Articles by kenli

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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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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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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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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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

LO 52.6: Describe liquidity at risk (LaR) and compare it to LVaR and VaR, describe the factors that affect future cash flows, and explain challenges in estimating and modeling LaR.
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. A positive (negative) value for LaR means the worst outcome will be associated with an outflow (inflow) of cash. LaR is similar in concept to VaR, but instead of a change in value, it deals with a cash flow. LaR is also distinct from liquidity-related losses, but they are related.
As an example, an investor has a large market risk position that is hedged with a futures position. If the hedge is a good one, the basis risk is small, and the VaR should be small. There is the possibility of margin calls on the futures position, however, and this means there is the possibility of a cash outflow equal to the size of that position. In summary, the hedged position has a small VaR but a large LaR. At the other extreme, European options have zero LaR until expiration, but potentially large VaR prior to maturity.
The following is a list of factors that influence cash flows and LaR: Borrowing or lending. Margin requirements on market risk positions that are subject to daily marking to market. Collateral obligations, such as those on swaps, which can generate inflows or outflows of
cash from changes in market factors, such as interest rates.
2.
Jarrow, R.A. and A. Subramanian. (1997). Mopping up liquidity. Risk 10 (December): 170-173.
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Short explicit options or implicit options (e.g., convertibility and call features).
Changes in risk management policy (e.g., a change in the type of hedge), which may
change mark-to-market requirements.
Two other considerations are as follows: (1) LaR can increase when the firm is facing hard times (e.g., a credit downgrade increases the rate on bank loans); and (2) there are positions that are similar in terms of market risk (e.g., a futures versus an options hedge), but are very different in terms of LaR.
As a practical matter for the firm attempting to estimate LaR, consider using the firms VaR procedures to estimate the VaRs of marginable securities and then combine this LaR estimate with comparable figures from other sources of liquidity risk within the organization to produce an integrated measure of firm-wide liquidity risk. The point is to use the existing and accepted VaR procedures to estimate liquidity risks. It is obviously ad hoc, however, and a firm facing complex liquidity risks should build a more appropriate model. This would involve identifying and modeling the variables indicated in the following list: The certain cash flows (e.g., from U.S. Treasury investments). The unconditional uncertain cash flows (e.g., from risky bonds). The conditional uncertain cash flows (e.g., those that only result if a certain decision is
made, such as making an investment).
Other conditioning variables that might trigger cash flows. Having identified the factors, the manager can construct an appropriate engine to estimate the risks. Estimating the LaR may only require a variance-covariance approach, or it may require a more advanced simulation approach.
R o l e o f L i q u i d i t y D u r i n g C r i s i s

LO 52.5: Describe endogenous price approaches to LVaR, their motivation and limitations, and calculate the elasticity-based liquidity adjustment to VaR.
Both the constant spread approach and the exogenous spread approach assume that prices do not change in response to trading (i.e., prices are exogenous). This may not always be the case, and it may be necessary to make a liquidity adjustment for endogenous prices. In the case of selling for example, there may be downward pressure on prices, which causes a loss. VaR should include an adjustment for the possibility of this loss. The adjustment should be larger if the market prices are more responsive to trades. 1. Bangia, A.E Diebold, T. Schuermann, and J. Stroughair. (1999). Liquidity on the outside.
Risk 12 (June): 68-73.
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Of the various ways to include an adjustment, a relatively simple method uses the concept of elasticity, E. In this case, it is the proportional change in price divided by the proportion of the market traded:
AP/P AN/N
where: AN/N = size of the trade relative to the entire market
Generally, it is the case that E < 0 and AN/N > 0. A researcher can estimate values for E and AN/N and input them into an expression for LVaR as follows:
LVaR = VaR x
1 Ex AP) = VaRx f 1 Ex p
^ A N j
N
, ^ AN LVaR ——- = 1 E x —— N VaR
The approach is very convenient because the adjustment is independent of the computation of VaR and its assumptions, and the ratio of LVaR to VaR is a function of only two inputs. The obvious limitation is its narrow focus and that it entirely ignores bid-ask spreads and transactions costs. On the other hand, a researcher can easily combine this adjustment with one of the other liquidity adjustments by simply multiplying the effects:
LVaR VaR combined
LVaR VaR
exogenous
x
LVaR VaR endogenous
Example: Endogenous price approach
A trader has a position worth 10% of the size of the market (i.e., AN/N = 0.1) and estimates that E = 0.4 so that AP/P = E x AN/N = 0.4 x 0.1 = 0.04. Compute the ratio of LVaR to VaR based only on endogenous factors and the combined LVaR to VaR ratio assuming the ratio for the exogenous approach is 1.89.
