Articles by kenli

LO 54.5: Describe the relationship between leverage and a firms return profile, calculate the leverage ratio, and explain the leverage effect.
A firms leverage ratio is equal to its assets divided by equity (total assets / equity). That is:
L = A = (E + D)
E E
D E
For an all-equity financed firm, the ratio is equal to 1.0, its lowest possible value. As debt increases, the leverage ratio (i.e., multiplier) increases. For example, a firm with $100 of assets financed with $50 debt and $50 equity has a leverage ratio equal to 2.0 ($100/$50 = 2).
Return on equity (ROE) is higher as leverage increases, as long as the firms return on assets (ROA) exceeds the cost of borrowing funds. This is called the leverage effect. The leverage effect can be expressed as:
rE = LrA – ( L ~ 1 )rD
where: rA = return on assets r = return on equity rD = cost of debt L = leverage ratio
It may help to think of this formula in words as follows:
ROE = (leverage ratio x ROA) [(leverage ratio 1) x cost of debt] For a firm with a zero cost of debt, return on equity is magnified by the leverage factor; however, debt is not free. Thus, return on equity (ROE) increases with leverage, but the cost of borrowing, because there is more debt, also increases. The L 1 factor multiplies the cost of debt by the proportion of the balance sheet financed with debt. For example, with a leverage ratio of 2, 50% of the balance sheet is financed with debt and 50% with equity. So for every $2 of assets, $1 comes from shareholders and $1 comes from borrowed funds. We multiply the cost of debt by 1 in this case. If the leverage ratio is 4, 25% is financed with equity and 75% is financed with debt. Thus, for every $4 of assets, $1 is equity and $3 is borrowed funds. In the formula, we multiply the cost of debt by 3. The higher the leverage factor, the bigger the multiplier but also the higher the debt costs. Leverage amplifies gains but also magnifies losses. That is why leverage is often referred to as a double-edged sword.
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The effect of increasing leverage is expressed as:
9 < r / <9L = rA – rD
where: < 9 r = change in retained earnings &L = change in the leverage ratio
This formula implies that, given a change in the leverage ratio, ROE changes by the difference between ROA and the cost of debt.
The equity in the denominator of the leverage ratio depends on the entity. If it is a bank, it may be the book value of the firm. It might also be calculated using the market value of the firm. The net asset value (NAV) of a fund is the appropriate denominator for a hedge fund. The NAV reflects the current value of the investors capital in the fund.
Example: Computing firm ROE (total assets = $2)
Martin, Inc., a U.S. manufacturing company, has an ROA equal to 5%, total assets equal to $2, and equity financing equal to $1. The firms cost of debt is 2%. Calculate the firms ROE.
Answer:
rE = L r A – ( L – 1)rD
rP = [(2 / 1) x 5%] – [(2 – 1) x 2%] = 8%
Example: Computing firm ROE (total asset = $4)
Martin, Inc., a U.S. manufacturing company, has an ROA equal to 5%, total assets equal to $4, and equity financing equal to $1. The firms cost of debt is 2%. Calculate the firms ROE.
Answer:
rE = LrA ~ ( L – 1)rD
rE = [(4 /1) X 5%] – [(4 –
1) X 2%\ = 14%
Given a cost of debt of 2%, increasing the leverage factor from 2 to 4 increased the firms ROE from 8% to 14%.
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Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
Leverage is also influenced by the firms hurdle rate (i.e., required ROE). For example, assume a firms hurdle rate (i.e., ROE) is 10%, ROA equals 6%, and its cost of debt equals 2%. The firm will choose a leverage ratio of 2.0. That is:
ROE = (2 x 6%) – (1 x 2%) = 10%
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L e v e r a g e

LO 54.4: Compare transactions used in the collateral market and explain risks that can arise through collateral market transactions.
Collateral markets have two important purposes. First, they enhance the ability of firms to borrow money. Cash is only one type of asset that is borrowed. Securities are also borrowed in collateral markets. Second, collateral markets make it possible to establish short positions in securities.
Firms with excess cash are more willing to lend at a low rate of interest if the loan is secured by collateral. Securities are used as collateral for secured loans. Collateralized loans can be short term or longer term. Overnight loans are often extended automatically. The full value of the securities is not lent in a collateralized loan. The difference is called a haircut. For example, a lender may be willing to lend $95 against $100 of collateral.
Collateral values fluctuate and most collateralized borrowing arrangements require that variation margin be paid to make up the difference (called remargining). Variation margin is the additional funds a broker requests so that the initial margin requirement keeps up with losses. The haircut ensures that the value of the collateral can fall by a certain percentage (i.e., 5% in the previous example) and still leave the loan fully collateralized. The variation margin protects the lender.
