CMA Final · Strategic Financial Management

Swaps: formula sheet

Full chapter guide

Key formulas

Net payment in a plain interest rate swap: Net payment = Notional × (Fixed rate − Floating rate) × (days ÷ year basis); Fixed-rate payer pays this if the result is positive and receives it if negative. Only the net amount is exchanged on each date.
Total gain from a swap (comparative advantage): Total gain = (Difference in fixed-rate spread) − (Difference in floating-rate spread); Take the absolute difference between the two firms' spreads in each market. The gain is then shared between the parties and the dealer, if any.
Dealer's earning: Dealer's spread = Offer rate − Bid rate; A dealer is a principal and earns the spread. A broker earns a commission instead.
Fixed payment per period: Fixed payment = Notional × Fixed rate × (Period in months ÷ 12); Use the day or month fraction given in the question. Annual settlement means a factor of 1.
Floating payment per period: Floating payment = Notional × Floating rate × (Period in months ÷ 12); Use the floating rate fixed at the start of the period (set in advance), unless the question says otherwise.
Net swap settlement: Net = Amount received − Amount paid; Only the difference is exchanged. The party owing the larger amount pays the net.
Effective cost after swap: Effective rate = Loan interest rate + Swap rate paid − Swap rate received; Express all items as a % of the same principal.
Total gain from comparative advantage: Total gain = |Difference in fixed-rate spreads − Difference in floating-rate spreads|; Share the gain as the question directs, often equally. Subtract any bank fee from the gain.
Principal in the second currency: Principal B = Principal A × Spot rate (B per unit of A) at start; Fixed at the start date. The same amounts are used for the final re-exchange.
Periodic interest on a leg: Interest = Principal of that currency × Swap rate for that leg × (months ÷ 12); Each leg pays interest only on its own currency principal. Use the rate type given: fixed or floating.
Final cash flow on a leg: Final payment = Principal + Last period's interest; Principal is returned at the original spot rate, not the rate at maturity.
Rupee value of a foreign flow: ₹ value = Foreign currency amount × Spot rate on the payment date; Use this to compare the swapped position with the unhedged position.
Net cash flow for a party: Net = Receipts on the swap − Payments on the swap (in one common currency); Convert both to rupees before netting. Never net dollars against rupees.
Quality spread differential (QSD): QSD = |Fixed-rate spread difference − Floating-rate spread difference|; Spread difference = Borrower B's rate − Borrower A's rate in that market. This is the total gain available to share.
Net gain to parties: Gain to parties = QSD − Bank's fee (if any); If gain is shared equally between two parties, each gets half of this amount. Follow the sharing ratio given in the question.
Net cost after swap: Net cost = Cost without swap − Share of gain; Apply it to the rate the party actually wanted (fixed or floating), not the rate it borrowed at.
Discount factor: DF(t) = 1 ÷ (1 + z_t)^t; z_t is the annual zero (spot) rate for t years.
Swap rate (par swap, annual payments): Swap rate = (1 − DF_n) ÷ Σ DF_t, for t = 1 to n; Makes the swap's value zero at start. For half-yearly payments, use period rates and multiply by the number of periods per year to annualise.
Forward rate from discount factors: F(t1, t2) = (DF_t1 ÷ DF_t2 − 1) ÷ (t2 − t1); Gives the simple forward rate for the period from t1 to t2. This is the floating rate you assume for future payments.
Value of swap by bond approach: Value to fixed payer = B_float − B_fixed; Value to fixed receiver = B_fixed − B_float; B_fixed = PV of fixed coupons plus notional. B_float = (Notional + next floating payment) × DF to next payment date.
Value of swap by FRA approach: Value to fixed payer = Σ (Forward rate − Fixed rate) × Notional × period × DF; Each period is treated as a forward rate agreement settled at its payment date. Both approaches agree.
Net swap settlement (fixed vs floating): Net payment = Notional × (Floating rate − Fixed rate) × Period in years; Positive means the fixed-rate payer receives. Negative means the fixed-rate payer pays. Check which side the question asks about.
Payer swaption exercise rule: Exercise if market swap fixed rate > strike rate; You pay the lower strike rate. Ignore the premium when deciding to exercise; include it when computing net gain.
Receiver swaption exercise rule: Exercise if market swap fixed rate < strike rate; You receive the higher strike rate.
Credit exposure of a swap: Exposure = Maximum of (Replacement value of swap, 0); Only the party for whom the swap has positive value faces credit loss. The notional is not at risk.
Amortising/accreting swap interest: Interest for a period = Notional outstanding in that period × Rate × Period in years; Use the notional of each period separately.

