. C. endogenous liquidity. D. operational liquidity.
Assuming the following parameters: p= 0, a = 0.006, spread = 0.01, and a 95% confidence level, the ratio of LVaR to VaR is closest to: A. 1.08. B. 1.51. C. 1.66. D. 2.04.
A trader has a position worth 5% of the size of the market (i.e., AN/N = 0.05) and estimates that the elasticity of price to size of trade is: E = 0.2. The ratio of LVaR to VaR based only on endogenous factors is closest to: A. 0.99. B. 1.01. C. 1.05. D. 1.40.
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C o n c e pt C h e c k e r A n s w e r s
1. B
2. D
3. C
4. B
LVaR= (1,000,000 x 1.65 x 0.02) + (0.5 x 1,000,000 x 0.01) = \$38,000
Larger and fewer traders will ultimately lower liquidity and increase liquidity risk.
It is endogenous because it is determined by the trading activity itself.
LVaR VaR
= 1 +
0.01
2 x [l-e x p (0.006×1.65)] = 1.508
5. B
AP/P = E x AN/N = -0.2 x 0.05 = -0.01
LVaR VaR
endogenous
= 1 ( 0.01) = 1.01
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The following is a review of the Operational and Integrated Risk Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
A s s e s s i n g t h e Q u a l i t y o f Ri s k M e a su r e s
Topic 53
E x a m F o c u s
This topic focuses primarily on model risk and model errors, with specific criticisms of the value at risk (VaR) model. It is important to understand model risk and the factors that could result in variability in VaR estimates. It is also important to understand the challenges associated with mapping risk factors to positions in making VaR calculations. Be ready to explain how incorrect mapping factors can understate certain risks including reputational, liquidity, market, and basis risk. The second part of this topic focuses on two specific case studies on the failures in strategies during 2005 and 2007-2009 related to modeling errors and the underestimation of key risks.
M o d e l R i s k