Hedging & Risk Path

**Hedgers** use futures and options to reduce risk arising from an existing or anticipated cash position. **Speculators** take on price risk in pursuit of profit. Both sides must coexist for futures markets to clear. Hedgers transfer unwanted price exposure to speculators, and speculators are compensated through an expected risk premium plus the liquidity they consume or provide.

A **short hedge** sells futures contracts today to lock in a future selling price. It suits anyone with **long cash exposure**, such as a commodity producer, an exporter holding foreign currency receivables, or a fund manager planning to liquidate equity. If the spot price falls, the gain on the short futures offsets the loss in the cash market. The effective price received equals $F_1 + b_2$, where $F_1$ is the futures price at hedge inception and $b_2$ is the **basis at the close date**.

A **long hedge** buys futures today to lock in a future purchase price. It suits anyone with **short cash exposure**, such as a manufacturer that will buy raw materials, an importer with future foreign-currency payables, or a fund manager who knows that new cash will need to be invested in equities. If the spot price rises, the gain on the long futures offsets the higher purchase cost. The effective purchase cost equals $F_1 + b_2$, where $F_1$ is the futures price at inception and $b_2$ is the **basis at the close date**.

**Basis** is the spot price of the asset being hedged minus the futures price of the contract used, $b = S - F$ (Hull convention). For a storable commodity in a normal market, basis is negative because the futures price embeds **cost of carry**. As expiry approaches, basis converges toward zero through arbitrage. A **strengthening basis** (less negative or more positive) benefits short hedgers, while a **weakening basis** benefits long hedgers.

**Basis risk** is the uncertainty in the basis $b_2 = S_2 - F_2$ at the close date of a hedge. A short hedger receives an effective price of $F_1 + b_2$, and a long hedger pays $F_1 + b_2$. Because $b_2$ is unknown when the hedge is opened, the realised outcome differs from the intended lock by the **basis change**. Three drivers of basis risk are (1) closing the hedge before delivery, (2) using a futures contract on a **different but correlated asset** (cross hedge), and (3) timing mismatches between physical delivery and contract maturity.

**Cross hedging** uses a futures contract on a different but correlated asset when no liquid future exists for the exact exposure. The classic case is an airline that hedges jet fuel with **WTI or Brent crude** futures, or a Pacific salmon farmer that hedges with **Norwegian salmon futures**. The procedure introduces **additional basis risk** because the hedged and hedging assets do not move in lockstep. The optimal hedge ratio is the **minimum-variance ratio** $h^* = \rho\,\sigma_S / \sigma_F$, not the naive 1:1.

The **minimum-variance hedge ratio** $h^*$ is the proportion of the spot exposure to be hedged with futures that minimises the variance of the hedged position. It equals $h^* = \rho\,\sigma_S / \sigma_F$, where $\rho$ is the correlation between the change in the spot price and the change in the futures price, and $\sigma_S$, $\sigma_F$ are their standard deviations. The result is the slope of the regression $\Delta S = a + h\,\Delta F + \varepsilon$, and the regression $R^2 = \rho^2$ measures **hedge effectiveness**.

**Tailing the hedge** adjusts the futures position downward to account for the **time value of daily mark-to-market** cash flows. A futures hedge pays or receives variation margin every day, so gains earn interest before they are needed and losses must be funded earlier than under a forward. The naive minimum-variance contract count slightly **over-hedges** in dollar terms. Multiplying by a tail factor of $e^{-rT}$, or equivalently scaling by the **spot-to-futures ratio** $V_A / V_F$, removes the bias.

**Portfolio beta hedging** uses stock index futures to neutralise the **systematic risk** of an equity portfolio without selling any underlying stocks. The Capital Asset Pricing Model implies that a portfolio with **beta $\beta$** moves on average by $\beta$ for every one unit move in the market. To remove that exposure, the manager shorts $N^* = \beta \times V_P / V_F$ index futures, where $V_P$ is the portfolio value and $V_F$ is the dollar value of one futures contract. In Australia, **ASX SPI 200 futures** at A$25 per index point are the standard instrument.

Stock index futures let a manager **dial portfolio beta up or down** without trading any of the underlying stocks. The required position is $N^* = (\beta^* - \beta) \times V_P / V_F$, where $\beta^*$ is the target beta, $\beta$ is the current beta, $V_P$ is the portfolio value, and $V_F$ is the value of one futures contract. **Long futures raise beta**, short futures cut it. On ASX SPI 200 futures the contract value is the index level times A$25.