Quick revision

A swap is an exchange of cash flows between two parties on agreed dates, based on a notional amount.
In a plain interest rate swap, only the interest is exchanged; the notional principal is not.
Comparative advantage is the base: swap gain comes from the difference in the spreads the two parties face.
Net gain = difference between the two spreads, after deducting any intermediary fee.
Check the final cost of each party against its own direct borrowing cost to confirm there is a saving.
A currency swap normally involves exchanging principal at the start and returning it at maturity, along with interest in each currency.
Interest in a currency swap is paid on the principal of that currency, not on the converted amount.
Swap valuation is the present value of one leg minus the present value of the other leg.
The fixed rate of a new swap is set so that its value at the start is nil to both parties.
A swaption gives the holder the right, but not the obligation, to enter into a swap at a set rate.
Always state the notional amount, period and rates clearly at the top of your answer.
End every numerical answer with a short recommendation.

Common mistakes

Saying the notional principal is paid or received in an interest rate swap. Fix: In a plain interest rate swap only interest amounts, usually netted, are exchanged. Principal exchange belongs to currency swaps.
Treating a swap broker and a swap dealer as the same. Fix: A dealer is a principal that takes the opposite side and earns the bid-offer spread. A broker is an agent that matches parties for a commission.
Treating the notional principal as an amount that is paid or received. Fix: State that the notional is only a base. Only interest, and only the net, is exchanged.
Forgetting the period fraction in semi-annual or quarterly settlements. Fix: Write the fraction (6 ÷ 12 or 3 ÷ 12) next to the rate before multiplying.
Applying the maturity spot rate to the principal re-exchange. Fix: The principal is re-exchanged at the same rate as at the start. Only the unhedged position uses the maturity spot rate.
Calculating interest on the wrong principal. Fix: Label each leg with its currency, principal and rate before calculating.
Letting each firm borrow in the market where its own rate is lower. Fix: Compare the spread differences. Each firm borrows where its relative advantage is greatest, and the swap converts to the form it wants.
Forgetting the bank's fee when the bank is an intermediary. Fix: Always write: gain to parties = QSD − bank margin. Then check that the three gains add back to QSD.
Treating the notional as the amount at risk in credit risk. Fix: Say that the notional is a reference amount. Credit loss is limited to the replacement cost or the net amount due.
Mixing up amortising and accreting swaps. Fix: Amortising means the notional reduces, like a loan being repaid. Accreting means the notional grows, like a loan being drawn.

Exam tips

Write definitions in one line, then features as short points: OTC, customised, notional, counterparty risk.
Always distinguish dealer and broker in a sentence of its own. Examiners ask this directly.
In numerical questions, show the fixed and floating legs separately before the net figure.
Link the swap to the risk it hedges. A bare definition earns fewer marks than an application to a case.
Write the direction of the swap first. Marks are lost most often on who pays and who receives.
Show the net settlement and the effective cost as separate lines. Examiners award marks for each.
In comparative advantage questions, always run the check: total cost after the swap = total cost of borrowing in the desired markets without the swap − total gain, with the gain shared as agreed.
If the paper gives a case scenario, expect MCQs on swap type and on whether a firm should pay fixed or floating given its view on rates.