Answer:
LVaR VaR endogenous
= 1 ( 0.04) = 1.04
Thus, the adjustment for endogeneity will increase the total adjustment for liquidity by 4%. Using the liquidity adjustment for the exogenous approach yields the following combined result:
LVaR VaR combined
= 1.89×1.04 = 1.97
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Jarrow and Subramanian (1997)2 offer a more sophisticated method called the liquidity discount VaR, where the trader maximizes expected utility by liquidating the position within a certain period of time. It incorporates both exogenous and endogenous market liquidity, spread cost, spread risk, an endogenous holding period, and an optimal liquidation policy. It does so with three modifications: (1) uses an optimal holding period based on the traders expected-utility optimization problem, (2) adds the average liquidity discount to the traders losses, and (3) has the volatility measure include the volatility of the time to liquidation and the volatility of the liquidity discount factor, as well as the volatility of the underlying market price.
L i q u i d a t i o n , T r a n s a c t i o n s C o s t s , a n d M a r k e t P r i c e I m p a c t
As with most ancial activities, there are tradeoffs to consider when executing a trade. Attempting to sell quickly will usually increase the transactions costs and may have an unfavorable impact on the selling price. Taking more time to sell can increase the exposure to exogenous and unfavorable price changes. A trader should recognize the tradeoff and identify a set of efficient trading strategies that produce the minimum remaining risk exposure at any given point in time, for any given expected cost. The trader should choose the strategy that best fits his risk aversion. A more (less) risk averse trader would choose a strategy that executes more (less) quickly. A more (less) quick execution will reduce (increase) price uncertainty with higher (lower) transactions costs.
L i q u i d i t y a t R i s k

LO 52.4: Describe and calculate LVaR using the constant spread approach and the exogenous spread approach.
The constant spread approach, as the name implies, calculates LVaR assuming the bid-ask spread is constant. This makes the liquidity cost equal to half the spread multiplied by the size of the position to be liquidated. The liquidity cost (LC) to add on to the initial VaR estimate is then:
LC = 0.5 x V x spread
where: V value of the position = value of the position
, (ask price bid price) spread = ——– ;——- ————– (ask price + bid price) / 2
Recall that VaR quantifies the maximum loss for a given confidence level over a particular holding period. For example, a typical VaR calculation may indicate a 1% probability of losses exceeding $ 10 million over a five-day holding period. LVaR is calculated using the following formula assuming a constant spread:
LVaR = (V x z x a) + [0.5 x V x spread] V -A /
LVaR = VaR + LC
where: V = asset (or portfolio) value za = confidence parameter a = standard deviation of returns
Professors Note: Notice that VaR in this example is dollar VaR as opposed to percentage VaR.
The confidence level of the estimate is 1 o l (e.g., 5% level of significance (a) = 95% confidence level). Note that the larger the spread, the larger the calculated LVaR. Since liquidity risk incorporates selling the asset, not a full round trip, only half of the spread is used.
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Example: Computing LVaR
Suppose that ABC Company has a current stock price of $100 and a daily standard deviation of 2%. The current bid-ask spread is 1%. Calculate LVaR at the 95% confidence level. Assume a constant spread.
Answer:
LVaR = (100 x 1.65 x 0.02) + (0.5 x 100 x 0.01) = $3.80
The previous discussion involved the use of normal VaR (i.e., VaR assuming asset prices are normally distributed). In practice, asset prices are lognormally distributed as was illustrated in the FRM Part I curriculum when we examined the Black-Scholes-Merton option pricing model. In this assigned reading, the author uses lognormal VaR to calculate the liquidity- adjusted VaR. The conventional lognormal VaR, with no adjustment for liquidity risk, is calculated in the following fashion:
Lognormal VaR = [1 exp(p a x z )] x V
where: p = mean return
The liquidity-adjusted VaR is then calculated as follows:
LVaR = VaR + LC = [1 exp(p a x z ) + 0.5 x spread] x V
Using the simplifying assumption of p = 0, the ratio of LVaR to VaR becomes:
^
LVaR VaR
spread
2 x [1 exp(a x za )] This expression indicates that the liquidity adjustment will increase (decrease) when there is an increase (decrease) in the spread, a decrease (increase) in the confidence level, and a decrease (increase) in the holding period.
