Understand spot vs futures pricing in commodities

2.3.3 · Stock-Market › Commodities, Forex & Crypto

Overview

Jab hum oil, gold, ya wheat jaisi commodities trade karte hain, toh humein do fundamental prices milte hain: spot price (ABHI kharido/becho) aur futures price (BAAD mein delivery ke liye locked-in price). Unke relationship ko samajhna arbitrage opportunities, hedging strategies, aur market sentiment padhne ke raaste kholata hai.

Figure — Understand spot vs futures pricing in commodities

Core Concepts

The Cost-of-Carry Model (Scratch se Derivation)

Starting Point: No-Arbitrage Principle

Core idea: Agar futures price, spot + carry costs se bahut zyada door chali jaaye, toh arbitrageurs ek saath sasta kharidke aur mahenga bechke prices wapas line mein le aate hain.

Chaliye step-by-step fair futures price derive karte hain:

Formula Cost-of-Carry Formula (Derived)

Diya gaya:

$S_{0}$ = Aaj ka spot price
$F$ = Time $T$ par delivery ke liye futures price
$r$ = Risk-free interest rate (annual, continuously compounded)
$c$ = Storage cost per unit per year (spot ke % ke roop mein, continuously compounded)
$y$ = Convenience yield (physical rakhne ka faida, % per year ke roop mein, continuously compounded)
$T$ = Time to maturity (years mein) Derivation (consistency ke liye sabhi costs ko continuous rates ki tarah treat kiya gaya hai):

Strategy A (Synthetic Futures): Abhi spot commodity kharido + $T$ tak rakho
- Aaj ki cost: $S_{0}$
- $S_{0}$ ko continuous rate $r$ par finance karo → debt time $T$ par $S_{0} e^{r T}$ ho jaati hai
- Storage ek continuous rate $c$ ke roop mein value par charge hoti hai, isliye ise financing ke through pay karne par kul amount $S_{0} e^{(r + c) T}$ ho jaati hai (interest aur storage ek hi tarah compound hote hain)
- Time $T$ par Total cost: $S_{0} e^{(r + c) T}$
Storage ko continuous rate kyun treat karein? Financing term ke saath consistency ke liye. Agar tum storage ko aaj pay ki gayi ek discrete lump-sum $U$ ki tarah model karo, toh formula ban jaata hai $F = (S_{0} + U) e^{r T}$ . Dono valid hain; hum is note mein continuous-rate convention chunte hain taaki har term ( $r$ , $c$ , $y$ ) ek hi exponent mein rahe. Pehle wala " $S_{0} \cdot c \cdot T$ " sirf $S_{0} (e^{c T} - 1)$ ka first-order Taylor approximation hai chhote $c T$ ke liye—hum ise exponential form ke saath mix nahi karte.
Strategy B (Direct Futures): $F$ par futures contract kharido, delivery par pay karo
- Time $T$ par cost: $F$
No-Arbitrage Condition: Agar $F > S_{0} e^{(r + c) T}$ , toh sabhi Strategy A karenge (spot kharido, store karo, futures ke against deliver karo → riskless profit). Agar $F < S_{0} e^{(r + c) T}$ , toh holders spot bechenge, proceeds invest karenge, futures wapas khareedenge.

Convenience Yield shamil karna (physical rakhne ka faida, jaise emergency access):

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

Yeh step kyun? Convenience yield $y$ futures price ko GHATAATA hai kyunki physical holders ko ek faida milta hai (turant use karne ki optionality, stockouts se bachna) jo futures holders ko nahi milta. $y$ ko commodity rakhne se milne wale "dividend" ki tarah socho.

Chhote $T$ ke liye simplified (linear approximation jab $T < 0.5$ years): $F \approx S_{0} (1 + (r + c - y) T)$

Har Term Kyun Matter Karta Hai

$r$ (interest rate): Spot kharidne ka paisa risk-free return kama sakta tha → futures ko compensate karna chahiye
$c$ (storage): Physical commodities ko warehouses, insurance chahiye → futures ko yeh cover karna chahiye
$y$ (convenience yield): Oil refiners ek premium pay karte hain ABHI oil haath mein rakhne ke liye vs. ek futures contract → futures price ghataata hai

Contango vs Backwardation

Worked Examples

Worked example Example 3: Arbitrage Calculation

Market anomaly (poore mein continuous-rate convention use karte hue):

Gold spot: $2000/oz
1-year gold futures: $2100/oz
Risk-free rate: $r = 3%$ (continuous)
Storage cost: $c = 0.5%$ per year (continuous rate)
Gold mein zero convenience yield hai ( $y = 0$ )

Fair futures price: $F = 2000 \cdot e^{(0.03 + 0.005) \cdot 1} = 2000 \cdot e^{0.035} = 2071.23$

Observed futures: $2100 (o v er p r i ce d b y$ 2100 - 2071.23 = 28.77$!)

Arbitrage strategy (poori tarah consistent — gold AUR storage DONO ko $r$ par finance karo):

Aaj: $2000 k o 3% p a r b or r o w k a r o (co n t in u o u s), 1 oz s p o t g o l d k ha r i d o, 1 - y e a r f u t u r es$ 2100 par becho. Storage continuously $c$ par position par charge hoti hai aur $r$ par gold ke saath finance hoti hai.
1 saal baad: Gold futures ke against deliver karo → $2100 receive karo
Saari financing repay karo (gold + storage ek saath compound ki gayi): $2000 \cdot e^{(0.03 + 0.005) \cdot 1} = 2071.23$
Profit: $2100 - 2071.23 = * *$ 28.77 riskless profit**

Yeh step kyun? Storage cost ko exponent ke andar usi continuous rate $r$ par finance karke, total repayment exactly fair futures price $S_{0} e^{(r + c) T}$ hoti hai. Isliye arbitrage profit precisely observed futures − fair futures = $28.77$ hai, discrete aur continuous conventions mix karne se koi leftover discrepancy nahi.

