Case 057Structured products and client solutionsHard

A client places USD 1 million for one month in a dual currency deposit paying 7% instead of 4.5%, spot 84.00, and the bank may repay in rupees at 84.50. Decompose it, price the extra yield, and show the client's position at 83.00 and 86.00.

The situation

A client of Ojasvi Private Bank holds USD 1 million and wants rupees eventually but not yet. The bank offers a one-month dual currency depositA deposit that pays a higher interest rate because the bank may repay it in a second currency at a pre-agreed rate instead of the deposit currency. paying 7% a year, against 4.5% on a plain dollar deposit. Spot USD/INR is 84.00. At maturity the bank may, at its choice, repay principal and interest in rupees converted at 84.50 instead of in dollars.

The client asks why the rate is higher, what the extra is worth in rupees, and what she ends up holding if the rate at maturity is 83.00 or 86.00.

Your task

Decompose the deposit into its parts, compute the extra yield in rupees, and show the client's outcome at each rate, including when the bank exercises its choice.

Quick check

Before working it: at which maturity rate will the bank choose to repay in rupees?

Worked solution

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

30-second answerThe answer to give first

The deposit is a plain dollar deposit plus a dollar call the client has sold to the bank, struck at 84.50, and the extra 2.5% a year is the option premium: USD 2,083 for the month, about Rs 1.75 lakh. At 83.00 the bank repays USD 1,005,833; the client is ahead of a plain deposit. At 86.00 the bank repays Rs 8.50 crore at 84.50, worth only USD 988,290 at the market rate, about USD 15,460 less than the plain deposit would have left her with.

Step 1Why is the rate higher, and what has the client sold?

A landlord who lets a tenant pay rent in either cash or, at the tenant's choice, in a fixed quantity of rice, will charge a little more rent, because the tenant will pay in whichever is cheaper that month. The bank is the tenant here: it has bought the right to repay in rupees at 84.50 instead of in dollars, and it will use that right only when rupees at 84.50 are the cheaper way to settle, which is when the dollar is worth more than 84.50. That right is a call on the dollar, struck at 84.50, and the client has sold it. The extra 2.5% a year is not higher interest; it is the premium on that call, paid in the form of interest.

The deposit is a deposit plus an option the client has soldPlain USD deposit1 month at 4.5% a yearinterest USD 3,750repaid in dollars, always+Sold USD call, strike 84.50bank may take the dollarsand pay Rs 84.50 for eachpremium USD 2,083=Dual currency deposit7% a year for one monthinterest USD 5,833repaid in USD or INR, bank's choiceWho chooses the currency: the bank, after it sees the rate.Rupee strong, USD/INR below 84.50: dollars are worth less than 84.50, so the bank repays in dollars.Rupee weak, USD/INR above 84.50: dollars are worth more than 84.50, so the bank keeps them and pays rupees at 84.50.The client earns the extra USD 2,083 either way; the second case is where the option costs them.
The dual currency deposit is a plain one-month dollar deposit at 4.5% plus a dollar call struck at 84.50 that the client has sold to the bank, and the extra 2.5% a year, USD 2,083 for the month, is that option's premium.
Step 2What is the extra yield worth in rupees?

One month of 7% on USD 1 million is USD 5,833.33; one month of 4.5% is USD 3,750.00. The difference, USD 2,083.33, is the whole of what the client is paid for the option, and at 84.00 it is about Rs 175,000, Rs 1.75 lakh. Hold that number next to the Rs 8.4 crore of principal: the client has sold a one-month option on Rs 8.4 crore of dollars for about 0.2% of its value. Whether that is a fair premium depends on the dollar's implied volatility, which the desk has and the client does not.

The relationship
premium=1,000,000×0.07−0.04512=USD 2,083.33≈Rs 1,75,000 at 84.00\text{premium} = 1{,}000{,}000 \times \frac{0.07 - 0.045}{12} = \text{USD } 2{,}083.33 \approx \text{Rs } 1{,}75{,}000 \text{ at } 84.00
0.07 - 0.045the yield pick-up over a plain deposit, 2.5% a year
1/12one month of a yearly rate
84.00spot at the start, used to state the premium in rupees
What it says in wordsThe option premium is the yield pick-up applied to the principal for one month, converted at today's rate.
Step 3What does the client hold at 83.00 and at 86.00?

At maturity the bank owes USD 1,005,833.33, principal plus a month of 7%. At 83.00 the rupee has strengthened; dollars are worth less than 84.50, so the bank repays in dollars and the client holds USD 1,005,833, which is Rs 8.3484 crore if she converts, against Rs 8.3311 crore from the plain deposit. She is ahead by the premium, and she still carries the rupee strength on her dollars exactly as she would have anyway.

At 86.00 the rupee has weakened past the strike. The bank exercises: it pays USD 1,005,833.33 times 84.50, Rs 84,992,917, about Rs 8.50 crore. Those rupees buy only USD 988,290 at the market rate of 86.00, so the client, who deposited USD 1 million, gets back fewer dollars than she started with, and about USD 15,460 fewer than the plain deposit would have returned. Measured in rupees she has Rs 15.09 lakh less than her dollars were worth. The option cost her roughly 9 times the premium she was paid for it.

What the client holds at maturity, in dollars, against the final rate985k995k1,005k82838484.50858687USD/INR at maturityat 83.00: USD 1,005,833, paid in dollarsat 86.00: Rs 8.50 crore = USD 988,29084.50: bank switches to rupeesplain deposit: USD 1,003,750worse than plain above 84.68
In dollar terms the client holds USD 1,005,833 at any rate up to 84.50, then less as the rupee weakens, falling below the plain deposit's USD 1,003,750 above about 84.68 and reaching USD 988,290 at 86.00, where the bank repays in rupees at 84.50.
Step 4What does the honest sales conversation say?

The product suits a client who genuinely wants rupees and would be content to convert at 84.50, a rate better than today's 84.00, because then being paid in rupees at 84.50 is the plan, not the penalty. For a client who wants to keep dollars, the deposit pays a small premium for giving up the dollar's rise, and she is repaid in the weaker currency exactly when it is weaker. The crossover is close: above about 84.68, less than 1% from spot, she is worse off than with the plain deposit. The limitation of the table is that it ignores the bank's own credit and any early withdrawal terms, both of which belong in the same conversation.

Where candidates lose it

Candidates get the direction of the option wrong, saying the bank repays in rupees when the rupee is strong. Ask every time: which currency is cheaper for the bank to deliver? Rupees at 84.50 are cheap for the bank only when a dollar is worth more than 84.50.

The second miss is quoting the extra 2.5% as if it were a yearly gain. It is one month of 2.5%, about 0.2% of principal, against a one-month option on the whole principal.

What the interviewer asks next

  • How would the bank price the 84.50 call, and what does one-month USD/INR implied volatility have to be for 2.5% a year to be fair?
  • The client wants the conversion rate moved to 85.50. What happens to the rate the bank can offer, and why?
  • If the client's spending is in rupees, is the exposure she is left with at 86.00 actually a loss? Argue both sides.

Company names and figures are illustrative.