Understand contango and backwardation — Hinglish notes

5.1.5 · Stock-Market › Futures

Overview

Contango aur backwardation futures prices aur current spot price ke beech ke relationship ko describe karte hain (aur different expiration dates par futures ke beech bhi). Yeh storage costs, financing costs, aur convenience yields ko reveal karte hain—jo traders ke liye futures contracts roll karne aur market structure samajhne mein critical hain.

Figure — Understand contango and backwardation

Core Concepts

Derivation: Cost of Carry Model

Question: Contango exist kyun karta hai? Chaliye relationship ko arbitrage-free pricing se derive karte hain.

Setup:

Current spot price: $S_{0}$
Time $T$ par delivery ke liye futures price: $F_{0}$
Risk-free rate: $r$
Storage cost per unit time: $c$ (spot price ke % ke roop mein)
Convenience yield: $y$ (physical hold karne ka benefit)

Arbitrage argument (cash-and-carry):

Do tarike consider karo asset ko time $T$ par apna banane ke:

Strategy A (buy forward): Aaj $F_{0}$ price par long futures mein enter karo (enter karne mein kuch nahi lagta). Delivery par $F_{0}$ dene ke liye itna cash alag rakho: abhi $F_{0} e^{- r T}$ risk-free invest karo, jo $T$ par exactly $F_{0}$ ban jayega. Aaj ka cost: $F_{0} e^{- r T}$ .
Strategy B (buy and carry): Physical asset abhi $S_{0}$ mein kharido, $[0, T]$ par storage pay karo, aur convenience yield collect karo. Asset carry karne ki net present cost aaj $S_{0}$ plus storage ka PV minus convenience benefit ka PV hai, jo (continuously compounding) ek future obligation $S_{0} e^{(r + c - y) T}$ ke equivalent hai jo wापस discount kiya gaya: aaj ka cost $= S_{0} e^{(c - y) T}$ ... lekin sabse important baat, dono strategies $T$ par same asset deliver karti hain.

No-arbitrage condition (dono strategies ko same effective future cost par $T$ par same asset produce karna chahiye): $F_{0} = S_{0} e^{(r + c - y) T}$

Yeh step kyun? Agar $F_{0} > S_{0} e^{(r + c - y) T}$ , to ek arbitrageur (mehnge) futures short karta hai, $S_{0}$ borrow karke physical kharidta hai, store karta hai ( $c$ pay karta hai, $y$ earn karta hai), aur $T$ par short mein deliver karta hai. Woh loan ( $S_{0} e^{r T}$ ) plus net carry repay karta hai, aur difference risk-free mein rakh leta hai. Yeh selling pressure $F_{0}$ ko neeche push karta hai jab tak equality hold na kare. Agar $F_{0} < S_{0} e^{(r + c - y) T}$ , to reverse trade (long futures, short physical) $F_{0}$ ko upar force karta hai.

Log lete hain: $ln (F_{0}) = ln (S_{0}) + (r + c - y) T$

Interpretation:

Contango: $(r + c - y) > 0$ → $F_{0} > S_{0}$ → futures price spot se zyada, curve upar slope karti hai
Backwardation: $(r + c - y) < 0$ → $F_{0} < S_{0}$ → futures price spot se neeche, curve neeche slope karti hai
Net cost of carry $(r + c - y)$ curve ka shape determine karta hai

Worked Examples

Worked example Example 3: Rolling Futures in Contango (Roll Yield Loss)

Scenario: Tum $F_{1} = 4500$ par 1-month S&P 500 futures hold karte ho. Spot $S_{0} = 4480$ hai. Expiration nearing par, futures spot par converge karte hain. Tum next month ke contract par $F_{2} = 4510$ par roll karte ho.

Question: Tumhara roll yield kya hai?

Solution:

Expiration par, $F_{1} \to S_{0} = 4480$ (convergence)
Tum expiring contract $4480$ par close karte ho, new position $F_{2} = 4510$ par open karte ho
Roll cost: $4510 - 4480 = 30$ points (tum new contract 30 points upar kharid rahe ho jahan old settle hua tha)
Roll yield: $\frac{4480 - 4510}{4510} = \frac{- 30}{4510} = - 0.665%$ (negative = loss)

Yeh step kyun? Contango mein, tum low par bechte ho (expiring contract spot par neeche converge karta hai) aur high par kharidote ho (next contract elevated hai). Repeated rolling returns ko bleed karta hai—long-term futures ETFs ke liye critical.

Backwardation scenario: Agar $F_{2} = 4460$ ho, roll yield $= \frac{4480 - 4460}{4460} = + 0.45%$ (positive = gain). Tum high par bechte ho, low par kharidote ho.

Common Mistakes

Common mistake Mistake 1: "Contango ka Matlab Prices Badhenge"

Galat idea: "Futures spot se upar hain, to spot futures se milne ke liye badhega." Yeh sahi kyun lagta hai: Curve upar slope karti hai, jo upward price movement suggest karta hai.

Fix: Contango futures price aur current spot ke beech ke relationship ko describe karta hai (aur different expiration dates ke beech bhi), spot price direction ki prediction nahi karta. Contango mein bhi spot gir sakta hai! Futures curve cost of carry reflect karti hai, forecast nahi. Jaise expiration paas aata hai, futures spot par converge karte hain, dusri tarah nahi.

