Finance-Theory · Unit 10 · Video 6 · Interactive Practice

Why Forward Contracts Break Down When Prices Move: Counterparty Risk and the Soybean Deal

IKey Formulas

FormulaNameWhat it needs
Vlong=Q (ST−F0,T),Vshort=Q (F0,T−ST)V_{\text{long}} = Q\,(S_T - F_{0,T}), \quad V_{\text{short}} = Q\,(F_{0,T} - S_T)Value of each side at deliveryQuantity QQ, forward price F0,TF_{0,T} and the spot price STS_T on the delivery date. One side's gain is exactly the other's loss: with spot at $100, the manufacturer's contract is worth 1,000 × ($100 − $165) = −$65,000 and the farmer's +$65,000
amount at risk=Q ∣ST−F0,T∣\text{amount at risk} = Q\,\lvert S_T - F_{0,T} \rvertCounterparty exposureCarried by the side that is owed money; it is zero when ST=F0,TS_T = F_{0,T} and grows with the size of the price move in either direction
F0,T−SF0,T\dfrac{F_{0,T} - S}{F_{0,T}}Rivals' cost advantageHow much less, per ton, a competitor buying at spot pays than the locked-in buyer: 65/165≈0.39465/165 \approx 0.394, so about 39% less at a spot of $100
(1−p) Q (F0,T−ST)>L(1-p)\,Q\,(F_{0,T} - S_T) > LWhen walking away pays (our illustration)An assumed lawsuit model: the court makes the buyer pay the seller's full loss with probability pp, and breaching costs LL in fees and reputation either way

Key Insight: A forward is worth nothing to either side when it is signed. After a large price move, one side is losing enough that defaulting can beat performing, which is why counterparty risk is smallest when prices are calm and largest after a sharp move.

IIWho Is Exposed, and by How Much

The side that is owed money carries the counterparty risk, and what it is owed grows with the price move.

IIIPerform or Walk Away

For the losing buyer, walking away is cheaper once its loss outweighs the expected cost of being sued.

💡 The lawsuit model is our illustration, not the video's: the video only says a suit may settle or may not. The lost market share it leaves out would tilt the manufacturer further toward walking away.

IVQuiz Questions

Problem 1 · Who Carries the Risk?

Given: A flour mill (long) agrees with a grain dealer (short) to buy 500 tons of wheat at $240 a ton in three months. On the delivery date wheat trades at $210 a ton. Find which side is tempted to default, and how much the other side stands to lose if it does.

✅ Correct! The mill must pay $240 for wheat worth $210, so it is losing 500×30=15,000500 \times 30 = 15{,}000 dollars, and that is exactly what the dealer is owed and would lose if the mill walked away.
❌ The sides are swapped. Spot fell below the forward price, so the buyer is paying more than the market. The long (the mill) is losing and tempted; the short (the dealer) is owed the gain.
❌ That is the market value of the wheat. 500×210=105,000500 \times 210 = 105{,}000 dollars is what the dealer still owns if the mill refuses. The dealer can sell it at spot; what it loses is only the gap, 500×(240−210)=15,000500 \times (240 - 210) = 15{,}000 dollars.
❌ Zero value holds only at signing. Once the spot price moves away from $240, one side's contract has positive value and the other's negative, and the positive side is exposed.
❌ Not quite. Compare the spot price with the forward price to see who is losing, then multiply the gap by the quantity.
Show solution

Value of each side at delivery, with Q=500Q = 500, F0,T=240F_{0,T} = 240, ST=210S_T = 210 (dollars per ton):

Vlong=Q (ST−F0,T)=500×(210−240)=−15,000V_{\text{long}} = Q\,(S_T - F_{0,T}) = 500 \times (210 - 240) = -15{,}000 Vshort=Q (F0,T−ST)=500×(240−210)=15,000V_{\text{short}} = Q\,(F_{0,T} - S_T) = 500 \times (240 - 210) = 15{,}000

The mill (long) is $15,000 worse off than if it bought at spot, so it has a reason to walk away. The dealer (short) is owed that $15,000, and it is the amount at risk if the mill defaults.

Problem 2 · How Much Cheaper for Rivals?

Given: A bakery has locked in wheat at $240 a ton. By the time it takes delivery the spot price is $180 a ton, and its competitors buy at spot. Find how much less per ton, as a percentage, the competitors pay than the bakery.

✅ Correct! The competitors save $60 on every $240 the bakery pays: 60/240=0.2560/240 = 0.25, so 25% less.
❌ Wrong base. 60/180≈0.33360/180 \approx 0.333 says the bakery pays about 33.3% more than its rivals. "How much less do rivals pay" is measured against the bakery's price: 60/240=0.2560/240 = 0.25.
❌ That is the dollar gap, not a percentage. The gap is $60 a ton; divide it by the $240 the bakery pays to get a percentage.
❌ That is the rivals' price as a share of the bakery's. 180/240=0.75180/240 = 0.75: rivals pay 75% of the bakery's price, which is 1−0.75=0.251 - 0.75 = 0.25, or 25% less.
❌ Not quite. Divide the price gap by the price the bakery pays.
Show solution

The rivals' advantage is measured against the bakery's locked-in price F0,T=240F_{0,T} = 240, with spot S=180S = 180:

F0,T−SF0,T=240−180240=60240=0.25\frac{F_{0,T} - S}{F_{0,T}} = \frac{240 - 180}{240} = \frac{60}{240} = 0.25

Competitors pay 25% less per ton, and they can cut the price of their bread accordingly, which is the market-share squeeze the tofu manufacturer faced in the video.

