7.8 Case studies

7.8.1Metallgesellschaft, 1993: a hedge that ran out of cash#

Context Metallgesellschaft AG was a large German industrial conglomerate. Its US subsidiary, MG Refining and Marketing (MGRM), began in 1992 to offer customers fixed-price supply contracts for gasoline, heating oil and diesel lasting up to 10 years. By September 1993 MGRM had sold forward over 150 million barrels at prices $3 to $5 a barrel above the prevailing spot price (Brealey, Myers and Allen's case write-up); other accounts put the position at 160–180 million barrels (Penn State EBF 301 course notes). MGRM was short long-dated forwards, so it lost if oil prices rose.

The hedge Long-dated futures were illiquid or did not exist. MGRM instead bought a stack of short-dated NYMEX futures and short-term OTC swaps, roughly one-for-one with its forward commitments, and rolled the stack each month into the next contract. Culp and Miller (1995) called this "synthetic storage". Its economics relied on the oil curve usually being in backwardation (positive convenience yield), so that each roll sold the expiring contract above the price of the next one and earned roll yield.

Timeline

• 1993: oil prices fell and the curve moved into contango. Each monthly roll now cost money, and every price fall triggered variation-margin payments on the long futures. The offsetting gains on the fixed-price forwards were real in value terms but would arrive as cash only over the next decade.
• December 1993: Metallgesellschaft's supervisory board replaced management, and the new management closed the futures positions and negotiated the cancellation of customer contracts.
• January 1994: the losses became public. They were later estimated at over $1 billion (Brealey, Myers and Allen), about $1.3 billion (Culp and Miller), or almost $1.5 billion (Penn State course notes): the range reflects different accounting of which losses are attributed to the hedge. The group was rescued by a $1.9 billion package from 120 banks (Brealey, Myers and Allen).
• Within eight months of the liquidation, oil prices had risen about 40% (Brealey, Myers and Allen). A hedge that had been held would have generated large cash inflows.

Mechanism, with this module's theory

1. Funding liquidity (7.2.2). A one-for-one hedge on 160 million barrels pays about $160 million in variation margin for each $1 a barrel fall in futures prices, immediately. The hedged forwards gain about the same in present value, but that gain is not cash. MTM converts a hedge that is sound in value terms into a cash drain whose size depends on the path of prices. The relevant question was never "is the position hedged?" but "can we finance the hedge's interim losses?"
2. Roll cost (7.4.4, 7.7). The stack-and-roll hedger pays $F_{\text{far}} - F_{\text{near}}$ per barrel per roll. In backwardation that is negative (income); in contango it is positive (a cost). MGRM's expected hedge return was a bet on the sign of the convenience yield. That is a speculative position on the shape of the curve layered on top of the hedge.
3. Hedge ratio (7.6.2). Long-dated oil prices move less than front-month prices: the term structure is mean-reverting, so a $1 shock to the spot moves a 5-year forward by much less than $1. With $\sigma_{LT} < \sigma_{ST}$, Prop. 7.8 gives $h^* = \rho\sigma_{LT}/\sigma_{ST} < 1$. A one-for-one stack was therefore an over-hedge in variance terms, and the excess was a long position in front-month oil. Mello and Parsons (1995) and Pirrong (1997) make versions of this argument; Problem 7.15 quantifies it.
4. Accounting. German accounting rules recognised realised futures losses while not allowing the unrealised gains on the forward contracts to offset them, so reported losses overstated economic losses (Penn State notes). Reported numbers drove the board's decision.

The debate Culp and Miller (1995) argued the hedge was economically sound and that the parent destroyed value by liquidating at the worst time. Mello and Parsons (1995) argued that the maturity mismatch created funding risk the strategy could not survive, so the hedge itself was flawed. Pirrong (1997) argued the one-for-one stack was a speculative position. All three agree on the mechanics above; they disagree on the counterfactual.

7.8.2The Nifty futures basis in the March 2020 crash#

Context In March 2020 the COVID-19 shock took the Nifty 50 from 11,132.75 (2 Mar close) to 7,610.25 (23 Mar close), a fall of 31.6% in three weeks (NSE index files). Twice the market-wide circuit breaker halted trading for 45 minutes: on 13 Mar 2020, when the Nifty fell 10% shortly after the open, and on 23 Mar 2020, when the Sensex hit its 10% lower circuit (Business Standard reports of both days). On the evening of 24 Mar the government announced a national lockdown. The RBI cut the repo rate from 5.15% to 4.40% on 27 Mar (RBI press release and circular of that date).

