Interest rate swaps as ALM tools

Interest Rate Swaps as ALM Tools

Interest rate swaps are the primary hedging instrument for ALM. Understanding how they work and how to use them is essential for any ALM manager.

Swap Basics

A swap is an agreement to exchange cash flows. In an interest rate swap:

• Party A agrees to pay fixed (say 5.0%) on a notional amount


• Party B agrees to pay floating (say SOFR)


• Payments are netted (only the difference is paid)

Example: $100M swap, 5-year maturity

• Fixed side: A pays 5.0% annually on $100M = $5.0M/year


• Floating side: B pays SOFR annually on $100M (variable)


• If SOFR is 4.5%, net payment: A pays $500K/year (5.0% - 4.5%)


• If SOFR rises to 5.5%, net payment: A receives $500K/year (5.0% - 5.5%)

No principal is exchanged (unless it's an amortizing swap), only interest payments.

Why Swaps Work for ALM Hedging

Problem: Bank originates 5-year mortgages at fixed 5.0%, funds with deposits at floating SOFR.

Rate risk: If SOFR rises, deposit cost increases but mortgage income stays at 5.0%.

Swap solution: Receive fixed 5.0% on $X mortgages via swap, pay SOFR.

• This converts the fixed mortgage to floating


• Now both sides reprice with SOFR


• No more margin compression if rates rise

This is the essence of ALM hedging: use swaps to convert the balance sheet from fixed/floating mismatch to matched.

Real Example: Mortgage Hedge Using Swap

Balance sheet:

• $100M mortgage at 5.0% fixed (5-year maturity)


• Funded by $100M deposit at SOFR (repricing monthly)


• Monthly interest income: $100M * 5.0% / 12 = $417K


• Monthly funding cost: $100M * SOFR / 12 = varies with SOFR

Unhedged scenario:

• Current SOFR: 4.5%


• Current net interest: $417K - $375K = $42K/month


• If SOFR rises to 5.5%: Net interest = $417K - $458K = -$41K/month (loss)


• Earnings are volatile

Hedged scenario using swap:

• Enter swap: Receive fixed 5.0%, pay SOFR on $100M


• Now: Mortgage income $417K + swap income (fixed side)


• Deposit cost: SOFR payment


• Swap flows: Receive 5.0% on $100M, pay SOFR


• Net cash flow: Mortgage (5.0%) + Swap (receive 5.0%, pay SOFR) - Deposit (SOFR) = 10.0% - SOFR


• No wait, this is double-counting. Let me recalculate

Correct hedged economics:

• Mortgage: Receive 5.0% on $100M


• Swap: Receive 5.0%, pay SOFR


• The mortgage and swap both receive 5.0%, so combined:

- We're receiving 5.0% twice? No, we only have one mortgage
- The swap receives 5.0%, pays SOFR
- Net: Mortgage receives 5.0%, we pay SOFR through swap
- Equivalent to: We've converted the mortgage to floating

After conversion:

• Cash received: $100M * SOFR (from mortgage and swap combined)


• Cash paid: $100M * SOFR (to depositor)


• Net: Zero (or 0 basis points spread)

This doesn't make sense either. Let me think through this more carefully.

Correct approach: The bank doesn't receive the swap cash separately. Here's the economic reality:

• Mortgage: Bank receives 5.0% from customer = $417K/month
• Swap: Bank receives fixed leg ($417K) and pays floating leg (SOFR leg = current rate * notional)

- If SOFR 4.5%: Bank pays $375K - Floating net: $417K - $375K = $42K

• Deposit: Bank pays SOFR to depositor = $375K/month
• Total earnings: Mortgage $417K + Swap net $42K - Deposit $375K = $84K

- Wait, this overcounts again

The clearest way to think about it:
Without swap:

• Mortgages earn: $417K


• Deposits cost: $375K (SOFR at 4.5%)


• Net: $42K

With swap (receive fixed 5.0% on $100M, pay SOFR):

• Mortgages earn: $417K


• Swap payments net: In netted markets, we don't pay separately. The swap's fixed leg ($417K at 5.0%) offsets the mortgage income, and we get back SOFR-based payments


• Actually, swaps are typically settled in the market as: (Fixed - Floating) * Notional, paid on net basis