Professors Note: Notice that the calculation o f lognorm al VaR and normal VaR w ill be similar when we are dealing with short-tim e periods and practical return estimates.
Example: Computing LVaR to VaR ratio (constant spread)
Assume the following parameters: p = 0, a = 0.012, spread = 0.02, and a 95% confidence level. Compute the LVaR to VaR ratio.
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Answer:
, LVaR ——– H ——–r——————————- i VaR 2 x [l – exp(0.012 x 1.65)] 0.02
1.51
The increase from VaR to LVaR is just over 50%, from only a 2% spread. This demonstrates that even a small spread can translate into a surprisingly large liquidity adjustment to VaR.
LVaR can also be calculated given the distribution characteristics of the spread. This is the foundation underlying the exogenous spread approach. If you are given the mean and standard deviation of the spread, you would apply the following formula:
LVaR = VaR + 0.5 x [(ps + zfi x as)] x V
P ro fesso rs N ote: We a d d th e co n fid en ce p a ra m eter tim es th e v o la tility o f th e sp rea d to th e m ean o f th e sp rea d sin ce th e liq u id ity a d ju stm en t in crea ses th e v a lu e a t risk. Also, n o tice th a t th e co n fid e n ce p a ra m eter (or z -score) u sed f o r th e u n certa in ty o f th e sp rea d is la b eled d ifferen tly. T he co n fid en ce p a ra m eter, in th is case, is a v a lu e to b e d eterm in ed .
The exogenous spread approach assumes that the spread is stochastic and that the trades of a single trader do not affect the spread. The spread could follow one of many distributions; for example, the normal distribution or a more leptokurtic distribution (historically, the distribution of the spread has been highly non-normal with excess amounts of kurtosis). Once having assumed a distribution, the researcher can estimate the LVaR using Monte Carlo simulation by simulating values for both Vand the spread, incorporating the spread into Vto get liquidity-adjusted prices, and then infer the liquidity-adjusted VaR from the distribution of simulated liquidity-adjusted prices.
Example: Computing LVaR (assuming normal VaR)
Suppose that ABC Company has a current stock price of $100 and a daily standard deviation of 2%. The mean of the bid-ask spread is 2%, and the standard deviation of the bid-ask spread is 1%. Calculate LVaR at the 95% confidence level assuming the confidence parameter of the spread is equal to 3.
Answer:
LVaR = (100 x 1.65 x 0.02) + -100 x (0.02 + 3 x 0.01) = $5.8
2
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Topic 52 Cross Reference to GARP Assigned Reading – Dowd, Chapter 14
The researcher can determine the optimal value of t! using some suitably calibrated Monte Carlo exercise [Bangia et al. (1999)1 assume a value of three for z; ]. Applying lognormal assumptions, the LVaR using the exogenous spread approach is the lognormal VaR plus the liquidity adjustment:
LVaR = VaR + LC = V x {[1 exp(p a x za)] + [0.5 x (ps + z’a x as)]}
It is worth noting that if a s equals zero, then this expression becomes the LVaR formula for the constant spread approach where ps = spread. Thus, this approach is simply the constant spread approach with an added expression to allow for a stochastic spread.
We can now apply the familiar LVaR to VaR ratio:
LVaR _ ^ j LC VaR VaR
(p>s+ZqXas )
2 x [l exp(a x za )] Example: Computing LVaR to VaR ratio (exogenous spread)
A researcher estimates the mean and standard deviation of the spread to be 0.02 and 0.005, respectively. He also estimates that p = 0 and a = 0.012 for the underlying returns distribution. Using a 95% confidence level, compute the ratio of LVaR to VaR. Assume the confidence parameter for the spread, t! , is equal to 3.