Collateralized loans are used to finance securities or other assets or trades. The securities pledged to one firm are often loaned or pledged again, hence the collateral circulates. This process is known as rehypothecation or repledging.
The role of collateral has expanded in contemporary finance, hand-in-hand with the development of securitization. Securitization creates securities that can be pledged as collateral for credit. Securitized assets generate cash flows, may appreciate in value, and can be used as collateral for other transactions.
Life insurance companies own large portfolios of high-quality assets. They may use these assets for collateralized loans to borrow at low rates and reinvest at higher rates. Hedge funds pledge securities to finance portfolios at rates cheaper than unsecured loans.
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Markets for collateral take the following forms: Margin loans. Margin loans are used to finance security transactions. The margin loan is collateralized by the security and is often provided by the broker intermediating the trade. The broker maintains custody of the securities in a street name account (i.e., securities are registered in the name of the broker rather than the owner). This structure makes it easier to seize and sell securities to meet margin calls. An added advantage to the broker is that securities in street name accounts can be used for other purposes, such as lending to other customers for short sales. In practice, the broker uses the customers collateral to borrow money in the money market to provide margin loans to customers. The margin loan to the broker is collateralized by the repledged customer collateral. The Federal Reserves Regulation T sets the initial margin requirement for securities purchases at 50%. Cross-margin agreements are used to establish the net margin position of investors with portfolios of long and short positions. In general, cross margin involves transferring excess margin in one account to another account with insufficient margin, resulting in lower overall margin for the investor.
Repurchase agreements or repos. Repurchase agreements, also known as repos and RPs,

are another form of collateralized short-term loans. They involve the sale of a security at a forward price agreed upon today. The interest on the loan is implied from the difference between spot and forward prices of the securities. While traditionally collateral had little or no credit risk (collateral was usually Treasury bills), today acceptable collateral encompasses whole loans, high-yield bonds, and structured credit products. Repos allow banks and other firms to finance inventories of structured credit products and allow for high investment grade ratings for senior tranches of asset-backed securities (ABSs) and collateralized debt obligations (CDOs). Securities lending. Securities lending involves the loan of securities to another party in exchange for a fee, called a rebate. The lender of the securities continues to receive the dividends and interest cash flows from the securities. Lenders of securities are often hedge funds or other large institutional investors of equities. Securities are held in street name accounts to make them available for lending to traders who want to short stocks. Fixed income securities lending typically involves the loan of Treasury securities for cash. The cash is invested in a higher risk bonds and the investors objective is to earn the spread between the two.
Total return swaps. In a total return swap (TRS), one party pays a fixed fee in exchange for the total return (both income and capital gains) on a reference asset, typically a stock. The advantage is that the party paying the fee can earn the return from the underlying asset without owning the asset. The party providing the return (such as a hedge fund) is, in essence, short the asset.
Professor’s Note: Securities lending, like repurchase agreements, are often structured as sales o f securities, not loans o f securities, so the holder o f the collateral can rehypothecate the securities, or even sell them in a timely fashion i f the loan is not repaid.
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L e v e r a g e R a t i o a n d L e v e r a g e E f f e c t

LO 54.3: Describe specific liquidity challenges faced by money market mutual funds and by hedge funds, particularly in stress situations.
Systematic funding risks were apparent in many market sectors during the subprime mortgage crisis. As loans become shorter term, lenders and borrowers are exposed to greater liquidity risks. Borrowers must be able to refinance in order to repay short-term loans. The risk is systematic in that it affects borrowers and lenders at the same time.
Liquidity issues arose during the recent financial crisis for a variety of investment strategies including: Leveraged buyouts (LBOs). Leveraged loans became the dominate type of syndicated
bank loans as LBOs and private equity grew before the crisis. Leveraged loans accounted for a large part of collateralized loan obligations (CLOs) and collateralized debt obligations (CDOs), which provided funding for LBOs. During the subprime mortgage crisis, LBO deals fell apart as funding dried up. Some loans, called hung loans, had not been distributed to investors and demand dried up. Banks incurred significant losses as prices fell sharply.
Merger arbitrage hedge funds. Hedge funds engaged in merger arbitrage experienced losses in the early stages of the subprime mortgage crisis. After a merger is announced, the targets stock price typically increases and the acquirers price sometimes declines due to increased debt. The merger arbitrage strategy exploits the difference between the current and announced acquisition prices. Hedge funds experienced large losses as mergers were abandoned when financing dried up.