• If we receive fixed and pay floating, we net the payment

Let me use a clearer framework:

Without swap:

• Mortgage income: 5.0% fixed


• Funding cost: SOFR


• Margin: 5.0% - SOFR


• Current margin: 5.0% - 4.5% = 0.5%


• If SOFR rises to 5.5%: Margin becomes 5.0% - 5.5% = -0.5% (loss)

With swap (receive fixed 5.0%, pay SOFR):

• Mortgage income: 5.0% fixed


• Swap net: Receive 5.0% fixed, pay SOFR = 5.0% - SOFR economic exposure


• Combined: (Mortgage 5.0% - SOFR from swap) + (Deposit SOFR)


• Wait, I'm still confusing myself

The correct accounting:
The mortgage, swap, and deposit should be viewed as three separate items:
1. Mortgage earns 5.0%
2. Swap: Receive 5.0%, pay SOFR (net amount paid is 5.0% - SOFR if positive, or SOFR - 5.0% if negative)
3. Deposit costs SOFR

Combined economic exposure:

• Receive from mortgage: 5.0%


• Receive from swap: 5.0% - SOFR (if positive) or pay SOFR - 5.0% (if negative)


• Pay to deposit: SOFR

If SOFR = 4.5%:

• Mortgage: +5.0%


• Swap: +5.0% - 4.5% = +0.5%


• Deposit: -4.5%


• Total: 5.0% + 0.5% - 4.5% = 1.0%

If SOFR = 5.5%:

• Mortgage: +5.0%


• Swap: +5.0% - 5.5% = -0.5%


• Deposit: -5.5%


• Total: 5.0% - 0.5% - 5.5% = -1.0%

Hmm, we still lose 100bps when SOFR rises 100bps. The swap didn't help.

Oh, I see the issue: The mortgage and swap both reference 5.0%. This is wrong for ALM. The swap should receive floating, not fixed.

Correct ALM hedge:

• Mortgage: Pay out 5.0% (customer receives fixed mortgage income)


• Swap: Pay fixed 5.0%, receive floating SOFR


• Combined: (Mortgage -5.0%) + (Swap: -5.0% + SOFR) = -10% + SOFR


• This is wrong. We want the mortgage to create a positive spread.

Let me restart with clearer definitions:

• Asset: Mortgage, bank receives 5.0% from customer


• Liability: Deposit, bank pays SOFR to depositor


• Hedge: Swap

Unhedged:

• NII = Mortgage (5.0%) - Deposit (SOFR) = 5.0% - SOFR


• If SOFR 4.5%: NII = 0.5%


• If SOFR 5.5%: NII = -0.5%

Hedged with swap (Pay fixed 5.0%, receive floating SOFR):

• Mortgage: Bank receives 5.0%


• Swap payment: Bank pays 5.0%, receives SOFR


• Deposit: Bank pays SOFR


• Net: Receive 5.0% (mortgage) + Receive SOFR (swap) - Pay 5.0% (swap) - Pay SOFR (deposit) = 0%


• This eliminates NII entirely, which is wrong

The correct hedge should be:

• Pay fixed 4.5% (not 5.0%), receive floating SOFR


• This creates: Receive 5.0% (mortgage) - Pay 4.5% (swap fixed) + Net swap spread = 0.5% + benefit from SOFR matching

OK so the key point: Swaps convert fixed-rate assets to floating or vice versa. The correct use for ALM is to swap mortgages from fixed to floating so they reprice with deposits, eliminating margin compression when rates change.

Interest Rate Swaps as ALM Tools: Execution and Valuation

Understanding Swap Pricing and Market Conventions

Swap pricing is both mechanical and market-driven. The fixed rate in a swap is determined by a simple formula that links it to the risk-free yield curve plus a spread that reflects market conditions.

The basic pricing relationship:
Fixed Rate = Treasury Yield (matching tenor) + Swap Spread

In practice, this looks concrete. If the 5-year Treasury yield is 4.2% and the 5-year swap spread is 50 basis points, then a 5-year swap fixed rate is 4.7%. The spread compensates swap dealers for credit risk (counterparty could default), liquidity risk (swaps are less liquid than Treasuries), and temporary supply-demand imbalances.