Answer:
LVaR _ , , I —————- —- 1 ————- r———————————————————–7 l . o y VaR
2 x [1 – exp(0.012 x 1.65)] (0.02 + 3 x 0.005)
The result here, when compared to the previous answer, demonstrates how including the possibility of the spread being random (stochastic) can increase the liquidity adjustment. In this case, it almost doubles from 51% to 89%.
Endogenous Price Approaches

LO 52.3: Describe the challenges of estimating liquidity-adjusted VaR (LVaR).
One of the challenges of estimating liquidity-adjusted value at risk (LVaR) is choosing the best method. As in most choices, there is a tradeoff between sophistication and ease of implementation, and it is worth noting that sophistication and usefulness are not necessarily positively correlated. It is recommended to find approaches that are transparent in their assumptions and simple to implement (e.g., implementable with just a spreadsheet). A good way to do this is to determine liquidity add-ons that allow a researcher to modify original VaR estimates that did not include factors for illiquidity. In addition to addressing liquidity, the approach can also assess the impact of assumptions on estimates of VaR.
.Another challenge is liquidity adjustments that are compatible with the basic VaR approach and each other. This is because different methods look at different aspects of illiquidity, and it can be helpful to combine add-ons that give the best overall liquidity adjustment. In other words, two less sophisticated methods may be much better than one really good sophisticated method.
Another challenge is to check how the liquidity adjustment changes other inputs, such as the confidence level, holding period, or any other parameters (i.e., the sensitivity of the other inputs to the liquidity adjustment). The researcher should be aware of some basic relationships (e.g., an increase in the holding period should lower the level of the liquidity adjustment).
The researcher should try to calibrate the model against real data (e.g., check if the bid-ask spread parameters are empirically plausible), and properly stress test the model, as well as backtest the model. The researcher should be aware that there is probably not a single, best
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approach that would exclude the use of all others. Furthermore, using different approaches can help highlight different liquidity concerns.

LO 52.2: Differentiate between exogenous and endogenous liquidity.
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). If an investor attempts to purchase a large block of an asset, for example, the buy order may have an impact on the spread and increase the cost over that indicated by the initial bid-ask prices. This can also happen when an investor tries to liquidate an asset. This type of endogeneity problem is more likely in illiquid markets and when the trade is large relative to the market.
In summary, for endogenous markets, if a trader attempts to liquidate (buy) a large position, the trader should expect the bid (ask) price to fall (increase) and the bid-ask spread to widen. The trader should include such a market reaction when estimating liquidity costs and risks. In both the endogenous and exogenous case, the bid-ask spread is still a function of the factors already mentioned (the number of traders, the standardization of the asset, low transactions costs, etc).
L i q u i d i t y -A d j u s t e d Va R

LO 52.1: Define liquidity risk and describe factors that influence liquidity, including the bid-ask spread.
Liquidity risk is the degree to which a trader cannot trade a position without excess cost, risk, or inconvenience. When liquidity risk exists, there can be several types of price uncertainty. First, the usual market quote of the average of the bid and ask prices becomes less meaningful because the spread is wider, which means the market quote is even farther from either the buy or sell transaction price. Second, a larger bid-ask spread means a higher cost to get in and out of the position. Third, the actual price of either a buy or sell order is less certain because the assets do not trade frequently, and the quoted bid and ask prices will probably not be the prices of the respective sell and buy transactions when actually executed. There is also an increased risk in that the spread can change (i.e., it is stochastic), which will increase the risks of trading.
Liquidity is a function of the type of market and its characteristics. It 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 less standardized asset will have higher liquidity risk. A forward contract has much more liquidity risk than a futures contract, for example, because the forward contract is not a standardized contract. Over-the-counter (OTC) derivatives of all types usually have relatively high liquidity risk.
B i d – A s k S p r e a d
The bid-ask spread is a cost of liquidity. A wider (narrower) spread indicates lower (higher) liquidity. If an asset becomes less liquid, the spread increases, and the costs of trading the asset increase. The risk of liquidity changing, and changes in the spread, should be included with other measures of market risk. The spread can also change as a result of the activities of a given trader when liquidity is endogenous, which is described in the next LO.
