Aug 23

Foreign Exchange. Off-balance-sheet currency hedge (2007 FRM)

by David Harper, CFA, FRM, CIPM

FRM | Risk |

 fxIntroNo2

Learning Outcome

  • LO 19.5: Explain off-balance-sheet hedging with forwards.

Learning Outcome

Yesterday, we looked at an on-balance-sheet currency hedge. Now let's look at an off-balance-sheet hedge. But first let's summarize the risk problem created by an asset/liability currency mismatch:

  • Assume the bank raises $200 by collecting CD deposits (liabilities) that pay interest of 5% (i.e., 5% is the bank's cost of funds)
  • The bank lends $100 (50% of the portfolio) to U.S. customers at a yield of 6%.
  • The bank lends the other $100 to British customers, where the British rate is 7% (all rates are illustrative)
  • At the start of the year (when these transactions occur), the spot currency exchange rate is $2 dollar/pound sterling (US $2 dollar to 1 pound sterling, or 0.5 pound sterling to $1 US dollar).

If the foreign currency depreciates (un-hedged), it erodes returns

Since the bank has a positive spread, everything is fine if the US/British currency is stable. If the spot currency exchange rate is unchanged over the year, the bank earns a weighted ROA of 6.5% (6% on US loans and 7% on UK loans). But instead assume that the pound depreciates against the dollar (i.e., the dollar appreciates against the pound), such that the spot currency exchange rate drops to $1.80 $/pound. In this case, the effective return on the British loan is negative: 

hedgeForward_problem

The $100 was invested into a 50 pound loan (100/2 = 50), which grows to 53.50 pound sterling (50 x 1.07 = 53.50), which is then converted back to $96.30 US dollars (53.50 pound sterling x $1.80 = $96.30). The 7% return was overwhelmed by a 10% currency depreciation.

Specifically, where rUK is the loan's return, ST is the future (spot) currency exchange rate, and S0 is today's (spot) currency exchange rate, the loss is given by: 

fxformula

Hedge with a forward contract: short the forward exchange rate

Now let's assume the bank hedges with a forward currency contract. Specifically, it sells forward its UK loan at the forward exchange rate. Let's assume the forward exchange rate is a 2% discount on today's spot: $1.96 dollar/pound.The scenario is the same until the end of the year: the $100 converts to 50 pound sterling, which grows to 53.50 pound sterling per the loan. But, this time, the bank delivers the 53.50 pound sterling to the buyer of the forward currency contract; the bank receives $104.86 per the agreed-upon forward exchange rate (53.50 pound sterling x $1.96 = $104.86):

hedgeForward_Forward

By shorting the forward currency contract, the bank eliminated its currency risk. Under these assumptions (specifically, a forward rate that is discounted to the spot rate), this does cost the bank: the 7% return is reduced to a 4.86% ROA on the British loan for a weighted ROA of 5.43%. But, we previously assumed cost of funds of 5% for this bank, so a profit is ensured.

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