Haircuts and Collaterals.

In a repo-style securities financing transaction, the repo buyer or lender is exposed to the borrower’s default risk for the whole duration with a market contingent exposure, framed on a short window for default settlement. A margin period of risk (MPR) is a time period starting from the last date when margin is met to the date when the defaulting counterparty is closed out with completion of collateral asset disposal. MPR could cover a number of events or processes, including collateral valuation, margin calculation, margin call, valuation dispute and resolution, default notification and default grace period, and finally time to sell collateral to recover the lent principal and accrued interest. If the sales proceeds are not sufficient, the deficiency could be made a claim to the borrower’s estate, unless the repo is non-recourse. The lender’s exposure in a repo during the MPR is simply principal plus accrued and unpaid interest. Since the accrued and unpaid interest is usually margined at cash, repo exposure in the MPR is flat.

A flat exposure could apply to OTC derivatives as well. For an OTC netting, the mark-to-market of the derivatives could fluctuate as its underlying prices move. The derivatives exposure is formally set on the early termination date which could be days behind the point of default. The surviving counterparty, however, could have delta hedged against market factors following the default so that the derivative exposure remains a more manageable gamma exposure. For developing a collateral haircut model, what is generally assumed is a constant exposure during the MPR.

The primary driver of haircuts is asset volatility. Market liquidity risk is another significant one, as liquidation of the collateral assets might negatively impact the market, if the collateral portfolio is illiquid, large, or concentrated in certain asset sectors or classes. Market prices could be depressed, bid/ask spreads could widen, and some assets might have to be sold at a steep discount. This is particularly pronounced with private securitization and lower grade corporates, which trade infrequently and often rely on valuation services rather than actual market quotations. A haircut model therefore needs to capture liquidity risk, in addition to asset volatility.

In an idealized setting, we therefore consider a counterparty (or borrower) C’s default time at t, when the margin is last met, an MPR of u during which there is no margin posting, and the collateral assets are sold at time t+u instantaneously on the market, with a possible liquidation discount g.

Let us denote the collateral market value as B(t), exposure to the defaulting counterparty C as E(t). At time t, one share of the asset is margined properly, i.e., E(t) = (1-h)B(t), where h is a constant haircut, 1 >h ≥0. The margin agreement is assumed to have a zero minimum transfer amount. The lender would have a residual exposure (E(t) – B(t+u)(1-g))⁺, where g is a constant, 1 > g ≥ 0. Exposure to C is assumed flat after t. We can write the loss function from holding the collateral as follows,

L(t + u) = E_t(1 – B_t+u/B_t (1 – g)/(1 – h))⁺ = (1 – g)B_t(1 – B_t+u/B_t (h – g)/(1 – g))⁺ —– (1)

Conditional on default happening at time t, the above determines a one-period loss distribution driven by asset price return B(t+u)/B(t). For repos, this loss function is slightly different from the lender’s ultimate loss which would be lessened due to a claim and recovery process. In the regulatory context, haircut is viewed as a mitigation to counterparty exposure and made independent of counterparty, so recovery from the defaulting party is not considered.

Let y = (1 – B_t+u/B_t) be the price decline. If g=0, Pr(y>h) equals to Pr(L(u)>0). There is no loss, if the price decline is less or equal to h. A first rupee loss will occur only if y > h. h thus provides a cushion before a loss is incurred. Given a target rating class’s default probability p, the first loss haircut can be written as

h_p = inf{h > 0:Pr(L(u) > 0) ≤ p} —– (2)

Let VaR_q denote the VaR of holding the asset, an amount which the price decline won’t exceed, given a confidence interval of q, say 99%. In light of the adoption of the expected shortfall (ES) in BASEL IV’s new market risk capital standard, we get a chance to define haircut as ES under the q-quantile,

h_ES = ES_q = E[y|y > VaR_q]

VaR_q = inf{y₀ > 0 : Pr(y > y₀) ≤ 1 − q} —– (3)

Without the liquidity discount, h_p is the same as VaR_q. If haircuts are set to VaR_q or h_ES, the market risk capital for holding the asset for the given MPR, defined as a multiple of VaR or ES, is zero. This implies that we can define a haircut to meet a minimum economic capital (EC) requirement C₀,

h_EC = inf{h ∈ R⁺: EC[L|h] ≤ C₀} —– (4)

where EC is measured either as VaR or ES subtracted by expected loss (EL). For rating criteria employing EL based target per rating class, we could introduce one more definition of haircuts based on EL target L₀,

h_EL = inf{h ∈ R⁺: E[L|h] ≤ L₀} —– (5)

The expected loss target L₀ can be set based on EL criteria of certain designated high credit rating, whether bank internal or external. With an external rating such as Moody’s, for example, a firm can set the haircut to a level such that the expected (cumulative) loss satisfies the expected loss tolerance L₀ of some predetermined Moody’s rating target, e.g., ‘Aaa’ or ‘Aa1’. In (4) and (5), loss L’s holding period does not have to be an MPR. In fact, these two definitions apply to the general trading book credit risk capital approach where the standard horizon is one year with a 99.9% confidence interval for default risk.

