Aug 22

Foreign Exchange. 2007 FRM: On-balance-sheet hedge on currency exposure

by David Harper, CFA, FRM, CIPM

FRM | Risk |

introFX

Learning Outcome

  • LO 19.4: Explain on-balance-sheet hedging.

Foreign currency exposure = portfolio exposure + trading exposure

In the previous post, I explained that exposure to a currency is a combination of balance sheet exposure (i.e., assets and liabilities denominated in foreign currencies) plus trading activities (i.e., purchases and sales on spot or forward foreign exchange markets).  The foreign exchange learning outcomes for the 2007 FRM are based on Saunders Chapter 15.

Un-hedged bank portfolio: Assumptions

Let's look at a hypothetical portfolio (balance sheet) that has currency exposure. Here are the assumptions:

  • We (the bank) raise $200 by collecting deposits into CDs. These deposits are liabilities to us; we owe customers an interest rate of 5%. This 5% is a cost of funds.
  • We invest $100 (50% of the portfolio) into U.S. loans that yield 6%. These loans are assets. Saunders calls the 6% yield here a return on asset (ROA). The difference (borrow at 5% and lend @ 6% = 1%) is our gross spread. This is the traditional way for a bank to make money.
  • We invest the other $100 into U.K. pound sterling loans. These are assets, too, but they will return a British rate of 7%.
  • We start the year with a spot currency exchange rate of $2.00 ($/pound = $2 to 1 pound sterling)
  • During the year, the pound depreciates against the dollar: at the end of the year, the spot currency exchange rate is $1.80 ($/pounds)

What happens to the un-hedged portfolio: currency movements overwhelm home country return

Here are the mechanics that explain how our un-hedged portfolio produces a negative return (under a scenario where the pound depreciates from $2 US/pound sterling to $1.80 US/pound sterling):

unhedged_poundDepreciates3

 

The reason our portfolio loses is that our foreign rate of 7% (dollars invested into pound sterling) was overwhelmed by a 10% drop in the currency. Specifically, see above:

  • The U.S. portion of our asset portfolio gained 6% but the British portion lost 3.70%. On a weighted average basis, therefore, the ROA on our assets was 1.15%
  • But the liabilities are fully denominated in U.S. dollars, where our cost of funds is 5%.
  • The ROA of 1.15% minus the COF of 5% produces an ROI of -3.85%

Make sure you follow the green/red arrows to understand the currency conversions. There are no forward contracts here. In regard to the green arrows:

  • We start the year by converting one-half of the portfolio into 50 pound sterling: $100/2=50.
  • This 50 pound sterling grows at 7% to finish the year at 53.50 pound sterling
  • At the end of the year, we convert the pound sterling into $96.30 US dollars: (53.50)(future spot of 1.80)=$96.30

This illustrates the un-hedged portfolio where assets and liabilities are mis-matched.

Now let's hedge the bank portfolio ("on-balance-sheet hedge") by matching liabilities to assets

Now let's employ on-balance-sheet hedging. Everything is the same, except now we fund one-half of our assets (loans) with British loans. If we do that, we have "matched" the $100 in assets that will be invested in pound sterling with a liability that is denominated in pound sterling.

This is illustrated below. The key difference is the liabilities. Note that instead of lending $200 U.S. dollars, we lend $100 U.S. dollars and 100 pound sterling.

hedged_poundDepreciates

The mechanics:

  • Our assets perform the same: the U.S. portion of our asset portfolio gained 6% but the British portion lost 3.70%. On a weighted average basis, therefore, the ROA on our assets was 1.15%
  • The cost of funds for our U.S. loan is 5%
  • But the cost of funds for our U.K. loan is -4.60%! We made a profit: we owed 6% on the loan but the 10% currency movement overwhelmed this. The currency movement penalized our assets but benefited our liabilities. This is the hedge.
  • The ROA of 1.15% minus the COF of 0.2% produces an ROI of almost 1%
  • Regardless of the currency movement, currency losses on the asset side of our balance sheet are offset by gains on the liability side of our balance sheet.

 Reference

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