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Weigh the pros and cons of hedging risk exposures and explain the difficulties that can come up when a hedging strategy is put into practice.

FRM® Part I · Foundations of Risk Management · How Do Firms Manage Financial Risk? · FRM1.FR.2.c

The idea

Hedging can add value by reducing the chance and expected cost of financial distress, protecting funds for investment, stabilising earnings for planning, and sometimes lowering taxes. Against it, shareholders can diversify firm-specific risk themselves, so hedging adds cost without a clear benefit. Hedging also has transaction costs, gives up gains when prices move favourably, and can be misused for speculation. In practice the main difficulty is basis risk, where the hedge instrument does not move one-for-one with the exposure. The hedge then removes only a fraction of the variance, equal to ρ² in the standard minimum-variance result. That result assumes a linear hedge at the optimal ratio and a stable correlation ρ. Maturity mismatches force rolling hedges. Funding liquidity risk arises because futures are settled daily in cash while the gain on the hedged exposure may be unrealised. Hedging an exposure that may never materialise, such as a bid that is not won, creates a speculative position. The exam favours the net benefit comparison and the basis and liquidity problems.

Formulas

Variance removed by a minimum-variance hedge

hedge effectiveness = ρ²

ρ
the correlation between changes in the spot exposure and the hedge instrument

Holds for a linear hedge at the optimal ratio with a stable correlation. The share left over, 1 − ρ², is basis risk; do not use ρ itself.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which is a commonly cited reason why hedging can add value to a firm?

  1. It raises expected profit because hedge instruments have positive expected payoffsWhy not: In fairly priced markets hedges have roughly zero expected payoff before costs; they reduce variability, not raise the mean.
  2. It removes the need for the firm to hold any capitalWhy not: Hedging reduces some risk but residual and counterparty risks remain, so capital is still required.
  3. It transfers risk to shareholders, who can then diversify itWhy not: This is an argument against hedging; shareholders diversifying themselves is why hedging may add no value.
  4. It lowers the probability and expected cost of financial distress - correct

Hedging lowers earnings volatility and so the chance of distress, which has direct and indirect costs and can force the firm to cut valuable investment.

A harder one

An airline hedges jet fuel with crude oil futures. The correlation between changes in the two prices is 0.85. Assuming the hedge ratio is chosen to minimise variance, what proportion of the variance of the fuel cost can the hedge remove?

  1. About 72% - correct
  2. About 85%Why not: Uses the correlation itself rather than its square as the proportion of variance removed.
  3. About 15%Why not: Uses 1 minus the correlation, which is neither the variance removed nor the variance remaining.
  4. About 28%Why not: Computes the proportion of variance that remains (1 - rho²), not the proportion removed.

In the standard minimum-variance hedge result (linear hedge at the optimal ratio, stable correlation), the variance reduction is rho² = 0.85² = 0.7225, about 72%. The remaining 27.75% is basis risk.

The hardest tier

A trading firm has sold fixed-price supply contracts to customers over three years and hedges by holding 2,000 long futures contracts of 1,000 barrels each. In the first week the futures price falls from USD 78 to USD 72 per barrel. Variation margin is paid in cash daily, whereas the offsetting gain on the supply contracts is not realised until deliveries. What cash must the firm fund immediately because of the hedge?

  1. Nothing, because the gain on the customer contracts offsets the futures lossWhy not: The offset is economic and unrealised; margin on futures is settled in cash daily and must be funded now.
  2. About USD 12.0 million - correct
  3. About USD 156 millionWhy not: Uses the notional value of the futures (78 x 2,000 x 1,000) rather than the price change times the position.
  4. About USD 0.012 millionWhy not: Multiplies the price move by the number of contracts but forgets the 1,000-barrel contract size.

Margin call = 6 x 2,000 x 1,000 = USD 12.0 million. The hedge is economically sound, but the mismatch in cash timing creates funding liquidity risk.

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