Case 005Global macro tradesWarm up

Anvika Family Office invests USD 10 million in a US fund expected to return 8% in dollars. It is told that hedging the dollar back to rupees through forwards costs 3% a year. When is hedging worth it, and what is the unhedged return if the rupee weakens 4%?

The situation

Anvika Family Office, based in Pune, puts USD 10 million, about Rs 83 crore at an illustrative Rs 83 to the dollar, into a US equity fund it expects to return 8% in dollars over the next year. The family's spending is all in rupees.

Its bank quotes a one-year forward at which Anvika can agree today to sell dollars for rupees: Rs 85.49, a 3% premium to spot, reflecting the gap between rupee and dollar interest rates. One board member says hedging costs 3% a year and is only worth it if the rupee is expected to strengthen.

Your task

Is the board member right about the cost? When is hedging worth it, and what does the family earn unhedged if the rupee weakens 4%?

Quick check

Anvika sells dollars forward at a 3% premium to spot. What does the hedge do to its rupee return?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The board member has the sign backwards: selling dollars forward at a 3% premium locks in about 11.2% in rupees, not 5%. Unhedged, the family earns 12.3% if the rupee weakens 4%, but only 3.7% if it strengthens 4%. Leaving the position unhedged pays only if the rupee weakens by more than 3%, the forward premium. The choice is a currency view, not a cost saving.

Step 1Who pays the forward premium, and who receives it?

A forward is simply an agreement today on a price for a trade next year. The rupee forward sits above spot because rupee interest rates are higher than dollar rates; if it did not, a bank could borrow dollars, convert, earn the higher rupee rate and lock in a riskless profit. Whoever sells dollars forward receives that premium, and a rupee investor holding dollar assets is a seller of dollars. An importer who must pay dollars next year buys dollars forward and pays the premium; for that importer it really is a cost. Anvika is on the other side of the trade.

The relationship
rhedged=(1+r$)×FS−1=1.08×1.03−1=11.24%r_{hedged} = (1 + r_{\$})\times\frac{F}{S} - 1 = 1.08 \times 1.03 - 1 = 11.24\%
r_$the fund's return in dollars, 8%
Fthe one-year forward rate, Rs 85.49
Sspot today, Rs 83
What it says in wordsThe hedged rupee return is the dollar return multiplied by the ratio of the forward rate to spot.
Step 2What does the family earn with and without the hedge?

Unhedged, the rupee return is the dollar return times whatever the rupee does. If the rupee weakens 4%, each dollar buys 4% more rupees, so the family earns 1.08 times 1.04, about 12.32%; if the rupee strengthens 4%, it earns only 3.68%. Hedged, the family earns 11.24% whichever way the currency moves. Break-even is a 3% fall in the rupee, the forward premium itself.

Hedged, the family locks in the forward premium; unhedged, it bets on the rupee3.68%Rupee +4%stronger8.00%Rupee flat11.24%Rupee -3%break-even12.32%Rupee -4%weaker16.64%Rupee -8%weakerHedged: 11.24% whatever the rupee doesUnhedged rupee return on the US fund; bars in red fall short of the hedged line
Hedged at a forward 3% above spot, Anvika earns 11.24% in rupees in every scenario; unhedged it earns 3.68% if the rupee strengthens 4%, 8.00% if it is flat and 12.32% if it weakens 4%, so leaving the dollars unhedged pays only if the rupee weakens by more than 3%.
Step 3So when is hedging worth it?

Frame it as a bet, because that is what the unhedged position is. Staying unhedged is a view that the rupee will weaken by more than the forward premium, and hedging is the absence of that view. For a family whose spending is in rupees, the natural starting point is hedged, then take currency risk deliberately and in a size it can afford to lose. If part of the family's future spending is in dollars, a child's university fees in the US for example, that part needs no hedge at all, because the dollars will be spent as dollars.

State the limits. A forward hedges a fixed amount, so if the fund returns minus 10% instead of plus 8%, Anvika has sold forward more dollars than it owns and has a currency position the other way. Hedges are usually rolled every one to three months and resized. And the premium is set by the interest rate gap on the day, so the 3% here is an illustration: the family should check the quote it is actually offered.

Where candidates lose it

The trap is accepting the premise. Hedging dollar assets back to rupees is a cost for someone buying dollars forward, and a gain for a rupee investor selling them, as long as rupee rates sit above dollar rates. Candidates who compute 8% minus 3% equals 5% have the sign wrong and miss the point of the question.

The second is answering hedge or do not hedge without naming the view. Unhedged is not neutral; it is a bet that the rupee falls by more than the premium.

What the interviewer asks next

  • What would change if US interest rates were above Indian rates?
  • The fund returns minus 10%. What is Anvika's position on the forward, and what does it do?
  • How would a US family office investing in an Indian fund think about the same hedge?

Company names and figures are illustrative.