Market C - Question 3 (Saunders FX) 
Question:
A U.S. bank is funded with $100 million in U.S. dollar-denominated liabilities (CDs). It invests $50 million (50%) in U.S. dollar denominated loans and the remaining $50 million in British (pound sterling denominated) assets (i.e., assets of $50 + $50 million = liabilities of $100 million). At the start of the year, the spot currency exchange rate is $2 per 1 GBP ($2/1 GBP or 0.5 GBP/1 dollar, near its current level).
The bank loans at 6% in the U.S and 9% in the U.K. (i.e., return on assets) and deposits/liabilities earn 5% in the U.S and 7% in the U.K. (i.e., cost of funds to the bank). The following questions refer to a simple single period.
(i) If the currency exchange rate does not move, what is the bank’s return on investment (ROI)?
(ii) If the pound sterling depreciates (dollar appreciates) to $1.90/GBP (0.53 GBP/$), what is the unhedged ROI?
(iii) Given the same pound depreciation/dollar appreciation, what is the bank’s ROI if the bank employs an on-balance sheet hedge?
(iv) Illustrate an off-balance sheet hedge if the bank can take a position in a forward currency contract, where the forward price is a 5% discount from the current spot.
(i)
In this case, the bank’s ROA = 7.5% (50% @ 6% and 50% @ 9%) and its cost of funds = 5%. So it’s ROI = 7.5%-5= 2.5%. In short, absent currency impacts, the bank maintains its spread.
(ii)
In this case, pound sterling depreciation erodes returns. ROI = -0.22%:
(iii)
The on-balance hedge implied $50 million in pound sterling ($50 = 25 million GBP) denominated liabilities fund the assets. The below show the same pound sterling depreciation to $1.90/GBP but it does not matter; the dollar could depreciate instead. Because the $50 million = 25 million GBP in liabilities will fluctuate up/down along with the assets. The ROI will always be positive.
(iv)
In the case, the forward foreign currency contract maintains the spread regardless of whether the spot erodes:
Key points:
* Un-hedged is a currency mis-match between assets & liabilities. The un-hedged exposure is a “double-edged sword” that can contribute a loss (if assets in the foreign currency depreciate) or a profit (if assets in the foreign currency appreciate)
* An on-balance sheet (currency) hedge matches assets with liabilities in regard to currency (do not confuse with duration matching). In the case of foreign currency depreciation, erosion to asset returns is offset (mitigated) by lower cost of funds.
* An off-balance sheet (currency) hedge “locks-in” the currency exchange rate with forward contract(s)