Swap spreads typically range from 30 to 80 basis points depending on market conditions, tenor length, and creditworthiness of potential counterparties. During normal times, spreads are stable and tight. During credit stress (like the 2008 crisis), spreads widen dramatically as counterparty risk becomes paramount. A bank considering a major swap hedge program should monitor spread levels carefully—executing when spreads are 40bps is vastly better than waiting and paying 80bps.

Swap curves exist for essentially every tenor from 2 years to 50 years, creating a complete term structure of available hedging instruments. A 5-year swap is most common for mortgage hedging (mortgages have similar average lives), but a bank with longer-duration assets might use 7-year or 10-year swaps, while a bank with shorter liabilities might use 2-year or 3-year swaps.

The Mechanics of Swap Execution and Terms

A standard 5-year interest rate swap operates under highly standardized terms agreed through market conventions. Understanding these terms is essential for ALM professionals because they directly impact hedge effectiveness and accounting treatment.

Standard terms for a $100 million notional swap:

• Notional Amount: $100M (principal amount; this is never exchanged)


• Fixed Rate: 4.7% per annum (paid by the fixed-rate payer)


• Floating Rate Index: SOFR (Secured Overnight Financing Rate) + 0 basis points


• Tenor: 5 years (60 months)


• Payment Frequency: Quarterly (every 90 days)


• Day Count Convention: 30/360 for fixed leg, Actual/360 for floating leg


• Settlement Date: T+2 (trade date plus 2 business days; swap becomes effective)


• Accrual Method: Each quarter accrues interest based on actual days and notional

The mathematics of quarterly settlement is worth walking through because it highlights why swaps are so useful for ALM. On each quarterly reset date, the net payment is calculated as follows:

Fixed Payment (quarterly): $100M × 4.7% × (90/360) = $1,175,000

Floating Payment (quarterly): $100M × SOFR_reset × (90/360) = varies based on actual SOFR

If SOFR is 5.2% when the quarter starts, the floating payment is $1,300,000. The bank (assuming it pays fixed) writes a net check of $125,000 that quarter. Next quarter, if SOFR has fallen to 4.1%, the bank receives a net check. This floating-rate cash flow pattern perfectly mirrors how the bank''s deposit costs change with SOFR, making the swap an elegant hedging tool.

Amortizing vs. Bullet Swaps: Matching Mortgage Prepayment

Most bank hedges use standard "bullet" swaps where the notional stays constant for the entire tenor. A $50B hedge means $50B notional for all 5 years, then the swap matures and the notional drops to zero.

But mortgages don''t work that way. Mortgages amortize—principal pays down monthly, so the outstanding balance declines over time. After 5 years, a 30-year mortgage has only paid down about 15% of principal, but every payment throughout that 5-year period includes some principal reduction. A bullet swap that stays at $50B notional for 5 years would be over-hedging in later years when the mortgage balance has shrunk.

This mismatch creates basis risk: the hedge is larger than the hedged asset. If rates rise and mortgages become more valuable, the swap loses value proportionally faster than the mortgage. The hedge doesn''t perfectly offset losses.

Sophisticated banks use amortizing swaps to solve this problem. An amortizing swap reduces notional on a pre-specified schedule:

• Years 1-2: $100M notional


• Years 2-3: $85M notional


• Years 3-4: $70M notional


• Years 4-5: $55M notional

The notional schedule mirrors the expected mortgage amortization schedule. This creates near-perfect matching. The fixed rate on an amortizing swap is slightly different from a bullet swap (the dealer prices the declining notional), but the alignment benefit usually justifies any pricing difference.

Mark-to-Market Valuation and Monthly Reporting

Swaps are derivative instruments, and like all derivatives, they must be marked to market at every reporting date. This valuation can be surprisingly large for long-dated, multi-billion-dollar positions.

Valuation methodology: The swap value is the present value of all future fixed rate payments minus the present value of all future floating rate payments, both discounted at current market rates.

Simplified example: A bank entered a 5-year receive-fixed 4.7% swap on $50B on day one. The swap is now 6 months old, and rates have fallen 50 basis points. The fixed-rate payment is now more valuable (the bank is locked in at 4.7%, but new swaps can only be done at 4.2%). The swap has gained value for the receive-fixed party.

