Notional principal

A derivative on interest rates has to be about interest on something. The notional principal is that something: the amount the interest is computed on. It is called notional because it never moves. No one lends it, no one borrows it, no one repays it.

This is what gives derivatives their leverage and what makes headline market figures so misleading. The workbook reports USD 548 trillion of notional outstanding in OTC interest rate contracts. Nobody has lent USD 548 trillion; that is the base the interest calculations run on, and the money actually at stake is a small fraction of it.

The workbook's own example makes the scale concrete. A Rs 100 crore notional swap settles for Rs 1,29,503. The notional is 772 times the cash flow.

Three products in this paper are sized in notional principal, each differently.

A forward rate agreement fixes a rate on a notional for a forward period. Only the rate difference settles, and because it settles at the start of the notional loan period while the interest saving would have accrued at the end, the settlement amount is discounted back.

An interest rate swap exchanges two interest streams on a notional. Only the net difference is paid, on each payment date.

Overnight MIBOR futures define the contract as interest on a notional principal of Rs 5 crore for one month on a 30/365 basis. The notional never appears in a settlement; the basis point value of Rs 411 is derived from it.

Bond futures sit outside this family. Their size is stated as face value of notional bonds — Rs 2 lakh a lot — because there is an underlying instrument, even if it is itself notional.

FRA settlement (undiscounted) = Notional × (Reference rate − FRA rate) × Days ÷ Year

                                    Undiscounted amount
FRA settlement (as paid)      = ──────────────────────────────────
                                 1 + (Reference rate × Days ÷ Year)

Swap net settlement           = Notional × (Fixed leg rate − Floating leg rate) × Days ÷ 365

MIBOR futures, 1 basis point  = Rs 5,00,00,000 × 0.01% × 30/365 = Rs 411

A 3×6 FRA, settled properly. The workbook's figures: a contract starting in 3 months and ending in 6, on a notional of Rs 10,00,000, at an FRA rate of 5%, with the floating rate at settlement turning out to be 6%.

Rate difference      = 6% − 5% = 1%
Interest difference  = 10,00,000 × 1% × 3/12 = Rs 2,500

But the FRA settles today, three months before that interest would have been paid, so it is discounted at the prevailing rate:

Settlement = 2,500 ÷ [1 + (6% × 3/12)]
           = 2,500 ÷ 1.015
           = Rs 2,463.05

The Rs 36.95 of discounting is the step candidates skip, and the workbook flags it in both of its FRA examples.

At institutional scale. Two parties agree to borrow Rs 100 crore after 60 days for 91 days at 5%, settling against the 91-day T-Bill yield. On the settlement date the 91-day yield is 5.5%:

Saving = Rs 100 crore × 0.5% × 91/365 = Rs 12,46,575

Rs 12.46 lakh — on Rs 100 crore of notional that never left anybody's account. Present-valued to the settlement date it is a little less again.

And the swap. A Rs 100 crore one-month OIS against Overnight MIBOR, fixed at 3.75%:

Floating leg   Rs 31,58,169
Fixed leg      Rs 32,87,671
Net settled    Rs  1,29,503

A counterparty limit set on notional would treat this as a Rs 100 crore exposure. The actual settlement risk is thirteen basis points of it — which is why notional is a sizing convention and not a measure of risk.

Chapter 2, section 2.2.1, introduces the notional principal through the forward rate agreement, works the 3×6 FRA with its discounted settlement and the Rs 100 crore 91-day example; section 2.2.4 carries it into the interest rate swap and states that most swaps involve cash flows based on a notional principal. Chapter 3, section 3.3, defines the Overnight MIBOR futures unit of trading as interest on a notional principal of Rs 5 crore for one month, and section 3.4.3 derives the Rs 411 basis point value from it.

Questions compute FRA and swap settlements from a notional, and test the definitional point that the notional is never exchanged.

• The notional is never exchanged. Only the net interest difference settles — on a Rs 100 crore swap, Rs 1.29 lakh.
• Discount the FRA settlement. It is paid at the start of the notional period while the interest it replaces would have accrued at the end; the workbook applies the discount in both its examples.
• Notional is not exposure. Headline notional outstanding figures are calculation bases, not amounts at risk.
• Match the day count to the product. The FRA examples use 3/12 and 91/365; the MIBOR futures contract uses 30/365. Substituting one for another changes every answer.
• Bond futures are sized in face value, not notional principal. Rs 2 lakh of notional bonds is a different concept from Rs 5 crore of notional principal.
• A long FRA position is a borrower. The party borrowing under an FRA is long in interest rate terms and gains when the benchmark exceeds the FRA rate.