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Select and use hedging methods that suit operational and financial risks, with pricing, foreign currency and interest rate risk as the cases in point.

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

The idea

For a commodity price risk, a producer fearing a fall sells futures or forwards, or buys puts. A consumer fearing a rise buys futures, pays fixed on a swap, or buys calls. For foreign currency risk, use forwards priced by covered interest parity or a money market hedge. Covered interest parity gives F = S × (1 + rd × T) ÷ (1 + rf × T). Here F and S are domestic-currency prices of one unit of foreign currency, and rd and rf are the domestic and foreign interest rates. Operational hedges such as matching the currency of costs and revenues reduce the net exposure first. For interest rate risk, a borrower with floating debt pays fixed on a swap, and a portfolio is hedged by selling futures until its DV01 matches the target. With an imperfect hedge instrument, the minimum variance ratio is h = ρ × σS ÷ σF. Here σS and σF are the volatilities of spot and futures price changes. Contracts = h × exposure ÷ contract size. A common mistake is hedging gross rather than net exposure or inverting the sigma ratio.

Formulas

Minimum-variance hedge ratio

h = ρ × σS ÷ σF

ρ
the correlation between changes in the spot and futures prices
σS
the standard deviation of changes in the spot price
σF
the standard deviation of changes in the futures price

Used when the hedge instrument is imperfect. The usual trap is inverting the volatility ratio.

Number of futures contracts for a minimum-variance hedge

N = h × exposure ÷ contract size

h
the minimum-variance hedge ratio
exposure
the size of the net exposure in units of the commodity
contract size
the units covered by one futures contract

Apply it to the net exposure after any operational hedge, not the gross one.

Currency forward by covered interest parity

F = S × (1 + rdom × T) ÷ (1 + rfor × T)

S
the spot rate in domestic currency per unit of foreign currency
rdom
the simple annual domestic interest rate
rfor
the simple annual foreign interest rate
T
the time to delivery in years

Simple interest, with the domestic rate on top because the quote is domestic per foreign.

A practice question

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

A firm has USD 200 million of floating-rate debt and wants to remove its exposure to rising interest rates. Which action is appropriate?

  1. Enter a pay-fixed, receive-floating interest rate swap - correct
  2. Enter a receive-fixed, pay-floating interest rate swapWhy not: This increases exposure to rising rates, since floating payments rise while the fixed receipts do not.
  3. Buy bond futuresWhy not: Long bond futures gain when rates fall and lose when rates rise, so they add to the exposure.
  4. Sell foreign currency forwardsWhy not: Currency forwards address foreign exchange exposure, not floating-rate interest payments.

Paying fixed and receiving floating converts the floating debt into effectively fixed-rate debt, so higher rates raise the swap receipts and offset higher interest costs.

A harder one

An airline will buy 2.1 million gallons of jet fuel and hedges with heating oil futures of 42,000 gallons each. The standard deviation of price changes is 3.2% for jet fuel and 4.0% for heating oil, and their correlation is 0.85. How many futures contracts give the minimum-variance hedge?

  1. 43Why not: Applies only the correlation (0.85) to the full 50-contract exposure, omitting the ratio of standard deviations.
  2. 34 - correct
  3. 50Why not: Uses a hedge ratio of 1, ignoring basis risk and the volatility difference.
  4. 53Why not: Inverts the volatility ratio, using rho x sigma(futures) / sigma(spot) instead of the other way round.

h = 0.85 x 0.032 / 0.040 = 0.68. Contracts = 0.68 x 2,100,000 / 42,000 = 0.68 x 50 = 34. The hedge ratio below 1 reflects the imperfect correlation.

The hardest tier

A US firm has EUR revenues of 120 million and EUR costs of 45 million, with spot at USD 1.10 per EUR. It sells EUR 37.5 million forward at 1.10, which is 50% of its net EUR exposure. The euro then falls 8% against the dollar, to 1.012. Ignoring any change in the forward's value from the original rate, what is the unhedged loss on the remaining exposure, in USD?

  1. USD 5.28 millionWhy not: Takes 50% of the gross revenue exposure and ignores the natural offset from EUR costs.
  2. USD 6.6 millionWhy not: Uses the whole net exposure of EUR 75 million and ignores the forward sale already in place.
  3. USD 3.3 million - correct
  4. USD 3.0 millionWhy not: Leaves the remaining EUR 37.5 million unconverted: 37.5 x 8% is in euros, not dollars.

Net exposure = 120 - 45 = EUR 75 million; hedged 37.5; unhedged 37.5. Loss = 37.5 x 1.10 x 0.08 = USD 3.3 million. The operational hedge of EUR costs is applied before the financial hedge.

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