Convertible arbitrage hedge funds. Convertible arbitrage strategies rely on leverage to enhance returns. Credit is extended by broker-dealers. When financing becomes unavailable due to market conditions, as experienced in the 20072009 financial crisis, convertible bond values drop precipitously. The funding liquidity problem was compounded by redemptions (i.e., a market liquidity problem). Also, because there is a limited clientele investing in convertible bonds, when the clientele develops a dislike for the product due to deteriorating market conditions, it is difficult to sell the assets without large price declines. The gap between convertible bond prices and replicating portfolios widened dramatically during the financial crisis, but it still did not bring arbitrage capital into the market.
The broader point is that investment strategies, such as merger arbitrage, convertible arbitrage, and leveraged buyouts, are not only exposed to idiosyncratic risks, but also to systematic risks (i.e., systematic funding risks in this case). The risks are soft risks because they are difficult to relate to a particular series of asset returns. Instead, analysts must examine data on credit and liquidity spreads as well as quantitative and anecdotal data on the availability of credit in the market to understand the probability of a liquidity freeze.
Money market mutual fund (MMMF) investors can write checks and make electronic bank transfers. Like banks, MMMFs are obligated to repay investors/depositors on demand. In general, underlying MMMF assets are high credit quality instruments with short maturities (e.g., a few weeks to a few months). However, the values of the underlying assets in the fund, despite their relative safety, are subject to change. As such, redemptions may be limited if asset values fall. The liabilities of MMMFs are, therefore, more liquid than their investments, similar to banks.
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MMMFs use a form of accounting called the amortized cost method, under the Securities and Exchange Commissions (SEC) Rule 2a 7. This means that MMMF assets do not have to be marked-to-market each day, as required for other types of mutual funds. The reason behind the difference is that extremely short-term securities are not likely to revalue based on changes in interest rates and credit spreads. MMMFs set a notional value of each share equal to $1.00. Flowever, credit write-downs cannot be disregarded and it is possible for net asset values (NAVs) to fall below $1.00. This is known as breaking the buck.
Liquidity risk can also cause NAVs to fall below $1.00. MMMFs, like depository institutions, are subject to runs. If a large proportion of investors try to redeem shares in adverse market conditions, the fund may be forced to sell money market paper at a loss. This can potentially result in write-downs and breaking the buck.
E c o n o m i c s o f t h e C o l
l a t e r a l M a r k e t

LO 54.2: Summarize the asset-liability management process at a fractional reserve bank, including the process of liquidity transformation.
Commercial bank assets are typically longer-term and less liquid than bank liabilities (e.g., deposits). Wholesale funding (i.e., non-deposit sources of funding like commercial paper, bonds, and so on) is generally longer term but deposits are sticky. Depositors generally change banks only if impelled to by a move or some other extenuating circumstance. Deposits make up approximately 60% of bank liabilities in the United States.
Banks only expect a fraction of deposits and other liabilities to be redeemed at any point in time. As a result, they do not hold all the deposits in liquid assets, but make loans with deposits instead. For example, a bank might take in $100 of deposits, hold $10 for redemptions, and lend the remaining $90. This is known as a fractional-reserve bank and the process of using deposits to finance loans is known as asset-liability management (ALM).
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The bulk of banks in history have been fractional-reserve banks. The alternative to a fractional-reserve system is one in which the bank uses owners money (i.e., equity) or money raised in capital markets to make loans, and keeps in reserve cash or highly liquid assets equal to its deposits.
If withdrawals are greater than the banks reserves, the bank is forced into a suspension of convertibility. This means the bank will not be able to, as expected by depositors, convert deposits immediately into cash. In the extreme, there may even be a run on the bank. In the case of a bank run, depositors who are concerned about bank liquidity may attempt to get money out of the bank before other depositors and lenders. While rollover risk associated with other short-term financing is less extreme than bank runs, it does increase the fragility of banks. Higher capital reduces bank fragility.
Frozen commercial paper markets in the wake of the Lehman Brothers failure illustrated the fragility of bank funding. Commercial funding couldnt be placed and thus fell dramatically after the Lehman bankruptcy. It became nearly impossible to roll over longer term paper and very short-term paper rose to account for approximately 90% of the market. The Federal Reserve stepped in after the Lehman bankruptcy and created the Commercial Paper Funding Facility (CPFF) and the Asset-Backed Commercial Paper Money Market Mutual Fund Liquidity Facility (AMLF).
S t r u c t u r e d C r e d i t P r o d u c t s a n d O f f – B a l a n c e S h e e t V e h i c l e s
Structured credit products, such as asset-based securities (ABSs) and mortgage-backed securities (MBSs), match investor funding needs with pooled assets. Because these products are maturity matched, they are not subject to funding liquidity issues. However, investor financing for structured credit products can create liquidity risk when investors rely on short-term financing. This type of financing was one of the main drivers of the recent subprime crisis and the increase in leverage in the financial system leading up to the crisis. Two types of short-term financing include: (1) securities leading (i.e., applying structured credit products as collateral to short-term loans), and (2) off-balance sheet vehicles.
