Welcome to the World of Swaps!
Hello there! Today, we are diving into one of the most important tools in the financial world: Swaps. While the name might sound like something you do with your lunch in middle school, in the FRM curriculum, swaps are powerful contracts used by multi-billion dollar companies to manage risk. By the end of these notes, you’ll understand how they work, why companies use them, and how to value them. Let’s get started!
1. What exactly is a Swap?
At its simplest, a swap is an agreement between two parties to exchange cash flows in the future. Think of it as a series of forward contracts bundled together. Instead of just one exchange on one date, you have multiple exchanges over a period of time.
The "Coffee Shop" Analogy:
Imagine you have a favorite coffee shop. You usually pay a "floating" price (the price changes every week based on bean costs). Your friend, however, prefers certainty and wants to pay exactly $4 every time. You might agree to a "swap": you pay your friend a fixed $4, and your friend pays whatever the actual market price is that day. You’ve just performed a swap!
Key Terms to Know:
- Notional Principal: The theoretical amount used to calculate interest payments. It usually never actually changes hands in an interest rate swap.
- Fixed Rate Payer: The party who pays a pre-determined, constant interest rate.
- Floating Rate Payer: The party whose payments change based on a market benchmark (like LIBOR or SOFR).
- Tenor: The life or duration of the swap contract.
Key Takeaway:
A swap is an Over-the-Counter (OTC) derivative where two parties trade cash flows. The most common types for the FRM exam are Interest Rate Swaps and Currency Swaps.
2. Plain Vanilla Interest Rate Swaps
The most common swap is the "Plain Vanilla" Interest Rate Swap. Here, one party pays a fixed rate and receives a floating rate from the other party.
How it works (Step-by-Step):
1. Company A has a loan with a floating interest rate. They are worried rates will rise.
2. Company B has a loan with a fixed interest rate but wants to benefit if rates fall.
3. They enter a swap. Company A pays Company B a fixed rate. Company B pays Company A a floating rate.
4. On payment dates, they net the payments. Only the difference is actually paid.
Formula for Floating Payment:
\( \text{Payment} = \text{Notional Principal} \times \text{Rate} \times \text{Time} \)
Example: If the notional is \$100 million, the fixed rate is 5%, and the floating rate is 4% (for a 6-month period), the fixed payer owes \( 100 \times 0.05 \times 0.5 = 2.5 \) million, and receives \( 100 \times 0.04 \times 0.5 = 2.0 \) million. The fixed payer nets a payment of \$0.5 million to the floating payer.
Quick Review: In an interest rate swap, the principal is not exchanged at the beginning or end. It is only used to calculate the interest.
3. Why Swap? The Comparative Advantage Argument
Don't worry if this seems tricky at first—the math is simple once you see the "Gap." Companies use swaps because of Comparative Advantage. Some companies are better at borrowing in fixed markets, while others are better in floating markets.
The Logic:
- Company AAA: High credit rating. Can borrow at 4% fixed or SOFR + 0.1% floating.
- Company BBB: Lower credit rating. Can borrow at 6% fixed or SOFR + 0.6% floating.
Notice the difference (the "spread"):
- In Fixed: BBB pays 2% more than AAA.
- In Floating: BBB pays 0.5% more than AAA.
Because the spreads are different (2% vs 0.5%), there is a total gain available of \( 2.0\% - 0.5\% = 1.5\% \). The companies can use a swap to split this 1.5% "profit" and both lower their borrowing costs!
Key Takeaway:
A swap creates value when the difference between fixed rates offered to two firms is different from the difference between floating rates offered to them.
4. Valuation of Interest Rate Swaps
There are two main ways to value a swap during its life. On day one, the swap value is usually zero. But as interest rates change, the swap becomes valuable to one party and a liability to the other.
Method A: Using Bonds
You can think of a swap as being long one bond and short another.
- Fixed Rate Payer: Position is like borrowing money (Short a Fixed Bond) and lending at a floating rate (Long a Floating Bond).
- Value to Fixed Payer: \( V_{swap} = B_{floating} - B_{fixed} \)
- Value to Floating Payer: \( V_{swap} = B_{fixed} - B_{floating} \)
Method B: Using Forward Rate Agreements (FRAs)
Since a swap is a bundle of forwards, you can value each future exchange separately using the prevailing forward rates and discount them back to the present.
Common Mistake to Avoid: When valuing a swap using the bond method, remember that at any payment date, the Floating Bond (\(B_{floating}\)) is always worth exactly its par value (100% of principal) immediately after a payment is made.
5. Currency Swaps
Currency swaps are a bit different. In these, parties exchange interest and principal in two different currencies.
The Big Differences:
1. Principal Exchange: Unlike interest rate swaps, the principal is exchanged at the start and is exchanged back at the end.
2. No Netting: Because the payments are in different currencies (e.g., USD vs EUR), you cannot net them. Full payments are made in both directions.
Valuation of Currency Swaps:
Just like interest rate swaps, you can value these as a "portfolio of two bonds."
\( V_{swap} (\text{in USD}) = B_{USD} - (S_0 \times B_{foreign}) \)
Where \( S_0 \) is the current spot exchange rate.
Did you know? Currency swaps were famously popularized in 1981 by a deal between the World Bank and IBM! IBM had too much Swiss Franc debt, and the World Bank wanted Swiss Francs. They swapped, and history was made.
6. Credit Risk in Swaps
Since swaps are OTC, there is always the risk that one party might default. This is called Counterparty Credit Risk.
Important Points on Risk:
- Credit Risk vs. Market Risk: Market risk is the risk that rates move against you. Credit risk is the risk the other person won't pay when you are "in the money."
- Replacement Cost: If your counterparty defaults, the loss to you is the current positive market value of the swap. If the swap has a negative value to you, you don't lose anything if they default!
- Risk Timing: For interest rate swaps, credit risk is highest in the middle of the swap's life. For currency swaps, credit risk is highest at the very end because that is when the large principal exchange happens.
Key Takeaway:
In an interest rate swap, the risk is lower because there is no principal exchange. In a currency swap, the risk is higher because the final principal exchange is huge.
Final Quick Review Box
- IRS: No principal exchange, payments are netted, interest only.
- Currency Swap: Principal is exchanged at start and end, no netting, two different currencies.
- Comparative Advantage: Look for the difference in spreads to find the total gain.
- Valuation: Treat the swap as Long Bond minus Short Bond.
- Default Risk: You only care if the swap has a positive value to you.
Great job! You've navigated the essentials of Swaps for the FRM Part I. Keep practicing the comparative advantage calculations, and you'll be a pro in no time!