Futures Markets and Hedging

An oil producer expects to deliver 100,000 barrels in three months. Spot is $80; the three-month futures price is $79. The producer sells futures to lock in the sale price. Three months later, spot is $72 and futures settled at $71. The producer sells barrels at $72 spot, closes futures at $8profit,andrealizes\$80net,almostexactlytheoriginaltarget.The$1 gap is basis risk, and basis risk is what FRM Part I tests on every futures-hedging question.

A futures contract is defined by six parameters set by the exchange.

• Underlying asset: what is delivered (10 oz of gold, 1,000 barrels of WTI crude, $100,000 face Treasury, etc.).
• Contract size: fixed multiplier; e.g., S&P 500 e-mini = $50 × index level.
• Delivery month and dates: specific months (March, June, September, December for many financials).
• Delivery location: physical commodities specify warehouses or pipelines.
• Quality grade and substitutes: Treasury futures allow a basket of bonds; cheapest-to-deliver bond optimizes the seller's economics.

Common mistakes

• Confusing volume and open interest. Volume measures activity; open interest measures positions. A futures contract with 100,000 daily volume but 5,000 open interest is dominated by intraday traders. A contract with 5,000 volume but 100,000 OI has structural participants.
• Computing the optimal hedge ratio with σ ratios reversed. $h^{\ast }=\rho \cdot {\sigma }_S/{\sigma }_F$, spot in numerator. Reversing gives $\rho \cdot {\sigma }_F/{\sigma }_S$, which is wrong. Trap: with $\rho =0.9$, ${\sigma }_S=0.04$, ${\sigma }_F=0.06$, the right answer is $0.9\times 0.667=0.60$, but candidates write $0.9\times 1.5=1.35$ and choose that as the hedge ratio.
• Using $\rho$ instead of ${\rho }^2$ for hedge effectiveness. Effectiveness is the fraction of variance eliminated and equals ${\rho }^2$. With $\rho =0.85$, effectiveness is 72.25%, NOT 85%. Trap: 85% sometimes appears as choice B and traps candidates who confuse correlation with effectiveness.

Bottom line

• Futures are exchange-traded forwards with standardized terms, daily mark-to-market, and central clearing; forwards settle once at maturity and carry full counterparty credit risk.
• Convergence: at delivery the futures price converges to spot, otherwise arbitrageurs take riskless profit.
• Basis = spot − futures. Basis risk is the variability in basis between hedge initiation and lift; perfect hedges (same asset, same date) have zero basis risk.
• Optimal hedge ratio: $h^{\ast }=\rho \cdot {\sigma }_S/{\sigma }_F$; minimizes variance of the hedged portfolio. Hedge effectiveness equals ${\rho }^2$.

Exam shortcut

When a question gives correlation, σ_S, σ_F, and exposure size, the answer chain is fixed: compute $h^{\ast }$, then $N^{\ast }$, then effectiveness ${\rho }^2$. If the question mentions long-dated horizons, check whether tailing matters. For basis problems, write $\text{Effective price}=F_1+b_2$ and substitute, and the algebra collapses cleanly. Memory aid: "Sigma-S over sigma-F, times rho, that's h-star." And remember: short hedgers root for the basis to strengthen, long hedgers root for it to weaken.

The full lesson (about 3,252 words, 22 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

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