Data NSE F&O bhavcopies (fo*MAR2020bhav.csv) and NSE index close files (ind_close_all_*032020.csv), downloaded from nsearchives.nseindia.com for this module. Basis is the near-month settlement price minus the Nifty 50 close; $d$ is calendar days to the 26 Mar expiry; implied carry is $\ln(F/S)/(d/365)$.

Date	Nifty close	Near (Mar) settle	Basis	Basis %	$d$	Implied carry (p.a.)	Apr basis %
2 Mar	11,132.75	11,123.70	−9.05	−0.08%	24	−1.2%	+0.33%
6 Mar	10,989.45	10,939.90	−49.55	−0.45%	20	−8.2%	+0.04%
12 Mar	9,590.15	9,546.60	−43.55	−0.45%	14	−11.9%	+0.09%
13 Mar	9,955.20	9,897.70	−57.50	−0.58%	13	−16.3%	−0.12%
16 Mar	9,197.40	9,118.45	−78.95	−0.86%	10	−31.5%	−0.41%
19 Mar	8,263.45	8,205.90	−57.55	−0.70%	7	−36.4%	−0.68%
20 Mar	8,745.45	8,723.10	−22.35	−0.26%	6	−15.6%	+0.10%
23 Mar	7,610.25	7,581.55	−28.70	−0.38%	3	−46.0%	−0.09%
24 Mar	7,801.05	7,849.90	+48.85	+0.63%	2	+113.9%	+0.68%
25 Mar	8,317.85	8,362.20	+44.35	+0.53%	1	+194.1%	+1.07%
26 Mar (expiry)	8,641.45	8,641.45	0.00	0.00%	0	n/a	+0.41%

For reference, a carry-model basis at the start of the month, with $r$ = 5.15% and the NSE dividend yield of 1.37%, would have been about +0.25% for the March contract, about +28 points.

Analysis

1. The band, not the line. Even on 2 Mar, before the worst of the crash, the near month traded slightly below spot, and the April contract's implied carry was about 2% a year against a model value of about 3.8%. Indian index futures often trade below full carry. The upper arbitrage bound (7.5) was never threatened; the question is why the lower bound did not bind.
2. Limits to arbitrage on the lower side. Correcting a discount requires selling the stock basket and buying futures. Only holders of the basket can do that cheaply (Prop. 7.4 discussion). In mid-March the holders (mutual funds facing redemptions, foreign portfolio investors reducing exposure) were sellers of stock for their own reasons, and margin requirements on all positions rose with volatility. A persistent discount of 0.4–0.9% with three days to three weeks to expiry, an annualised −8% to −46%, is consistent with scarce arbitrage capital and heavy futures selling by hedgers. The data cannot by themselves separate these explanations.
3. Noise at the end. The +0.5% to +0.6% basis with one or two days left (annualised over 100%) is not a tradable arbitrage of that size. On days when the index moved 3–5% intraday, the futures' half-hour VWAP settlement and the index close describe different moments, and the EOD basis absorbs the difference.
4. Convergence. On 26 Mar the March contract's final settlement price equalled the index close exactly, 8,641.45, as Prop. 7.7(a) requires for a cash-settled contract. However wide the basis gets, a hedge held to expiry ends with zero basis.

7.8.3WTI below zero, 20 April 2020 (brief; full treatment in M10)#

Context and timeline On 20 Apr 2020, the day before its expiry, the NYMEX May 2020 WTI crude futures contract settled at −$37.63 a barrel. WTI futures are physically delivered at Cushing, Oklahoma. With demand collapsing in the lockdowns and storage at Cushing close to full, holders of long May contracts who could not take delivery had to pay others to take their contracts. MCX's April crude contract, which expired the same day and is cash settled at the NYMEX front-month settlement converted to rupees, was first given a provisional settlement price of ₹1 a barrel, and then settled at minus ₹2,884 a barrel (MCX circular of 21 Apr 2020, reported by Business Standard/PTI, 22 Apr 2020). Brokers challenged the negative settlement; the Bombay High Court refused to stay MCX's circular (Business Standard, 30 Apr 2020).

Mechanism Prop. 7.10 prices storage as a smooth cost $u$. When storage capacity is close to exhausted, the marginal cost of storing one more barrel rises without bound, and the value of a barrel delivered now at a place where it cannot be stored can be negative. The near future converges to that local spot value (Prop. 7.7(a)). The next contract (June) traded far above the May price: a "super-contango" that equals the cost of finding storage for one month. A cash-settled Indian contract referencing that price inherited the negative number, and longs who had posted margin for a price that could only fall to zero found they owed more than their margin.