Different from VaR_q, definitions h_p, h_EL, and h_EC are based on a loss distribution solely generated by collateral market risk exposure. As such, we no longer apply the usual wholesale credit risk terminology of probability of default (PD) and loss given default (LGD) to determine EL as product of PD and LGD. Here EL is directly computed from a loss distribution originated from market risk and the haircut intends to be wholesale counterparty independent. For real repo transactions where repo haircuts are known to be counterparty dependent, these definitions remain fit, when the loss distribution incorporates the counterparty credit quality.

Advertisement

Long Term Capital Management. Note Quote.

Long Term Capital Management, or LTCM, was a hedge fund founded in 1994 by John Meriwether, the former head of Salomon Brothers’s domestic fixed-income arbitrage group. Meriwether had grown the arbitrage group to become Salomon’s most profitable group by 1991, when it was revealed that one of the traders under his purview had astonishingly submitted a false bid in a U.S. Treasury bond auction. Despite reporting the trade immediately to CEO John Gutfreund, the outcry from the scandal forced Meriwether to resign.

Meriwether revived his career several years later with the founding of LTCM. Amidst the beginning of one of the greatest bull markets the global markets had ever seen, Meriwether assembled a team of some of the world’s most respected economic theorists to join other refugees from the arbitrage group at Salomon. The board of directors included Myron Scholes, a coauthor of the famous Black-Scholes formula used to price option contracts, and MIT Sloan professor Robert Merton, both of whom would later share the 1997 Nobel Prize for Economics. The firm’s impressive brain trust, collectively considered geniuses by most of the financial world, set out to raise a $1 billion fund by explaining to investors that their profoundly complex computer models allowed them to price securities according to risk more accurately than the rest of the market, in effect “vacuuming up nickels that others couldn’t see.”

One typical LTCM trade concerned the divergence in price between long-term U.S. Treasury bonds. Despite offering fundamentally the same (minimal) default risk, those issued more recently – known as “on-the-run” securities – traded more heavily than those “off-the-run” securities issued just months previously. Heavier trading meant greater liquidity, which in turn resulted in ever-so-slightly higher prices. As “on-the-run” securities become “off-the-run” upon the issuance of a new tranche of Treasury bonds, the price discrepancy generally disappears with time. LTCM sought to exploit that price convergence by shorting the more expensive “on-the-run” bond while purchasing the “off- the-run” security.

By early 1998 the intellectual firepower of its board members and the aggressive trading practices that had made the arbitrage group at Salomon so successful had allowed LTCM to flourish, growing its initial $1 billion of investor equity to $4.72 billion. However, the miniscule spreads earned on arbitrage trades could not provide the type of returns sought by hedge fund investors. In order to make transactions such as these worth their while, LTCM had to employ massive leverage in order to magnify its returns. Ultimately, the fund’s equity component sat atop more than $124.5 billion in borrowings for total assets of more than $129 billion. These borrowings were merely the tip of the ice-berg; LTCM also held off-balance-sheet derivative positions with a notional value of more than $1.25 trillion.

The fund’s success began to pose its own problems. The market lacked sufficient capacity to absorb LTCM’s bloated size, as trades that had been profitable initially became impossible to conduct on a massive scale. Moreover, a flood of arbitrage imitators tightened the spreads on LTCM’s “bread-and-butter” trades even further. The pressure to continue delivering returns forced LTCM to find new arbitrage opportunities, and the fund diversified into areas where it could not pair its theoretical insights with trading experience. Soon LTCM had made large bets in Russia and in other emerging markets, on S&P futures, and in yield curve, junk bond, merger, and dual-listed securities arbitrage.

Combined with its style drift, the fund’s more than 26 leverage put LTCM in an increasingly precarious bubble, which was eventually burst by a combination of factors that forced the fund into a liquidity crisis. In contrast to Scholes’s comments about plucking invisible, riskless nickels from the sky, financial theorist Nassim Taleb later compared the fund’s aggressive risk taking to “picking up pennies in front of a steamroller,” a steamroller that finally came in the form of 1998’s market panic. The departure of frequent LTCM counterparty Salomon Brothers from the arbitrage market that summer put downward pressure on many of the fund’s positions, and Russia’s default on its government-issued bonds threw international credit markets into a downward spiral. Panicked investors around the globe demonstrated a “flight to quality,” selling the risky securities in which LTCM traded and purchasing U.S. Treasury securities, further driving up their price and preventing a price convergence upon which the fund had bet so heavily.