Special-purpose vehicles (SPVs) serve as off-balance sheet vehicles by issuing secured debt in the form of asset-backed commercial paper (ABCP). ABCP conduits finance purchases of assets, such as securities and loans, with ABCP. They receive liquidity and credit support via credit guarantees. Structured investment vehicles (SIVs) differ slightly from ABCP conduits because they do not receive full liquidity and credit support.
Prior to the subprime crisis, both ABCP conduits and SIVs profited from the spread between funding costs and asset yields. The assets held by these vehicles typically had longer maturities than the ABCP that fund the assets. In addition to maturity transformation, these vehicles also provided liquidity transformation. This was accomplished by creating ABCP that was more liquid and had shorter terms than the assets held in the conduit and SIV. However, despite being off-balance sheet, which permitted firms to hold less capital, these vehicles did not entirely transfer risk. As a result, they still contributed to the leverage issues and fragility of the financial system during the recent subprime crisis.
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S y s t e m a t
i c F u n d i n g L i q u i d i t y R i s k

LO 54.9: Explain interactions between different types of liquidity risk and explain how liquidity risk events can increase systemic risk.
Liquidity is defined in many ways in financial markets. In general, an asset is liquid if it is close to cash. This means that the asset can be sold quickly, cheaply, and without moving the price too much. A market is liquid if positions can be unwound quickly, cheaply (i.e., at low transactions costs), and without undue price deterioration.
Liquidity has two essential properties, which relate to two essential forms of risk. Transactions liquidity deals with financial assets and financial markets. Funding liquidity is related to an individuals or firms creditworthiness. Risks associated with liquidity include: Transactions (or market) liquidity risk is the risk that the act of buying or selling an
asset will result in an adverse price move.
Funding liquidity risk or balance sheet risk results when a borrowers credit position is either deteriorating or is perceived by market participants to be deteriorating. It also occurs when the market as a whole deteriorates. Under these conditions, creditors may withdraw credit or change the terms of credit (e.g., increase the required collateral for the loan). The position may, as a result, be unprofitable or may need to be unwound. Balance sheet risks are higher when borrowers fund longer term assets with shorter term liabilities. This is called a maturity mismatch. Maturity mismatching is often profitable for firms because short-term investors bear less risk and have a lower required rate of return. This means that short-term debt financing contributes less to the overall cost of capital of a borrowing firm. The incentive to maturity mismatch is even greater when the yield curve is upward sloping. However, funding long-term assets with short-term
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financing exposes the borrower to rollover risk (sometimes called cliff risk), the risk that the debt cannot be refinanced or can only be refinanced at escalating rates. Systemic risk is the risk that the overall financial system is impaired due to severe financial stress. With this risk, credit allocation is impaired across the financial system. Risks associated with liquidity are interrelated and can exacerbate problems. For example, if collateral requirements are increased, a counterparty may be forced to unwind a position early and at a potential loss. In this case, the increase in funding liquidity risk increases the transactions liquidity risk.
An important connection between funding and transactions liquidity is leverage. An investor with a long position may be forced to sell an asset if future funding for the asset dries up. This in turn would reduce the number of potential asset holders, leading to a reduction in asset valuation. It may be the case that this decline in price is temporary, however, the length of the depressed asset price could be long enough to adversely impact the solvency of the investor who initially purchased the asset. A rapid deleveraging of assets could lead to a debt-deflation crisis.
Transactions liquidity could also impair funding liquidity. For example, if a hedge fund is facing redemptions, it is forced to raise cash by selling assets and therefore must decide which assets to sell first. Selling highly liquid assets will lead to fewer adverse price impacts, but will leave the hedge fund with a more illiquid portfolio. On the other hand, selling highly illiquid assets will increase realized losses, which may put additional pressure on the portfolio from a funding liquidity standpoint.
The level of economy-wide liquidity directly impacts the level of systemic risk. When market conditions deteriorate, liquidity tends to become constrained just when investors need it the most. Liquidity risk events could potentially become systemic risk events through disruptions in payment, clearing, and settlement systems. Severe stress to the financial system would impact market participants simultaneously, suggesting that the illiquidity or insolvency of one counterparty may have a domino effect on other market participants throughout the system.
L i q u i d i t y T r a n s f o r m a t i o n b y B a n k s

LO 54.1: Differentiate between sources of liquidity risk, including balance sheet/ funding liquidity risk, systematic funding liquidity risk, and transactions liquidity risk, and explain how each of these risks can arise for financial institutions.

LO 53.4: Explain major defects in model assumptions that led to the underestimation of systematic risk for residential mortgage backed securities (RMBS) during the 20072009 financial downturn.