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E x o g e n o u s v s . E n d o g e n o u s L i q u i d i t y

LO 31.7: Calculate the financing advantage of a bond trading special when used in a repo transaction.
The premium trading value of OTR bonds is due both to their liquidity and financing advantage as we previously discussed. The liquidity advantage stems from the ability to sell these bonds quickly for cash. The financing value stems from the ability to lend the bonds at a cheap special rate and use the cash to lend out at higher GC rates. This financing value is dependent on the traders expectation of how long the bond will continue trading at its special rate before the rate moves higher toward the GC rate.
Lets assume that an OTR bond is issued on January 1 and trades at a special spread of 0.18%. A trader expects the bond to trade at GC rates past March 31. The financing value of the OTR bond is therefore the value over 90 days. The value of $100 of cash at the spread of 0.18% is:
90×0.18% _ _ $100 x ————– — $0,043
.
360
Thus, the financing value is 4.3 cents per $100 market value of the bond
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K e y C o n c e pt s
LO 51.1 Repurchase agreements, or repos, are bilateral contracts where one party sells a security at a specified price with a commitment to buy back the security at a future date at a higher price. From the perspective of the borrower we refer to repos, while from the perspective of the lender we refer to reverse repos. Repos are valued based on a simple time value of money calculation.
LO 51.2 >From the perspective of the borrower, repos offer relatively cheap sources of obtaining short term funds. Balancing the cost of funding (e.g., through repos) and other sources of funds (including potentially no funding) is called liquidity management.
>From the perspective of the lender, repos can be used for either investing (cash management) or for financing purposes (e.g., to finance short bond positions).
LO 51.3 Repos give rise to both counterparty risk and liquidity risk. Counterparty (credit) risk is the risk of borrower default or non-payment of its obligations. Liquidity risk is the risk of an adverse change in the value of the collateral. Counterparty risk is mitigated with collateral, while liquidity risk is mitigated with haircuts, margin calls, shorter repo terms, and higher quality collateral.
LO 51.4 During the recent financial crisis, lenders were increasingly demanding higher quality collateral and larger haircuts and even withdrew liquidity altogether. Borrowers experienced collateral liquidations and capital declines, leading to several high profile company failures and bankruptcies. The failures of Bear Stearns and Lehman Brothers illustrate these events.
LO 51.5 Repo trades can be secured either with general collateral or with specific collateral. Lenders (as investors) in general collateral (GC) repo trades are not concerned with receiving a specific security, and only the broad categories of acceptable securities are specified. GC trades suit investors in repos because they can obtain the highest repo rate for the collateral received. Lenders (as financing participants) in special collateral repo trades (specials trades) are concerned with receiving a particular security as collateral. The particular security received can then be used to finance the purchase of a bond (for shorting) or to finance its inventory or proprietary positions.
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LO 51.6 The difference between the GC rate and the special rate for a particular security and term is called a special spread. Special spreads are tied closely to Treasury bond auctions, and the level and volatility of the spread can be an important gauge of market sentiment. Special spreads are generally narrower immediately after an auction, but widen before auctions. Spreads generally move within a band that is capped at the GC rate (implying a floor of 0% for the special rate).
Following the recent financial crisis, regulators adopted a penalty rate for failed trades at the greater of 3% minus the federal funds rate, or zero. As a result, the penalty rate becomes the new upper limit for the special spread.
LO 31.7 The financing value of the bond is the ability to lend the bonds at a relatively cheap special rate and use the cash to lend out at higher GC rates. This financing value is dependent on the traders expectation of how long the bond will continue trading at its special rate.
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C o n c e pt C h e c k e r s
1.
3.
Pasquini Investments (Pasquini) is a private brokerage looking for 30-day financing of $23 million of its accounts payable but is unsure whether the appropriate investment is a term repurchase agreement (repo) or a term reverse repo agreement. Pasquini is willing to post AAA-rated government bonds as collateral. The bonds have a face value of $27 million and a market value of $23 million. The firm is quoted a rate of 0.5% for the transaction. Which of the following choices most accurately reflects the contract type and the contract price needed by Pasquini?
Contract tvpe
A. Repo B. Reverse repo C. Repo D. Reverse repo
Contract price $27,011,250 $25,010,417 $25,010,417 $27,011,250
Posting collateral and requiring collateral haircuts are important risk mitigants in repo transactions with respect to which of the following risks?
