An overseas investment with a partial currency hedge
Series XXI-B case study · set 3, case 3 of 6 · 5 questions · 2 marks each
Question 1 of 5Case practice
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A manager converts ₹80 lakh into US$1,00,000 at ₹80 per dollar and buys a foreign security. One year later the holding is worth US$1,10,000, including all investment returns, and the spot exchange rate is ₹76 per dollar. At inception, the manager also entered a hypothetical forward contract to sell US$1,00,000 in one year at ₹81 per dollar. For the exercise it settles in cash: the manager receives (forward rate minus final spot rate) multiplied by the contracted dollars. Assume no upfront forward premium, margin funding cost, taxes or other charges. The forward covers the initial dollar amount only. The final gain in dollar holdings was not known when the contract was entered.
The simplified forward is cash-settled and has no upfront premium, margin cost or other charge.
The exchange rates and security returns are hypothetical.
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The case and its answers
Every question of this case, with its answer and why each other option is wrong.
A manager converts ₹80 lakh into US$1,00,000 at ₹80 per dollar and buys a foreign security. One year later the holding is worth US$1,10,000, including all investment returns, and the spot exchange rate is ₹76 per dollar. At inception, the manager also entered a hypothetical forward contract to sell US$1,00,000 in one year at ₹81 per dollar. For the exercise it settles in cash: the manager receives (forward rate minus final spot rate) multiplied by the contracted dollars. Assume no upfront forward premium, margin funding cost, taxes or other charges. The forward covers the initial dollar amount only. The final gain in dollar holdings was not known when the contract was entered.
The simplified forward is cash-settled and has no upfront premium, margin cost or other charge.
The exchange rates and security returns are hypothetical.
Q1What is the foreign security’s return measured in US dollars?
Option A. 10% — Correct answer
Option B. 1.25%
Why it is wrong: This is the forward rate’s premium to the initial spot rate.
Option C. 4.50%
Why it is wrong: This is the unhedged return after translating to rupees.
Option D. 5%
Why it is wrong: This confuses currency movement with the investment return.
Answer: A. (US$1,10,000/US$1,00,000 − 1) × 100 = 10%. Remember: Separate the asset’s local-currency return from currency translation.
Hint, shown before you answer in practice mode: Compare final dollar value with the initial dollar investment.
XXIB-S3-C03-Q1easynumerical
Q2Without the forward, what would the investment’s rupee return be?
Option A. 15.50%
Why it is wrong: This treats the dollar’s weakening against the rupee as a gain.
Option B. 4.50% — Correct answer
Option C. 10%
Why it is wrong: This ignores the fall in rupees received per dollar.
Option D. 5%
Why it is wrong: This simply subtracts percentage movements and omits compounding.
Answer: B. Final value = US$1,10,000 × ₹76 = ₹83.60 lakh. Return = ₹83.60/₹80 − 1 = 4.50%. Remember: Domestic-currency return compounds asset and exchange-rate changes.
Hint, shown before you answer in practice mode: Translate the entire final dollar holding at ₹76.
XXIB-S3-C03-Q2mediumnumerical
Q3How much cash does the forward pay the manager at maturity?
Option A. ₹5 lakh — Correct answer
Option B. ₹1 lakh
Why it is wrong: This compares the forward rate with the initial spot rather than final spot.
Option C. ₹5.50 lakh
Why it is wrong: This applies the contract to all final dollars, although only US$1,00,000 was contracted.
Option D. The manager pays ₹5 lakh
Why it is wrong: Selling dollars at ₹81 is favourable when spot is ₹76.
Answer: A. (₹81−₹76) × US$1,00,000 = ₹5,00,000 received. Remember: Derivative settlements use their contracted notional, not an assumed future asset value.
Hint, shown before you answer in practice mode: Use the contract’s stated settlement formula and dollar notional.
XXIB-S3-C03-Q3mediumnumerical
Q4What is the combined rupee return including the forward settlement?
Option A. 10.75% — Correct answer
Option B. 9.50%
Why it is wrong: This adds a five-percentage-point exchange-rate move to the unhedged return instead of calculating cash proceeds.
Option C. 11.375%
Why it is wrong: This incorrectly applies the ₹81 rate to the full final US$1,10,000.
Option D. 6.25%
Why it is wrong: This is the forward gain as a percentage of the initial rupee investment, excluding the security return.
Answer: A. Total ending value = ₹83.60 lakh + ₹5 lakh = ₹88.60 lakh. Combined return = ₹88.60/₹80 − 1 = 10.75%. Remember: Calculate the asset and hedge together on a consistent initial capital base.
Hint, shown before you answer in practice mode: Add the settlement to the rupee value of the security before calculating return.
XXIB-S3-C03-Q4hardnumerical
Q5Which part of the final holding remained exposed to the final spot rate?
Option A. All US$1,10,000, because cash settlement provides no hedge
Why it is wrong: The cash settlement offsets currency movement on the contracted amount.
Option B. None. Any forward automatically hedges the whole position
Why it is wrong: The contract’s dollar amount is fixed.
Option C. Only the original US$1,00,000
Why it is wrong: That is the amount explicitly covered by the forward.
Option D. The US$10,000 investment gain beyond the contracted US$1,00,000 — Correct answer
Answer: D. The contract covers US$1,00,000. The additional US$10,000 has no matching forward sale and is translated at the final spot rate. Remember: Hedges can become partial when the underlying investment value changes.
Hint, shown before you answer in practice mode: Compare the final dollar holding with the forward notional.
XXIB-S3-C03-Q5mediumapplication
A share split in two differently weighted indices
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