Consider the following balance sheet of a U.S. FI. [table]
Assets | Liabilities $20 million | U.S. loans (10 percent) | $40 million | U.S. CDs (9 percent) $20 million | U.K. loans (16 percent) (Loans made in sterling) | |
[/table] This U.S. FI is raising all of its $40 million liabilities in dollars (one-year CDs) but investing 50 percent in U.S. dollar assets (one-year maturity loans) and 50 percent in U.K. pound sterling assets (one-year maturity loans). Suppose the promised one-year U.S. CD rate is 9 percent, to be paid in dollars at the end of the year, and that one-year, credit risk-free loans in the United States are yielding only 10 percent. Credit risk-free one-year loans are yielding 16 percent in the United Kingdom. If the exchange rate had fallen from $1.60/₤1 at the beginning of the year to $1.50/₤1 at the end of the year, the weighted return on the FI's asset portfolio would be

Question

Consider the following balance sheet of a U.S. FI. [table]
Assets | Liabilities $20 million | U.S. loans (10 percent) | $40 million | U.S. CDs (9 percent) $20 million | U.K. loans (16 percent) (Loans made in sterling) |  | 
[/table] This U.S. FI is raising all of its $40 million liabilities in dollars (one-year CDs) but investing 50 percent in U.S. dollar assets (one-year maturity loans) and 50 percent in U.K. pound sterling assets (one-year maturity loans). Suppose the promised one-year U.S. CD rate is 9 percent, to be paid in dollars at the end of the year, and that one-year, credit risk-free loans in the United States are yielding only 10 percent. Credit risk-free one-year loans are yielding 16 percent in the United Kingdom. If the exchange rate had fallen from $1.60/₤1 at the beginning of the year to $1.50/₤1 at the end of the year, the weighted return on the FI's asset portfolio would be

BlackTom AI · Accepted Answer

Foreign-currency asset return in domestic dollars equals (1 + foreign interest rate) × (E_end / E_begin) − 1, where E is dollars per foreign currency.

1) Relevant knowledge points and concepts
- A UK loan yields 16% in sterling; converting its final sterling receipts back to dollars requires using the end-of-period exchange rate.
- The U.S. loan yields 10% in dollars, so its dollar return is straightforward.
- The portfolio is 50% in U.S. dollar loans and 50% in U.K. sterling loans by dollar value, so the overall asset return is the weighted average of the dollar returns on each asset.

2) Step-by-step reasoning
- Start with $20 million invested in U.S. loans and $20 million invested in U.K. loans (total assets $40 million).
- U.S. loan dollar return: 10% directly on $20 million.
- Convert the $20 million into pounds at the initial rate $1.60/£1 to find the sterling principal, apply the 16% sterling interest, then convert back at the final rate $1.50/£1.

3) Calculations with intermediate steps
- U.S. loan: $20,000,000 × 1.10 = $22,000,000 (end value). Dollar gain = $2,000,000 → return = 10.00%.
- U.K. loan in sterling: initial £ = $20,000,000 / 1.60 = £12,500,000.
- After 1 year in sterling: £12,500,000 × 1.16 = £14,500,000.
- Convert back to dollars at $1.50/£: $ = £14,500,000 × 1.50 = $21,750,000.
- Dollar gain on U.K. loan = $21,750,000 − $20,000,000 = $1,750,000 → return = 1,750,000 / 20,000,000 = 8.75%.
- Portfolio weighted return = 0.5×10.00% + 0.5×8.75% = 5.00% + 4.375% = 9.375%.

4) Why this answer is correct
The calculation correctly accounts for sterling interest and the depreciation of sterling in dollar terms (exchange rate fell from $1.60 to $1.50), which reduces the dollar return on the UK loan. Averaging the dollar returns by portfolio weights yields 9.375%.

5) Why other options are incorrect (brief)
- 8.75% is the return on the UK loan only, not the weighted portfolio.
- 13.29%, 12.56% are results of incorrect combinations or forgetting the exchange-rate effect.
- 16% is the sterling interest rate (not the dollar return after exchange-rate change).

6) Conclusion
Therefore, the weighted return on the FI’s asset portfolio is 9.375%, which matches the provided correct answer.

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