The subprime RMBS valuation and risk models have been widely employed by credit rating agencies to assign bond ratings, by traders and investors in bond valuations, and by issuers in structuring RMBS. During the 2007-2009 financial downturn, two major defects in model assumptions became apparent: 1. Assumption o f future house price appreciation. The RMBS risk model generally assumed that future house prices would rise, or at least not fall, based on relatively few historical data points. When house prices actually did drop beginning in 2007, this incorrect assumption led to a significant underestimation of the potential default rates and systematic risk in RMBS because the credit quality of the loans was dependent on borrowers ability to refinance without additional equity.
2. Assumption o f low correlations. The RMBS model assumed low correlations among
regional housing markets, implying that loan pools from different geographical regions were well diversified. When house prices declined, correlations increased and loan defaults were much higher than previously expected under the model stress scenarios. These two model errors led to a significant underestimation of systematic risk in subprime RMBS returns. When mortgage default rates began to increase, rating agencies were required to downgrade most issues, and by the end of 2009, approximately 45% of the initially AAA-rated U.S. RMBS had been downgraded. The downgrades of RMBS from their AAA-equivalent ratings shocked markets and exposed the degree to which systemic risk had been underestimated and mispriced.
There have been several explanations proposed for the inaccuracy of the rating models. First, the compensation of rating agencies by bond issuers led to a potential conflict of interest scenario that resulted in lower ratings standards. Second, an increase in demand for higher rated bonds with a modestly higher yield resulted in searching for yield. Finally, mapping problems led to misleading risk measurement results, as highly rated securitized products were frequently mapped to highly rated corporate bond spread indices. This resulted in incorrect VaR estimates, as incorrect mappings indicated it would be unlikely that bonds would decline significantly in value. In reality, the most highly rated RMBS lost a significant portion of their value, declining close to 70% during the subprime crisis, while lower investment-grade RMBS lost virtually all of their value.
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K e y C o n c e p t s
LO 53.1 Model risk is the risk of incorrect trading or risk management decisions due to errors in models and model applications, which can lead to trading losses and potential legal, reputational, accounting, liquidity, and regulatory risk. Errors can be introduced into models through programming bugs, securities valuations or hedging, VaR estimates, and position mappings.
LO 53.2 Firms use software to compute the risk measures from the data collected using specific formulas, which can be performed in a variety of ways and lead to potential issues. Variability in risk measures, including lack of uniformity in the use of confidence intervals and time horizons, can lead to variability in VaR estimates. Other factors can also cause variability, including length of time series, ways of estimating moments, mapping techniques, decay factors, and number of simulations.
Mapping refers to the assignment of risk factors to positions, and mapping choices can considerably impact VaR results.
Cash flow mapping results in greater accuracy of estimates. Duration-convexity mapping requires fewer risk factors and less complex computations, which reduces costs, data errors, and model risks. Locating data that addresses specific risk factors may also be difficult.
Liquidity risk arises from large divergences in model and market prices that are difficult to capture with market data, and as a result, VaR estimates based on replicating portfolios can understate risk and create liquidity risk.
Basis risk is the risk that a hedge does not provide the required or expected protection. Basis risk arises when a position or its hedge is mapped to the same set of risk factors.
LO 53.3 Volatility in credit markets in the spring of 2005 fueled by company bankruptcies and losses led to defaults in the IG3 and IG4 index series of the CDX.NA.IG index, causing large selloffs that resulted in widening spreads. This also resulted in modeling errors from both misinterpretation and incorrect application of models, which led to trade losses.
LO 53.4 Two significant model errors in the RMBS valuation and risk models led to a significant underestimation of systematic risk in subprime RMBS returns during 2007-2009. First, the RMBS risk model assumed future house prices to rise or at least stay flat. The eventual decline in house prices starting in 2007 led to a significant underestimation of the potential default rates and systematic risk in RMBS. Second, the RMBS model assumed low correlations among regional housing markets. When house prices declined, correlations and loan defaults increased.
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C o n c e p t C h e c k e r s
1.
2.
3.
4.
Due to a recently discovered error in its valuation model, Samuelson, Inc. had previously recorded certain trades as profitable even though the positions were unprofitable. The risk that best characterizes this error is: A. operational risk. B. liquidity risk. C. market risk. D. hedge risk.
Duane Danning is a junior risk analyst at a large risk management firm. He has been asked to assess the firms risk modeling practices and evaluate potential ways in which errors could be introduced into models. In his analysis, Danning indicates that errors can be introduced into models through programming bugs and errors in VaR estimates but rarely through incorrect position mappings. Dannings analysis is most accurate with regard to: A. only programming bugs and incorrect position mappings. B. only programming bugs and errors in VaR estimates. C. only errors in VaR estimates. D. only incorrect position mappings.