None of LTCM’s sophisticated theoretical models had contemplated such an internationally correlated credit market collapse, and the fund began hemorrhaging money, losing nearly 20% of its equity in May and June alone. Day after day, every market in which LTCM traded turned against it. Its powerless brain trust watched in horror as its equity shrank to $600 million in early September without any reduction in borrowing, resulting in an unfathomable 200 leverage ratio. Sensing the fund’s liquidity crunch, Bear Stearns refused to continue acting as a clearinghouse for the fund’s trades, throwing LTCM into a panic. Without the short-term credit that enabled its entire trading operations, the fund could not continue and its longer-term securities grew more illiquid by the day.

Obstinate in their refusal to unwind what they still considered profitable trades hammered by short-term market irrationality, LTCM’s partners refused a buyout offer of $250 million by Goldman Sachs, ING Barings, and Warren Buffet’s Berkshire Hathaway. However, LTCM’s role as a counterparty in thousands of derivatives trades that touched investment firms around the world threatened to provoke a wider collapse in international securities markets if the fund went under, so the U.S. Federal Reserve stepped in to maintain order. Wishing to avoid the precedent of a government bailout of a hedge fund and the moral hazard it could subsequently encourage, the Fed invited every major investment bank on Wall Street to an emergency meeting in New York and dictated the terms of the $3.625 billion bailout that would preserve market liquidity. The Fed convinced Bankers Trust, Barclays, Chase, Credit Suisse First Boston, Deutsche Bank, Goldman Sachs, Merrill Lynch, J.P. Morgan, Morgan Stanley, Salomon Smith Barney, and UBS – many of whom were investors in the fund – to contribute $300 million apiece, with $125 million coming from Société Générale and $100 million from Lehman Brothers and Paribas. Eventually the market crisis passed, and each bank managed to liquidate its position at a slight profit. Only one bank contacted by the Fed refused to join the syndicate and share the burden in the name of preserving market integrity.

That bank was Bear Stearns.

Bear’s dominant trading position in bonds and derivatives had won it the profitable business of acting as a settlement house for nearly all of LTCM’s trading in those markets. On September 22, 1998, just days before the Fed-organized bailout, Bear put the final nail in the LTCM coffin by calling in a short-term debt in the amount of $500 million in an attempt to limit its own exposure to the failing hedge fund, rendering it insolvent in the process. Ever the maverick in investment banking circles, Bear stubbornly refused to contribute to the eventual buyout, even in the face of a potentially apocalyptic market crash and despite the millions in profits it had earned as LTCM’s prime broker. In typical Bear fashion, James Cayne ignored the howls from other banks that failure to preserve confidence in the markets through a bailout would bring them all down in flames, famously growling through a chewed cigar as the Fed solicited contributions for the emergency financing, “Don’t go alphabetically if you want this to work.”

Market analysts were nearly unanimous in describing the lessons learned from LTCM’s implosion; in effect, the fund’s profound leverage had placed it in such a precarious position that it could not wait for its positions to turn profitable. While its trades were sound in principal, LTCM’s predicted price convergence was not realized until long after its equity had been wiped out completely. A less leveraged firm, they explained, might have realized lower profits than the 40% annual return LTCM had offered investors up until the 1998 crisis, but could have weathered the storm once the market turned against it. In the words of economist John Maynard Keynes, the market had remained irrational longer than LTCM could remain solvent. The crisis further illustrated the importance not merely of liquidity but of perception in the less regulated derivatives markets. Once LTCM’s ability to meet its obligations was called into question, its demise became inevitable, as it could no longer find counterparties with whom to trade and from whom it could borrow to continue operating.

The thornier question of the Fed’s role in bailing out an overly aggressive investment fund in the name of market stability remained unresolved, despite the Fed’s insistence on private funding for the actual buyout. Though impossible to foresee at the time, the issue would be revisited anew less than ten years later, and it would haunt Bear Stearns. With negative publicity from Bear’s $38.5 million settlement with the SEC regarding charges that it had ignored fraudulent behavior by a client for whom it cleared trades and LTCM’s collapse behind it, Bear Stearns continued to grow under Cayne’s leadership, with its stock price appreciating some 600% from his assumption of control in 1993 until 2008. However, a rapid-fire sequence of negative events began to unfurl in the summer of 2007 that would push Bear into a liquidity crunch eerily similar to the one that felled LTCM.