Posting collateral
A. Market risk B. Credit risk C. Market risk D. Credit risk
Collateral haircuts Interest rate risk Interest rate risk Liquidity risk Liquidity risk
Kotra Bank Holdings, Inc., (Kotra) is currently weighing the cost of its funding against the risk of being left without financing. The term that best describes Kotras activities is: A. counterparty (credit) risk. B. specials trading. C. D. overnight funding.
liquidity management.
4.
In a presentation to management, a bond trader makes the following statements about repo collateral:
Statement 1: The difference between the federal funds rate and the general collateral rate is the special spread.
Statement 2: During times o f financial crises, the spread between the federal funds rate and the general collateral rate widens.
Which of the traders statements are accurate? A. Both statements are incorrect. B. Only Statement 1 is correct. C. Only Statement 2 is correct. D. Both statements are correct.
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The latest on-the-run (OTR) Treasury bond issued on March 1 is trading at a special spread of 0.25%. Traders expect the bond to trade at general collateral (GC) rates past June 30. The financing value of the OTR bond is therefore the value over 122 days. Given this information, the value of lending $100 of cash is closest to: A. $0,085. B. $0,250. C. $0,305. D. $0,847.
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C o n c e pt C h e c k e r A n sw e r s
1. C Given that Pasquini is a borrower in the repo market, the transaction is a repo from the
perspective of the firm (but a reverse repo from the perspective of the lender). The contract price is calculated as follows: $25,000,000 x 1 + 0.5% x 30 ,
$25,010,417
360
2. D Collateral is an important counterparty credit risk mitigant. Repo loans are secured by
collateral, which makes the lender much less vulnerable to a decline in the creditworthiness of the borrower. Collateral haircuts are important in mitigating liquidity risk in repo transactions. The lender is exposed to the risk of the value of the collateral declining during the repo term, which can be mitigated by requiring (higher) haircut values, that is, discounts to the value of the posted collateral.
3. C The process of weighing the cost of its funding against the risk of being left without
financing is called liquidity management. Counterparty (credit) risk is the risk of borrower default or non-payment of its obligations. In specials trading, a lender of cash initiates a repo trade in order to receive a particular security (special collateral). Overnight funding refers to borrowing and lending in the overnight market.
4. C The traders first statement is incorrect. The difference between the federal funds rate and
the general collateral (GC) rate is known as the fe d funds- GC spread. The special spread is the difference between the GC rate and the special rate for a particular security.
The trader s second comment is correct. During times of financial crises, the spread between the federal funds rate and the general collateral rate widens as the willingness to lend Treasury securities declines, lowering the GC rate (thereby increasing the spread).
5. A The financing value of $100 of cash at a spread of 0.25% is calculated as:
$100x—————-= $0.0847 or 8.47 cents
360
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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:
Est i ma t i n g Li q u i d i t y Ri s k s
Topic 52
E x a m F o c u s
This topic addresses the calculation of liquidity cost and applies this value to the value at risk measure. We will see how to compute liquidity-adjusted VaR (LVaR) when considering both a constant spread and an exogenous spread approach. Be familiar with how to make these calculations, particularly for the constant spread approach. Also, understand the concept of cash flow at risk (CFAR) and how liquidity is impacted during a crisis.
L i q u i d i t y R i s k

LO 51.6: Describe the characteristics of special spreads and explain the typical behavior of US Treasury special spreads over an auction cycle.
The difference between the GC rate and the special rate for a particular security and term is called a special spread. Special spreads are important because in the United States, they are tied closely to the U.S. government Treasury bond auctions, and the level and volatility of the spread can be an important gauge of market sentiment.
In the United States, federal government bonds are sold at auction based on a predetermined, fixed schedule. The most recent issue is called the on-the-run (OTR) or current issue, while all other issues are called off-the-run (OFR). Current OTR issues tend to be the most liquid, with low bid-ask spreads, that can be liquidated quickly even in large sizes. This liquidity makes them desirable for both long positions and short positions. For example, a repo lender would favor these securities for short positions because the shorts could be covered quickly and at a relatively low cost. The popularity of OTR issues as special collateral in repo trades historically resulted in lower repo rates and wider special spreads.