An advantage of duration mapping over cash flow mapping is that duration mapping: A. B. uses cash flows that are mapped to specific fixed income securities without the
is more accurate than cash flow mapping, thus reducing mapping errors.
use of approximations.
C. uses more complex computations, thus reducing data errors and model risk. D. uses fewer risk factors, thus reducing data errors and model risk.
A common trade during 2004 and 2005 was to sell protection on the equity tranche and buy protection of the mezzanine tranche of the CDX.NA.IG index. Which of the following statements regarding this trade is least accurate? A. The trade was set up to be default-risk neutral at initiation. B. The trade was short credit spread risk on the equity tranche and long credit
spread risk on the mezzanine tranche.
C. The main motivation for the trade was to achieve a positively convex payoff
profile.
D. The trade was designed to benefit from credit spread volatilities.
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5.
Which of the following two model errors in the RMBS valuation and risk models are considered to have contributed the most to a significant underestimation of systematic risk in subprime RMBS returns during 2007-2009? A. The assumption of future house price appreciation and the assumption of high
correlations among regional housing markets.
B. The assumption of future house price declines and the assumption of high
correlations among regional housing markets.
C. The assumption of future house price appreciation and the assumption of low
correlations among regional housing markets.
D. The assumption of future house price declines and the assumption of low
correlations among regional housing markets.
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C o n c e p t C h e c k e r A n s w e r s
1. A Recording trades as profitable that have, in fact, lost money is an example of operational risk.
2. B Dannings analysis is most accurate with regard to only programming bugs and errors in VaR
estimates. Incorrect position mappings can also lead to material errors in risk models.
3. D Duration mapping (or duration-convexity mapping) requires the use of fewer risk factors
and less complex computations, thus reducing costs, data errors, and model risks. Cash flow mapping results in greater accuracy of estimates, however, because cash flows are mapped to specific fixed income securities without the use of approximations.
4. B The trade was long credit and credit spread risk on the equity tranche and short credit and
credit spread risk on the mezzanine tranche. The other statements are accurate.
5. C The two model errors considered to have contributed the most to a significant
underestimation of systematic risk were (1) the assumption of future house price appreciation, and (2) the assumption of low correlations among regional housing markets.
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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:
Li q u i d i t y a n d Le v e r a g e
Topic 54
E x a m F o c u s
This topic analyzes the effects of liquidity and leverage on firm risk. For the exam, understand the distinction between transactions liquidity and funding liquidity, and the role banks play in providing liquidity. Also, be able to calculate a firms leverage ratio and the leverage effect, and know how to construct the economic balance sheet given trades such as buying stock on margin, selling stock short, and taking positions in derivatives. Finally, be able to explain tightness, depth, and resiliency as they relate to liquidity risk.
S o u r c e s o f L i q u i d i t y R i s k

LO 53.3: Identify reasons for the failure of the long-equity tranche, short- mezzanine credit trade in 2005 and describe how such modeling errors could have been avoided.
Credit Trade Description and Modeling Issues
Volatility in credit markets in the spring of 2005 caused significant modeling errors from both misinterpretation and incorrect application of models. Trades incurred losses as only certain dimensions of risks were hedged, while others were ignored.
A popular strategy in credit markets for hedge funds, banks, and brokerages was to sell protection on the equity tranche and buy protection on the junior (mezzanine) tranche of the CDX.NA.IG index, the investment-grade CDS index. As a result, the trade was long credit and credit spread risk on the equity tranche and short credit and credit spread risk on the mezzanine tranche. The trade was primarily executed on the IG3 and IG4 index series. The trade was designed to be default-risk neutral at initiation with equal credit spread sensitivities on the two legs. The motivation of the trade was to have a positively convex payoff profile with the two positions benefiting from credit spread volatility, while earning a positive net spread on the positions (positive carry). This allowed trades to have a position similar to delta-hedged, long option portfolios by receiving, rather than paying, time value.
The hedge ratio for the delta-hedged portfolio then determined the dollar amount of the mezzanine to be shorted for every dollar of the long equity. In other words, the hedge ratio was the ratio of the profit and loss impact of a 1 bp widening of the CDX index on the equity and mezzanine tranches. The proper hedge ratio then allowed for the creation of a portfolio based on the CDX index that, at the margin, was default-risk neutral. The CDX trade benefited from a large change in credit spreads and essentially behaved like an option straddle on credit spreads with an option premium paid to the owner of the option. The hedge ratio for the CDX index was around 1.5 to 2 in early 2005, which resulted in a net flow of spread income to the long equity/short mezzanine trade.