Problem 3 · Perform or Walk Away?

Given: An airline (long) has a forward to buy 1,000,000 gallons of jet fuel from a supplier at $3.20 a gallon. At delivery the spot price is $2.60. Assume (the illustrative model of Section III): if the airline walks away and buys at spot, a court makes it pay the supplier's full loss with probability 70%, and breaching costs it $150,000 in legal and reputation costs either way. Find the cheaper choice on expected cost, and by how much.

✅ Correct! Performing costs $3,200,000; walking away is expected to cost 2,600,000+420,000+150,000=3,170,0002{,}600{,}000 + 420{,}000 + 150{,}000 = 3{,}170{,}000 dollars, which is $30,000 less.
❌ That ignores the lawsuit. $600,000 is the airline's full loss on the contract. Walking away is a breach: it carries expected damages of 0.7×600,000=420,0000.7 \times 600{,}000 = 420{,}000 dollars plus the $150,000 cost.
❌ The damages are missing. 600,000−150,000=450,000600{,}000 - 150{,}000 = 450{,}000 counts the breaching cost but not the 70% chance of paying the supplier's $600,000 loss, an expected $420,000.
❌ The damages are not certain. Paying the full $600,000 for sure plus $150,000 would indeed make performing cheaper, but the court awards damages only with probability 70%, so expected damages are $420,000.
❌ Not quite. Compare the cost of performing with spot cost + expected damages + breaching cost.
Show solution

Perform. The airline pays the forward price for the full quantity:

1,000,000×3.20=3,200,0001{,}000{,}000 \times 3.20 = 3{,}200{,}000

Walk away. It buys at spot, and the supplier's loss is 1,000,000×(3.20−2.60)=600,0001{,}000{,}000 \times (3.20 - 2.60) = 600{,}000 dollars:

1,000,000×2.60⏟fuel at spot+0.7×600,000⏟expected damages+150,000⏟breaching cost=2,600,000+420,000+150,000=3,170,000\underbrace{1{,}000{,}000 \times 2.60}_{\text{fuel at spot}} + \underbrace{0.7 \times 600{,}000}_{\text{expected damages}} + \underbrace{150{,}000}_{\text{breaching cost}} = 2{,}600{,}000 + 420{,}000 + 150{,}000 = 3{,}170{,}000

Walking away is cheaper on expected cost by 3,200,000−3,170,000=30,0003{,}200{,}000 - 3{,}170{,}000 = 30{,}000 dollars. Equivalently, (1−p) Q (F−S)=0.3×600,000=180,000>150,000=L(1-p)\,Q\,(F - S) = 0.3 \times 600{,}000 = 180{,}000 > 150{,}000 = L, and the difference is again $30,000.

Problem 4 · When Does Default Switch On?

Given: The same airline contract and the same assumed lawsuit model as Problem 3: 1,000,000 gallons at $3.20, a 70% chance of paying the supplier's full loss, and a $150,000 cost of breaching. Find the spot prices at delivery for which walking away is the airline's cheaper choice.

✅ Correct! Walking away pays once 0.3×1,000,000×(3.20−S)0.3 \times 1{,}000{,}000 \times (3.20 - S) exceeds 150,000, that is once the price has fallen more than 50 cents. Small moves create no temptation; a sharp move does.
❌ Wrong probability. Using 70% gives 150,000/700,000≈0.214150{,}000 / 700{,}000 \approx 0.214. What walking away saves is the part of the loss the airline escapes, which happens with probability 1−0.7=0.31 - 0.7 = 0.3.
❌ The expected damages are missing. 150,000/1,000,000=0.15150{,}000 / 1{,}000{,}000 = 0.15 treats the airline as escaping its whole loss. It escapes it only with probability 30%, so the price must fall 0.15/0.3=0.500.15 / 0.3 = 0.50.
❌ Losing is not enough. Below $3.20 the airline is losing, but walking away has its own expected cost, so default only pays once the loss is large enough to beat it.
❌ Not quite. Set the part of the loss the airline escapes, (1−p) Q (F−S)(1-p)\,Q\,(F - S), equal to the breaching cost and solve for SS.
Show solution

Walking away costs QS+pQ(F−S)+LQS + pQ(F - S) + L and performing costs QFQF. Walking away is cheaper when

QS+pQ(F−S)+L<QF  ⟺  (1−p) Q (F−S)>LQS + pQ(F - S) + L < QF \iff (1 - p)\,Q\,(F - S) > L

With p=0.7p = 0.7, Q=1,000,000Q = 1{,}000{,}000, F=3.20F = 3.20 and L=150,000L = 150{,}000:

0.3×1,000,000×(3.20−S)>150,000  ⟺  3.20−S>0.50  ⟺  S<2.700.3 \times 1{,}000{,}000 \times (3.20 - S) > 150{,}000 \iff 3.20 - S > 0.50 \iff S < 2.70

Walking away is cheaper at any spot price below $2.70 a gallon; at exactly $2.70 the two choices cost the same. This is consistent with Problem 3, where a spot of $2.60 made walking away $30,000 cheaper. The supplier is safe after a small drop and exposed after a large one.

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