Common Mistakes & Steel-Manning

Active Recall Practice

Recall Feynman: Ek 12-saal ke bachche ko explain karo

Socho tum PlayStation 5 kharidna chahte ho, lekin store kehta hai abhi stock nahi hai aur tum ek sirf 3 mahine mein le sakte ho. Woh tumhe do deals offer karte hain:

Restock hone tak wait karo aur us waqt jo bhi price ho woh pay karo (3 mahine baad spot price)
**AAJKE DIN $520 p a y k a r o a p na P S 53 - mahin e d e l i v er y k e l i y e l oc k k a r n e k e l i y e * *, c hah e aaj k a c a s h p r i ce$ 500 hai (futures price)

Deal 2 $520 k y u nk a r e g aj ab P S 5 aaj$ 500 mein hain? Kyunki store ko tumhara PS5 ek warehouse mein rakhna padega (storage cost) aur woh ise bech kar $500 invest kar sakta tha (interest cost). Yeh contango hai—locked-in future price aaj ke spot SE UPAR hai.

Ab ise paltao. Ek paagal holiday shortage imagine karo jahan sabko ABHI PS5 chahiye. Spot price aaj $600 t ak u p a r c ha l ij aa t ihai . L e k in s abk o p a t ahaik i 3 mahin e m e in e k ba d ana y a s hi p m e n t aa y e g a, t o h s t or e t u m se 3 - mahin e d e l i v er y k e l i y es i r f$ 560 ka promise karta hai. Yeh backwardation hai—future price ( $560) aaj k es p o t ($ 600) SE NEECHE hai, kyunki console turant paas mein rakhna ek premium ka worthy hai aur future supply plenty hogi.

Oil aur gold jaisi commodities isi tarah kaam karti hain. Spot = abhi. Futures = locked-in future price. Contango = future price upar; backwardation = future price neeche.

Memory Aids

Connections

Commodity Trading Strategies - Spot-futures spreads ko exploit karna
Hedging with Futures - Producers/consumers futures use karte hain prices lock karne ke liye
Cost of Carry Arbitrage - Mispricing se riskless profit
Convenience Yield in Oil Markets - Energy mein backwardation kyun dominate karta hai
Contango Bleed in Commodity ETFs - Rolling futures returns destroy karta hai
Basis Risk - Spot-futures spread hamesha perfectly converge nahi karta
Normal Backwardation Theory - Futures risk premium par Keynes ka view
Gold vs Oil Futures Curves - Storage costs curve shape determine karte hain

Flashcards

#flashcards/stock-market

What is the spot price in commodities? :: Kisi physical commodity ki immediate delivery (2 business days ke andar) ke liye current market price. Yeh real-time supply-demand reflect karta hai.

What is a futures price in commodities?

Ek standardized contract price jo aaj agree ki jaati hai ek specific future date par commodity ki delivery ke liye. Tum abhi price lock karte ho, baad mein settle karte ho.

Define contango

Jab futures price > spot price. Futures curve upar slope karti hai. Un commodities ke liye typical jahan storage sasti ho aur carry costs convenience yield se zyada hon.

Define backwardation

Jab futures price < spot price. Futures curve neeche slope karti hai. Baar baar hota hai (rare nahi) jab immediate demand high ho ya convenience yield carry costs par haavi ho.

Cost-of-carry formula for futures pricing

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

jahan

r

= risk-free rate,

c

= storage cost (continuous rate ke roop mein),

y

= convenience yield,

T

= time to maturity.

Why does the risk-free rate

r

increase futures price?

Spot commodity kharidne mein lagaya capital risk-free return kama sakta tha. Futures ko is opportunity cost ke liye compensate karna padta hai, jo futures price ko spot se upar push karta hai.

What is convenience yield

y

Ek physical commodity rakhne ka faida (turant access, stockouts se bachna, operational flexibility). Yeh futures price ko GHATAATA hai kyunki futures holders ko yeh faida nahi milta.

If gold spot =

2000, 1 - y e a r f u t u r es =

2080, risk-free rate = 3%, storage = 1%, what is implied convenience yield?

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

→

2080 = 2000 e^{(0.03 + 0.01 - y)}

→

1.04 = e^{0.04 - y}

→

0.04 - y = ln (1.04) = 0.0392

→

y = 0.08%

(almost zero, gold ke liye typical).

Why is agricultural commodity backwardation common before harvest?

Current supply tight hai (high spot), lekin harvest jald supply flood kar dega (lower futures). Immediate demand > expected future demand.

What is roll yield?

Ek expiring futures contract close karke next month ka contract open karne se hone wala profit/loss. Contango mein negative (upar kharido), backwardation mein positive (neeche kharido).

When is arbitrage possible between spot and futures?

Jab

F \neq = S_{0} e^{(r + c - y) T}

. Agar futures bahut upar hain, toh spot kharido + store karo + futures becho. Agar bahut neeche hain, toh spot becho + invest karo + futures kharido.

Does futures price predict future spot price?

Nahi. Futures price = spot + cost of carry - convenience yield. Yeh ek no-arbitrage price hai, koi forecast nahi. Spot predict karne ke liye fundamentals use karo.