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The critical error in the trade, however, was that it was set up at a specific value of implied correlation. A static correlation was considered a critical flaw as the deltas that were used in setting up the trade were partial derivatives that ignored any changes in correlation. With changes in credit markets, changing correlations doubled the hedge ratio to close to 4 by the summer of 2005. As a result, traders now needed to sell protection on nearly twice the notional value of the mezzanine tranche to maintain portfolio neutrality. Stated differently, as long as correlations remained static, the trade remained profitable. However, once correlations declined and spreads did not widen sufficiently, the trade became unprofitable.
Therefore, while the model did not ignore correlation, it assumed a static correlation and instead focused on anticipated gains from convexity. The error could have been corrected by stress testing correlation or by employing an overlay hedge of going long, single-name protection in high default-probability names.
Credit Market Example
Problems in credit markets were already evident by the spring of 2005. The problems were largely related to the automobile industry, specifically the original equipment manufacturers (OEMs), including Ford, Chrysler, and General Motors (GM), which had been experiencing troubles for some time. OEMs were particularly important in the U.S. investment-grade bond market, and the emerging threat of a downgrade to junk status rattled markets. Although the OEMs were not directly part of the CDX.NA.IG index, several of their related finance companies were. Outside of OEMs, several auto parts manufacturers were included in two series of the index, the IG3 and IG4 indices.
The immediate priority of the OEMs in early 2005 was to secure a relief from the United Auto Workers (UAW) union of health benefit commitments to retirees. When GM and the UAW were unable to reach an agreement in the spring of 2005, which coincided with the announcement of large losses for GM, GM and Ford were downgraded to junk status by S&P and Moodys. This created a sharp widening of corporate spreads, including the spreads on the automotive finance companies and other industry names. Several auto parts manufacturers filed for Chapter 11 bankruptcy protection. As a result, the market was now anticipating the possibility of defaults in the IG3 and IG4 indices, and the probability of extreme losses became real. In addition, the convertible bond market was also experiencing a sellofif that resulted in widening of spreads. The IG indices widened in line with the credit spread widening of the index constituents. The mark-to-market value and the implied correlation of the equity tranche dropped sharply. The implied correlation fell given that (1) the auto parts supplier bankruptcies were in the IG4 series, which led to close to 10% of the portfolio now close to default, and (2) the widening of the IG4 series was constrained by hedging, which led to a fall in correlation. Participants could hedge short credit positions in the equity tranche by selling credit protection on the mezzanine tranche or the IG4 index series. Concurrently, the mezzanine tranche saw a small widening as market participants were covering their positions by selling protection on the mezzanine tranche (that is, they were taking on credit risk). These events led to the unwinding of the equity/mezzanine tranche trade with the relative value trade experiencing large losses.
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R i s k U n d e r e s t i m a t i o n i n 2007-2009

LO 53.2: Explain how model risk and variability can arise through the implementation of VaR models and the mapping of risk factors to portfolio positions. * 1
Risk management is typically implemented via computer systems that help to automate gathering data, making computations, and generating reports. These systems can be made available commercially, and are typically used by smaller firms, while larger firms tend to use their own in-house systems, often in combination with commercial models. The implementation process for computing risk is usually referred to as the firms VaR m od el, although the general computation process can apply to any risk measure other than VaR.
Data preparation is crucial in risk measurement systems. There are three types of data involved: 1. M ark et data is time series data (usually asset prices) that is used in forecasting the
distribution of future portfolio returns. Market data involves obtaining the time series data, removing erroneous data points, and establishing processes for missing data. All of these steps can be costly but necessary.
2. S ecurity m aster data is descriptive data on securities, including maturity dates,
currency, and number of units. Building and maintaining data for certain securities, including equities and debt, can be challenging; however, it is critical from a credit risk management perspective.
3. P osition data matches the firms books and records but presents challenges as data must
be collected from a variety of trading systems and across different locations.
Once the data is collected, software is used to compute the risk measures using specific formulas, which are then combined with the data. Results are then published in documents for reporting by managers. All of these steps can be performed in numerous ways and can lead to several issues within the risk measurement system. We focus on two of these issues: the variability of the resulting measures and the appropriate use of data.
Variability in risk measures, including VaR, is both a benefit and a problem. Managers have significant discretion and flexibility in computing VaR, and parameters can be freely used in
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many different ways. This freedom in measuring VaR leads to two significant problems in practice: 1. Lack o f standardization o f VaR param eters. Given the variability in VaR measurements and managers discretion, parameters including confidence intervals and time horizons can vary considerably, leading to different measurements of VaR.
2. D ifferen ces in VaR m easurem ents. Even if VaR parameters were standardized, differences
in measuring VaR could lead to different results. These include differences in the length of the time series used, techniques for estimating moments, mapping techniques (discussed in the next section) and the choice of risk factors, decay factors in using exponentially weighted moving average (EWMA) calculations, and the number of simulations in Monte Carlo analysis.