Calculating the gain: The bank is now receiving 4.7% in a 4.2% market. That 50bp benefit accrues quarterly for the remaining 4.5 years. Using present value calculations, a 50bp difference on $50B for 4.5 years is worth approximately $250M in current value. The bank''s swap position is in-the-money by $250M. This mark-to-market gain is recorded monthly.

Accounting treatment: If the swap qualifies for hedge accounting (as discussed in the ASC 815 module), this $250M gain flows through Other Comprehensive Income (OCI) and doesn''t hit earnings. The corresponding loss on the mortgage asset (which declined in value because rates fell) also flows through OCI, and the two largely offset, creating stable earnings.

If the swap doesn''t qualify for hedge accounting, the $250M gain hits earnings immediately, creating a massive spike in quarterly results. This is why ALM professionals care intensely about maintaining hedge accounting qualification—not to hide economic reality, but to create stable, predictable earnings that reflect the underlying economics of a natural hedge.

Practical Trade Execution and Decision-Making

When an ALM manager decides to execute a swap hedge, the process follows a standardized path:

Step 1: Determine the hedge specification

• How much notional to hedge? Typically expressed as percentage of mortgage portfolio. A bank with $100B mortgages and a 60% hedge ratio targets $60B notional


• What tenor? Match the weighted average life of the assets being hedged. Mortgages have 5-6 year average lives, so 5-year swaps are standard


• Pay fixed or receive fixed? Determines direction of the hedge

- For mortgages (which pay fixed rate), the bank "receives" fixed and "pays" floating to convert the fixed mortgages into floating-rate assets
- For other assets or liabilities, the direction reverses

Step 2: Request pricing from swap dealers
The bank''s treasurer calls the derivatives desk at JPMorgan, Goldman Sachs, Bank of New York Mellon, or another major swap dealer:

"We want to receive fixed, pay SOFR on $60 billion, 5-year, amortizing notional following the attached schedule."

The dealer quotes a "bid-ask" spread, meaning:

• "I bid 4.65%" (the dealer will receive fixed at 4.65%)


• "I offer 4.67%" (the dealer will pay fixed at 4.67%)

This 2bp spread (200 basis points times notional) represents the dealer''s profit on the trade and typically covers their costs and risk capital. In this case, the 2bp spread on a $60B notional trade is worth about $1.2M to the dealer.

Step 3: Execute and document
The bank chooses which side of the spread it prefers. If it wants to pay 4.67% fixed (the dealer''s offer), it agrees:

• I will pay 4.67% fixed


• I will receive SOFR


• Starting in 2 business days (T+2)


• For 5 years


• On the specified amortizing notional schedule

The dealer sends a confirmation document (usually within hours) detailing all terms. Both parties sign. The trade is now legally binding and cannot be unwound without agreement from both sides.

Step 4: Settlement and ongoing operations
Two business days later, the swap becomes effective. The first quarterly payment exchange occurs 90 days after settlement. From that point forward, the swap is marked to market daily (for treasury management), reported monthly (for accounting), and managed quarterly (for rebalancing).

Swap Basis Risk and Hedging Effectiveness

No swap hedge is perfect. Swaps are priced based on SOFR (the overnight risk-free rate), but mortgages don''t directly price off SOFR. Mortgages price off retail competition, customer rates, and market conditions. A mortgage rate is typically "Prime + Spread" or "SOFR + Spread," but the spread can vary based on credit quality, loan size, geography, and season.

When SOFR moves but the mortgage spread widens or tightens independently, the swap doesn''t capture that spread change. This is basis risk.

Example of basis risk in practice:
A bank hedges $50B of mortgages using SOFR swaps. Rates are stable, the hedge works well, and effectiveness is 85%. Then credit markets stress (perhaps a regional bank failure creates uncertainty). Credit spreads widen by 50 basis points. Mortgages''s effective rates rise by the full 50bp (SOFR component plus credit spread), but SOFR itself hasn''t moved. The swap provides zero protection for the credit spread widening. The hedge becomes less effective—now only 70% effective—because the basis has widened.

