Part V · Commodities, macro and geopolitics · M10 · week 6 · 16 h

Commodities: gold, silver, crude

Storage theory and convenience yield, roll yield, Hotelling and gold as a durable asset, Indian gold import parity, what drives gold and silver, crude market structure and India's exposure, and MCX contracts.

Start reading · Learning outcomes

Builds on M02 Statistics of returnsM07 Forwards and futuresM08 Option pricing

Prerequisites M07 (cost of carry $F = S e^{(r+u-y)T}$ , basis, convergence, hedging), M08 (Black-76 for options on futures), M02 (log returns, autocorrelation). Mathematics: constrained optimisation (one Hamiltonian), AR(1) processes, the Ornstein–Uhlenbeck process, unit-root asymptotics at the level of "the statistic converges to a functional of Brownian motion". Time: ~16 hours (notes 9 h, problems 5 h, code 2 h). Primary texts: Hull, Options, Futures, and Other Derivatives (11th ed.), chapter on forward and futures prices (commodity section) and chapter on futures options; Geman, Commodities and Commodity Derivatives (Wiley, 2005); Williams and Wright, Storage and Commodity Markets (CUP, 1991); Pindyck (2001), "The dynamics of commodity spot and futures markets: a primer".

Learning outcomes

Prove the cash-and-carry upper bound $F \le S e^{(r+u)T}$ , prove that no arbitrage lower bound exists for an agent without inventory, and state the bound that does exist for an inventory holder or a metal borrower.
Derive, from the competitive-storage equilibrium, why low inventories produce backwardation and high inventories produce contango close to full carry, and read a futures curve as an inventory signal.
Decompose a futures excess return exactly into spot return and roll yield, and compute how much a long-only index investor loses to a contango curve.
Derive the Hotelling rule and the Barsky–Summers "gold as a durable asset" relation, and say where each fails.
Price Indian gold from the international price by import parity (troy-ounce conversion, USDINR, BCD, AIDC, GST), reproduce an MCX price to within 0.1%, and decompose a rupee gold return into gold, FX and duty parts.
Test the gold/silver ratio for mean reversion properly: ADF with correct critical values, AR(1) half-life $h = -\ln 2/\ln\varphi$ , its OU interpretation, its small-sample bias and its confidence interval.
Describe the crude market's structure (OPEC+, shale, Brent/WTI/Dubai, the Indian basket, EIA inventories, crack spreads) and trace an oil shock through INR, CPI and OMC stocks.
Read an MCX contract specification (lot, quote, tick, tender period, devolvement of options), and price an MCX option on futures with Black-76.

Sections ≈ 5 h of study

Foundation 7 sections · ≈ 1 h 20 min
Core 10 sections · ≈ 2 h 55 min
Advanced 2 sections · ≈ 45 min

Learning outcomes Foundation 5′
10.1 What is different about commodities Foundation 5′
10.2 The theory of storage Core 25′
Figure Theory of storage: inventories set the slope of the curve
10.3 Roll yield Core 15′
Figure Roll yield: what rolling a long futures position costs in contango
10.4 Exhaustible resources and durable assets: Hotelling and Gibson Advanced 15′
Figure The Hotelling rule
10.5 Pricing Indian gold: import parity Core 20′
Figure Pricing Indian gold: import parity as a waterfall
Lab Rupee gold: import parity against an Indian price
10.6 What drives gold Core 15′
Lab Gold against US real yields: a rolling beta
10.7 Silver and the gold/silver ratio Core 15′
Figure Half-life of the gold/silver ratio
Lab Gold/silver ratio: is it mean-reverting?
10.8 Crude oil Foundation 20′
Lab Brent–WTI spread
10.9 Natural gas and base metals (brief) Foundation 5′
10.10 MCX: contracts, options and hours Foundation 15′
10.11 Case studies Core 20′
10.12 Positioning: the CFTC Commitments of Traders report and MCX open interest Core 30′
10.13 Seasonality: demand calendars and how to test them Advanced 30′
10.14 Trading on MCX I: costs, tax and choosing the contract Foundation 20′
10.15 Trading on MCX II: margins, the evening session, expiry, delivery and options Core 20′
Summary of key results Foundation 10′
Readings and resources Core 5′
Facts that change Core 10′