Hedge Ratio

The hedge ratio is the size of a hedging position expressed as a proportion of the exposure it is meant to protect. A company that expects to receive 10 million euros and sells 6 million euros forward has a hedge ratio of 0.6, or 60 percent. The measure is used by corporate treasurers, fund managers, commodity producers and payment companies to describe how much of a risk has been neutralised and how much is still open to market movements.

The term appears most often in FX hedging, where it describes the share of a currency exposure covered by forwards, options or swaps, but it applies equally to interest rates, commodities and equity portfolios. It has two related meanings: the simple ratio of hedge to exposure, which is a policy choice, and the optimal or minimum-variance hedge ratio, which is a statistical estimate of the hedge size that removes the most risk.

The basic calculation is:

Suppose a United States importer must pay 5 million euros in three months and buys 3.5 million euros under an FX forward contract. The hedge ratio is 3.5 divided by 5, which is 0.7. If the euro rises by 4 percent against the dollar before the payment date, the importer bears the extra cost only on the unhedged 1.5 million euros. A ratio of 1 is a full hedge, a ratio of 0 is no hedge, and a ratio above 1 is an over-hedge, which leaves the company with a position in the opposite direction.

When the hedging instrument does not move exactly in step with the exposure, hedging one for one does not give the lowest risk. This happens when a company hedges with a futures contract on a related but different asset, or hedges an illiquid currency with a more liquid proxy. The ratio that minimises the variance of the combined position is:

• $h^{*}$ is the optimal hedge ratio.
• $\rho$ is the correlation between changes in the value of the exposure and changes in the price of the hedging instrument.
• $\sigma_{S}$ is the standard deviation of changes in the value of the exposure.
• $\sigma_{F}$ is the standard deviation of changes in the price of the hedging instrument.

If the correlation is 0.9, the exposure has a standard deviation of 4 percent and the futures price has a standard deviation of 5 percent, the optimal ratio is 0.9 times 4 divided by 5, which is 0.72. The company would hedge 72 percent of the exposure's value. The risk that remains after the hedge is basis risk.

In practice most corporate treasury departments set hedge ratios by policy, not by statistics. A common approach is a layered or rolling programme: a high ratio for exposures expected in the next quarter, when forecasts are reliable, and progressively lower ratios for later periods. A firm might cover 80 percent of forecast flows for the next three months, 60 percent for the following three and 40 percent beyond that, adding to the hedges as each period comes closer.

Several factors drive the choice:

• Certainty of the exposure. Contracted amounts, such as a signed invoice, are often hedged in full. Forecast sales are hedged in part because the cash flow may not arrive, and an over-hedge creates a new risk.
• Cost of hedging. Forward points, option premiums and credit lines all carry a cost, which is higher for currencies with large interest rate gaps or those that trade only as a non-deliverable forward.
• Offsetting flows. A natural hedge, in which revenue and costs fall in the same currency, lowers the amount that needs a financial hedge.
• Margins and pricing power. A business with thin margins and fixed price lists usually hedges more than one that can reprice quickly.

For an FX option, the hedge ratio usually means delta: the change in the option's value for a small change in the exchange rate. A dealer who has sold an option with a delta of 0.4 buys 40 percent of the underlying amount to stay neutral, and adjusts as delta changes. This is called dynamic or delta hedging.

Under hedge accounting rules, the ratio designated in the documentation should match the ratio the company actually uses to manage the risk. Accounting standards require a test of hedge effectiveness, and a deliberately unbalanced ratio can lead to ineffectiveness being recognised in profit or loss. In a cash flow hedge of forecast transactions, an over-hedge beyond the highly probable amount cannot be designated.

A hedge ratio describes quantity, not quality. Two companies with a 70 percent ratio may carry very different risk if one hedges with forwards and the other with out-of-the-money options. The minimum-variance ratio depends on historical correlations and volatilities, which shift over time and tend to break down in stressed markets. Ratios based on forecasts are only as good as the forecasts, and a high ratio on an exposure that fails to materialise turns a hedge into a speculative position. For these reasons the ratio is normally reported together with the instruments used, the tenor of the hedges and the remaining currency risk.