Example: Gold contango mein $F = 2060$ , $S = 2000$ par. Agar expiration par gold $S = 1950$ par gir jaye, to $F$ $1950$ par converge karta hai, $2060$ par nahi. Initial contango sirf storage costs reflect karta tha.

Common mistake Mistake 2: Long-Term Futures Holdings mein Roll Yield Ignore Karna

Galat idea: "Main bas monthly futures roll karta rahunga; asset hold karne jaisa hi hai."

Yeh sahi kyun lagta hai: Har futures contract underlying track karta hai, isliye rolling se exposure preserve hona chahiye.

Fix: Contango mein, har roll tumhe expiring contract (spot par neeche converge karta hua) bechne aur next contract (spot se upar elevated) kharidne par majboor karta hai. Yeh negative roll yield time ke saath compound hoti hai, returns erod karti hai chahe spot move na kare.

Calculation: Agar spot flat hai lekin tum contango mein monthly roll par 0.5% lose karte ho, annual drag $\approx 1 - (0.995)^{12} = 5.8%$ . Commodity ETFs (jaise oil ke liye USO) persistent contango ki wajah se spot se bahut kam perform kar sakti hain.

Backwardation mein: Roll yield positive hoti hai—tum har roll par gain karte ho, jo spot performance se upar returns boost kar sakti hai.

Memory Aids

Recall 12-Saal ke Bacche ko Explain Karo

Imagine karo summer mein ice cream trucks (garmi ka din = ice cream shortage).

Aaj ki ice cream cone: $5 (s ab A B H I c hah t e hain — baha r g a r mihai!) * * D ece mb er m e ini cecr e am d e l i v er k a r n e k a p r o mi se * * :$ 3 (sardi, koi desperate nahi, trucks ke paas plenty stock hai) Yeh backwardation hai—"future delivery" "abhi" se sasti hai kyunki log immediate ice cream ke liye extra pay karne ko taiyar hain jab scarce ho.

Ab flip karo: Sardi hai. Aaj ice cream $3 hai . L e k in s u mm er t ak i cecr e am s t or e k a r n e m e in p ai s a l a g t ahai (f r eez er s, bij l i) . T os u mm er m e in d e l i v er k a r n e k a p r o mi se$ 5 hai—yeh contango hai. Future price aaj ki price se zyada hai storage + waiting costs ki wajah se.

Stock market mein, contango = future contracts aaj ki spot se mehnge (jaise gold store karna—tum safes, insurance pay karte ho). Backwardation = future contracts spot se saste (jaise war ke dauran oil—sab oil ABHI chahte hain, 6 mahine mein nahi).

Connections

5.1.01-Futures-Contract-Basics – Futures mechanics ki foundation
5.1.03-Futures-Pricing-and-Fair-Value – Term structure ke underlying cost-of-carry model
5.1.06-Rolling-Futures-Contracts – Rolls par contango/backwardation ka practical impact
5.2.04-Commodity-Futures-and-ETFs – Contango ETF returns ko kaise destroy karta hai
4.3.02-Implied-Volatility-Term-Structure – Options mein similar concept (VIX futures aksar contango mein)
6.1.05-SupplyDemand-Imbalances – Backwardation tight supply signal karta hai

Flashcards

Contango kya hai?

Ek market condition jahan futures prices current spot price se upar hoti hain aur baad ki expiration dates ke saath badhti hain, typically positive cost of carry ki wajah se (storage + financing > convenience yield).

Backwardation kya hai?

Ek market condition jahan futures prices current spot price se neeche hoti hain aur baad ki expiration dates ke saath girti hain, typically immediate demand ya supply shortages se high convenience yield ki wajah se.

Futures pricing ke liye cost of carry formula?

F_{0} = S_{0} e^{(r + c - y) T}

jahan

r

= risk-free rate,

c

= storage cost,

y

= convenience yield,

T

= time to expiration.

Contango kab hota hai (condition)?

Jab

r + c > y

(financing + storage costs convenience yield se zyada), futures ko spot se mehnge aur far futures ko near futures se mehnge banate hain.

Backwardation kab hota hai (condition)?

Jab

y > r + c

(convenience yield carry costs se zyada), immediate demand/scarcity ki wajah se futures ko spot se sasta banate hain.

Contango mein roll yield kya hota hai?

Contango mein futures roll karne par incurred loss—tum expiring contract (spot par neeche converge karta hua) bechte ho aur next contract (spot se upar elevated) kharidote ho, chahe spot flat ho negative returns create karta hai.

Backwardation tight supply kyun signal karta hai?

High convenience yield market participants ki willingness reflect karta hai immediate delivery ke liye waiting se zyada premium dene ki, jo current scarcity ya urgent demand indicate karta hai.

Contango commodity ETFs ko kaise affect karta hai?

Persistent contango negative roll yield create karta hai kyunki ETFs repeatedly low par bechti hain (expiring contracts) aur high par kharidti hain (next month), ETF ko time ke saath spot commodity se underperform karati hain.

Convenience yield spike kyun karta hai?

Supply disruptions, geopolitical events, ya seasonal demand surges jo physical asset ki immediate possession ko future delivery se wait karne se zyada valuable banate hain.

Futures convergence principle?

Jaise expiration paas aata hai, futures price spot price par converge hoti hai (delivery par dono equal honi chahiye), chahe market contango mein ho ya backwardation mein.