Varying parameters can lead to materially different VaR results. For example, one study using different combinations of parameters, all within standard practice, of portfolios consisting of Treasury bonds and S&P 500 index options indicated that VaR results differed considerably by a factor of six or seven times. A simple read of the different VaR models published in the annual reports of some of the larger banks can give an indication of the variability in their measurements.
R i s k F a c t o r M a p p i n g f o r Va R C a l c u l a t i o n s
Mapping refers to the assignment of risk factors to positions. Mapping choices can also impact VaR results. These could include practical choices among alternatives where each alternative has its benefits and disadvantages. For example, managers have a choice between cash flow mapping and duration-convexity mapping for fixed income securities. Cash flo w m a p p in g leads to greater accuracy (each cash flow is mapped to a fixed income security with an approximately equal discount factor); however, du ration -convex ity m a p p in g requires fewer and less complex computations, reducing costs and potential data errors as well as model risks.
It may also be difficult to locate data that addresses specific risk factors. One example is the previously widespread practice of mapping residential mortgage-backed securities (RMBS) or other securitized products to corporate credit spreads of the same rating. Because data on securitization spreads is typically not widely available, using a proxy risk factor of generic corporate bond spreads can be misleading, especially since previously lower spreads on securitizations widened considerably more during the recent financial crisis than did corporate spreads. This is an example of model risk and the inefficiency of VaR estimates in modeling large movements in market prices.
Incorrect mapping to risk factors can create risks such as liquidity risk and basis risk. Liquidity risk arises from divergences in model and market prices. For example, convertible bonds can be mapped to risk factors including implied volatilities, interest rates, and credit spreads based on the theoretical (model) price of the convertible bond using a replicating portfolio. However, significant divergences in model and market prices are difficult to capture with market data, and as a result, VaR estimates based on the replicating portfolio can considerably understate risk, creating liquidity risk.
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Basis risk is the risk that a hedge does not provide the required or expected protection. Basis risk arises when a position or its hedge is mapped to the same set of risk factors, which can be done when it is difficult to distinguish between two closely related positions. While this results in a measured VaR of zero, the positions have significant basis risk. Basis risk is also present in the risk modeling of securitization exposures where securitizations are hedged with corporate credit default swap (CDS) indices of similar ratings.
Other strategies can also lead to misleading VaR estimates. For example, event-driven strategies have outcomes that are close to binary and depend on a specific event occurring, including mergers or acquisitions, bankruptcy, or lawsuits. For these trades, the range of results cannot be measured based on historical return data. Dynamic strategies are another example, where risk is generated over time rather than at a specific point in time.
C r e d i t M a r k e t i n E a r l y 2005

LO 53.1: Describe ways that errors can be introduced into models.
Models are highly useful in simulating real-life scenarios; however, they can suffer from several risks. M o d el ris k is the risk of incorrect trading or risk management decisions due to errors in models and model applications, which can lead to trading losses and give rise to legal, reputational, accounting, and regulatory risk. Biases in models themselves do not necessarily cause model risk; however, inaccurate or inappropriate inputs can create distortions in the model.
There are several ways in which errors can be introduced into models. These include bugs in the programming of model algorithms, securities valuations or hedging, variability of value at risk (VaR) estimates, or inaccurate mapping of positions to risk factors.
For example, bugs in programming occurred in May 2008 when Moodys used flawed programming to incorrectly assign AAA ratings to certain structured credit products. It happened again in October 2011 when bugs in the quant programming used by AXA Rosenberg1 led to investor losses. For Moodys, model risk was related to reputational and liquidity risk because the model errors had been discovered prior to being made public and coincided with a change in ratings methodology that resulted in no change to the ratings of certain products. As a result, Moodys was suspected of tailoring its model to the desired ratings, which damaged the companys reputation. For AXA Rosenberg, the discovery of the model error had not been made public in a timely manner, leading to both regulatory fines and considerable reputational damage to the firm. 1
1. AXA Rosenberg Group, LLC is a division of the French insurance company AXA.
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Model errors in securities valuations or in hedging can create losses within a firm and lead to market risk and operational risk. M arket risk is the risk of buying overvalued (or, at a minimum, fairly valued) securities in the market that are thought to be undervalued. O perational risk is the risk of recording unprofitable trades as profitable.
Relying on market prices rather than model prices through marking positions to market can theoretically avoid model errors and reduce valuation risk. A problem with this approach, however, is that certain positions, including long-term bank commercial loans, are difficult to mark-to-market due to infrequent trading and complexities in valuation.
V a r i a b i l
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