Case 080Investment and portfolio riskWarm up

A rupee fund's US equities return 8% in dollars while the rupee falls 3%. What is the rupee return, and what would it have been if the dollar exposure had been hedged with a 4% forward premium?

The situation

Juhvani Global Fund raises rupees from Indian investors and buys US equities. Over the year the portfolio returns 8% in dollars. The rupee depreciates 3% against the dollar, from Rs 84.00 to Rs 86.52.

A board member asks whether the fund should hedge the currency. The desk's draft note says hedging dollars back into rupees would have cost 4% a year, the gap between rupee and dollar interest rates, and that the one-year forward at the start of the year was Rs 87.36, 4% above spot. Assume the hedge is resized through the year so it covers the whole portfolio.

Your task

What was the rupee return unhedged, what would it have been hedged, and is the note right that the hedge costs 4%?

Quick check

For this rupee investor, what does hedging the dollar do to the year's return?

Worked solution

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

30-second answerThe answer to give first

Unhedged, the rupee return is 11.24%; hedged at the forward, it would have been about 12.32%, so the note has the sign wrong. A rupee investor who hedges sells dollars forward at a 4% premium, which is earned. The premium is the market's price for expected rupee weakness: hedging swaps the rupee's actual 3% fall for a known 4%. It pays a dollar-based investor hedging rupee assets, not this fund.

Step 1How do the dollar return and the currency combine?

Multiply, do not just add. If you send a relative Rs 84 to buy a US$1 book that sells for US$1.08 a year later, and the dollar now costs Rs 86.52, the sale brings home Rs 93.44. A falling rupee adds to a rupee investor's foreign return: 1.08 times 1.03, less one, is 11.24%. The 0.24 on top of 8 plus 3 is the cross term, the 3% currency gain earned on the 8% profit as well as on the original money.

Step 2Which way does the hedge trade, and does it cost or earn?

The fund owns dollars, so it hedges by agreeing today to sell dollars for rupees in a year. Rupee interest rates are about 4 points above dollar rates, and covered interest parityThe rule that a forward exchange rate sits away from spot by the interest rate gap, so borrowing in one currency and lending in the other with a hedge earns nothing extra. sets the forward that far above spot: Rs 87.36. Selling dollars at Rs 87.36 against Rs 84.00 today locks in a 4% premium, so the hedged rupee return is 1.08 times 1.04, less one, about 12.32%. The note read the rate gap from the side of a dollar investor, who does pay it to hedge rupee assets.

The relationship
Runhedged=(1.08)(1.03)−1=11.24%Rhedged=(1.08)(1.04)−1=12.32%R_{\text{unhedged}} = (1.08)(1.03) - 1 = 11.24\% \qquad R_{\text{hedged}} = (1.08)(1.04) - 1 = 12.32\%
1.08one plus the dollar return of the portfolio
1.03one plus the actual rise in the rupee price of a dollar
1.04one plus the forward premium locked in by selling dollars forward
What it says in wordsUnhedged, the fund earns whatever the rupee actually did; hedged, it earns the premium fixed at the start, whatever the rupee does.
Rupee return on the same US portfolio, three waysUnhedged8.0 in $+3.0 rupee11.24%Hedged at the forward8.0 in $+4.0 premium12.32%Wrong: premium as a cost8.0 - 4.04.00%0%4%8%12%Rupee fell 3%: Rs 84.00 to Rs 86.52 a dollar. Forward sold at the start: Rs 87.36, a 4% premium.The hedge beat the open position because the rupee fell less than the 4% premium locked in at the start.
The same 8% dollar return becomes 11.24% in rupees unhedged and 12.32% hedged at a 4% forward premium; reading the premium as a cost gives a wrong 4.0%.
Step 3So should the fund always hedge?

Not on this one year's evidence. The forward premium is roughly the depreciation the market expects. Hedging wins in any year the rupee falls less than 4% and loses in any year it falls more, so it is a choice to swap an unknown currency return for a known one, not a free gain. In a year when the rupee falls 6%, the unhedged fund earns 14.5% and the hedged one still about 12.3%. Some investors in a global fund want the dollar exposure, because it tends to rise when Indian markets are under stress.

Then name the risk the note missed. A forward that loses money at maturity must be settled in cash, so a hedged fund needs liquidity when the rupee falls sharply, exactly when investors may also redeem. A risk manager asks for the size of that settlement in a bad year and where the cash comes from before approving the policy.

Where candidates lose it

The common error is to repeat that hedging costs the rate gap without asking who is hedging what. The gap is a cost for someone selling a high-interest currency forward to buy a low-interest one; a rupee fund selling dollars is on the receiving side.

The second is adding 8% and 3% and stopping at 11%. The interviewer is listening for the cross term and for the reason the currency helps a rupee investor when the rupee falls.

What the interviewer asks next

  • The rupee instead rises 2% against the dollar. Compare the hedged and unhedged returns.
  • How would you size the cash buffer for settling the forward if the rupee fell 10%?
  • Why might a fund hedge half its dollar exposure rather than all or none?

Company names and figures are illustrative.