Basis risk exists in several forms:

1. Timing mismatch: The swap might reset quarterly while mortgages reprice on a different schedule (perhaps monthly or upon prepayment)
2. Index mismatch: Swaps reset on SOFR, but mortgages might reprice on Prime or another index
3. Maturity/Duration mismatch: The swap tenor might not perfectly match the weighted average life of the mortgages
4. Spread risk: Credit spreads or mortgage-specific spreads widen or tighten independently of rates
5. Optionality mismatch: Mortgages have prepayment options; swaps don''t

Good ALM programs manage basis risk through:

• Using the same index for hedge and hedged item when possible


• Stress testing to identify basis risk exposure


• Layering in option-based hedges (swaptions, caps, floors) to address optionality mismatch


• Dynamic rebalancing to correct timing and maturity mismatches

Quarterly Rebalancing: A Detailed Walkthrough

Swap positions don''t remain static. As mortgages prepay or as new originations occur, the hedge must evolve in parallel. A concrete quarterly rebalancing example illustrates the process:

Q1 Starting Position:

• Mortgage portfolio: $95B at 5.4% weighted-average coupon, 5.5-year duration


• Hedge position: Receive fixed on $50B 5-year swaps at 4.5%


• Hedge ratio: 52.6%


• Monthly mark-to-market: Rates have fallen 20bp in the quarter


• Cumulative MTM gain on swaps: $5.2M (swaps became more valuable as fixed rates became more valuable)


• Quarterly NII: $1,180M (normalized)


• Hedge effectiveness: 75% (good, indicating the swap offset about 75% of rate-driven NII changes)

Q2 Portfolio Evolution:

• Mortgages prepaid (customers refinanced at lower rates): -$6.2B


• New mortgages originated (rate environment stabilized): +$4.1B


• Net mortgage balance: $92.9B


• New mortgages originated at: 4.8% (the current market rate, up from Q1''s 4.5%)


• Wholesale funding actions: Raised $1.5B at SOFR+95bps, 2-year maturity


• Deposits: Net inflow of $600M


• New liability composition: More SOFR-sensitive given wholesale funding

Q2 Rebalancing Decision:

• Old hedge ratio (50B / 95B) = 52.6% still relevant


• New mortgage balance: $92.9B


• New target hedge notional: $92.9B × 52.6% = $48.8B


• Current hedge: $50B (over-hedged by $1.2B)


• Action required: Reduce hedge by $1.2B

Q2 Execution:

• The bank calls the swap dealer and initiates an unwind


• "We want to unwind $1.2B of our 5-year receive-fixed swap that''s currently paying 4.5%"


• Current market rate: 4.8% (rates have risen since Q1)


• The bank locked in at 4.5%; new swaps pay 4.8%


• Unwinding at 4.8%: Realizes a loss of 30bp on $1.2B = $3.6M loss


• The unwind settles T+2

Q2 New Trade:

• New mortgages at 4.8% need hedging


• The bank trades new: Receive fixed on $4.1B 5-year swaps at 4.85%


• Cost: Bid-ask spread of approximately 25bp = $102K cost

Q2 Post-Rebalancing Position:

• Receive fixed on $48.8B original swaps (at blended rate of approximately 4.48%)


• This is the net of unwinding $1.2B old swaps and trading $4.1B new swaps


• Hedge ratio: 48.8B / 92.9B = 52.5% (maintained)


• Expected effectiveness: 76% (similar to before, possibly slightly better with new originations)

Cost Analysis:

• Unwind loss: $3.6M


• New trade bid-ask: $102K


• Total cost: $3.7M


• Is it worth it? Yes, because:

- Maintains the 52.5% hedge ratio (avoiding drift)
- Aligns notional with the actual mortgage portfolio
- Preserves hedge effectiveness
- The cost (3.7M) is approximately 3bps on the entire mortgage portfolio—negligible compared to the earnings stability benefit

This rebalancing process repeats quarterly throughout the year, adjusting positions as the balance sheet evolves. Over a full year, a bank might execute 8-12 rebalancing trades, incurring $12-20M in spread costs but maintaining a carefully calibrated hedge that protects earnings from rate volatility while allowing the bank to capture the benefit of a correctly executed strategy.