题目
A bank has a USD 4 million portfolio available for investing. The cost of funds for the $4 million is 5.5%. The bank lends 50% of the assets to domestic customers for an average loan rate of 7.35%. The rest of the portfolio is lent to some UK clients at 8% at a current exchange rate of 1.62 USD per GBP. At the same time, the bank sells a forward contract to eliminate exchange rate risk equal to the expected receipts one year from now. The forward rate is 1.52 USD per GBP. The net interest margin on the bank’s investment balance sheet is closest to:
选项
A.-1.16%
B.1.93%
C.2.18%
D.4.34%
答案
A
解析
Assuming no default risk, the domestic return is 7.35%. The return on the UK investments is: (USD$2,000,000)/1.62 = GBP1,234,568, which turns into GBP1,234,568×1.08=GBP1,333,333 one year from now. Since the forward contract guarantees the exchange rate in the future, this translates into GBP1,333,333×1.5200=USD2,026,666. This is a dollar return to the bank of USD2,026,666/USD2,000,000-1=1.33%. Hence, the weighted average return to the bank’s investments is (0.5)×(7.35%)＋(0.5)×(1.33%)=4.34%. Since the cost of funds for the bank is 5.5%, the net interest margin for the bank is 4.34%-5.50%=-1.16%. 假设没有违约风险，国内回报率为7.35%。英国投资的收益为:(USD$2,000,000)/1.62= GBP1,234,568，一年后变为GBP1,234,568×1.08=GBP1,333,333。 由于远期合同保证了未来的汇率，所以换算成美元为:1,333,333×1.5200=USD2,026,666。美元回报1.33%。因此，加权平均回报率是(0.5)×(7.35%)＋(0.5)×(1.33%)=4.34%。 由于银行的资金成本为5.5%，银行的净息差为4.34% - 5.50%= - 1.16%。