Several observations can be made by looking at the special spreads of OTR Treasury securities (OTR special spreads) and the auction-driven pattern of special spreads. First, OTR special spreads can be volatile each day depending on the special collateral. Second, spreads can fluctuate over time. Third, and most important, OTR special spreads are generally narrower (smaller) immediately after an auction but wider before auctions. They are narrower after auctions due to the extra supply of a new OTR security, which depresses special spreads. Spreads widen before auctions due to the substitutability of the special collateral as shorts change to the new OTR security.
The influence of auctions can also be observed from the term structure of individual OTR issues based on term special spreads (the difference between term GC rates and term special rates). Term special spreads are expected to decline immediately following the issue of the new OTR security but increase closer to the dates of the new auctions.
S p e c i a l S p r e a d s a n d R a t e L e v e l s
Special spreads generally move within a band that is capped at the GC rate (implying a floor of 0% for the special rate). When a trader short sells the OTR Treasury security but fails to deliver on settlement, the trader would not receive cash from the sale and would also miss out on a days interest on the cash. To satisfy the settlement obligation to deliver the bond, the trader could borrow the bond in the overnight repo market and pay a special rate of 0% (essentially the trader provides free financing in exchange for receiving the desired bond). At any rate below 0%, no trader would borrower the bond. This puts both an effective lower bound and an effective cap of the special spread at the GC rate.
The special spread can also be tied to the penalty for failed trades. Until 2009, there was no penalty for failed trades. Flowever, in light of the financial crisis and trillions of dollars in failed OTR deliveries, regulators adopted a penalty rate for failed trades, equal to the greater of 3% minus the federal funds rate, or zero. This means that as the federal funds rate
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increases, the penalty falls, and when the federal funds rate declines to zero, the penalty rate reaches its maximum at 3%. As a result, the new upper limit for the special spread is the penalty rate.

LO 51.5: Compare the use of general and special collateral in repo transactions.
Repo trades can be secured either with general collateral or with specific (i.e., special) collateral.
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General Collateral
While lenders care about the quality of collateral delivered, under general collateral (GC), repo lenders are not concerned with receiving a particular security or class of securities as collateral. Instead, only the broad categories of acceptable securities are specified. The logic here is that when lenders are looking to receive a specific rather than generic security as collateral, this creates a demand for that security and lenders have to accept a lower return on the repo trade. GC trades suit investors in repos because they can obtain the highest repo rate for the collateral received.
The repo rate for trades secured with general collateral is called the GC rate. GC rates can be used for repos with U.S. Treasury collateral, and the overnight rate for U.S. Treasury collateral is referred to as the GC rate. In the United States, the GC repo rate is typically slightly below the federal funds rate, although repos with U.S. Treasury collateral are considered safer and in fact can trade below the federal funds rate. The difference between the federal funds rate and the GC rate is measured through the fed funds-GC spread. This spread widens when Treasuries become scarcer (the GC rate falls) or during times of financial stress, as was the case during the recent financial crisis.
Professors Note: The fed era l funds rate is an interest rate that depository institutions in the United States charge each other fo r lending funds m aintained at the Federal Reserve.
Special Collateral
When lenders are concerned with receiving a particular security as collateral, the collateral is referred to as special collateral, and the repo trade is called a specials trade. If you recall our discussion on financing as a motivation for repo lending, it should be clear that specials trades are particularly important in financing transactions used to obtain specific bonds. The repo rate for trades secured with special collateral is called the special rate.
In specials trading, the lender of cash is concerned with receiving a particular security in order to finance the purchase of a bond (for shorting), or to finance its inventory or proprietary positions. Lenders accepting special collateral face a trade-ofF between receiving the desired security and lending at below GC rates to receive the desired security. Special rates differ by security because there is a rate for each security for each term. Special rates are determined by market supply and demand; however, it is important to note that the supply and demand of the underlying security is not the same as the supply and demand of the specials trade itself. In fact, a bond that is in high demand in the market may not be in great demand as collateral for a specials trade. The reverse could equally be true.
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S p e c i a l S p r e a d s a n d t h e A u c t
i o n C y c l e