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: Technical Mechanics and Execution

Swap Pricing

Swap fixed rates are determined by market supply/demand and the Treasury curve.

Swap pricing formula:
Fixed Rate = Treasury Yield (matching tenor) + Swap Spread

Example:

• 5-year Treasury yield: 4.2%


• 5-year swap spread: 50bps


• 5-year swap fixed rate: 4.7%

The spread reflects:

• Credit risk of swap counterparties (banks are generally AA-rated)


• Liquidity of swap market


• Supply/demand imbalances

Swap spreads are typically 30-80bps, depending on tenor and market conditions.

Swap Terms and Mechanics

Standard 5-year swap terms:

• Notional: $100M (principal amount, not exchanged)


• Fixed rate: 4.7% (paid by one party annually)


• Floating rate: SOFR + 0bps (received or paid by other party, resets quarterly)


• Tenor: 5 years


• Payment frequency: Quarterly (90 days)


• Day count: 30/360 (fixed), Actual/360 (floating)


• Settlement: T+2 (effective in 2 business days)

Each quarterly period, the net payment is calculated:

• Fixed payment: $100M 4.7% (90/360) = $1,175K


• Floating payment: $100M SOFR (90/360) = varies


• Net: (Fixed - Floating) Notional (days/360)

Swap Curves and Key Rates

Swaps exist for multiple tenors: 2Y, 3Y, 5Y, 7Y, 10Y, 30Y, etc.

The swap curve shows fixed rates for each tenor:

• 2-year swap: 4.3%


• 3-year swap: 4.4%


• 5-year swap: 4.7%


• 10-year swap: 4.9%

The slope of the curve (upward-sloping) reflects term premium (longer duration costs more).

Amortizing vs. Bullet Swaps

Bullet swap: Notional stays constant

• Hedge entire mortgage portfolio of constant size


• Simple pricing


• Most common

Amortizing swap: Notional decreases over time

• Hedge mortgages that are amortizing (principal paying down)


• Matches declining mortgage balance


• Slightly complex pricing (lower notional in later years)

Example amortizing swap:

• Year 1-2: $100M notional


• Year 2-3: $80M notional (some mortgages paid off)


• Year 3-5: $60M notional


• Prices the swap given the declining notional schedule

Swap Accounting and Mark-to-Market

Swaps are derivatives, marked-to-market at each reporting date.

Monthly reporting:

• Swap value = PV of all future fixed payments - PV of all future floating payments


• If swap has $10M fair value gain: Swap is in-the-money for the receive-fixed party


• Accounting treatment: Flows through earnings or OCI depending on hedge designation

Scenario: Rates fall 50bps after swap is executed

• Swap was: Pay fixed 4.7%, receive SOFR


• New market rate: Pay fixed 4.2%, receive SOFR (50bp lower fixed rate)


• Bank locked in at 4.7%, now could pay 4.2% if exiting


• Swap value: Bank has unfavorable position (locked into higher fixed rate)


• Mark-to-market loss: approximately $2.5M (on $100M notional, 5-year tenor)

Settlement and Execution

When executing a swap:

Step 1: Determine swap need

• How many mortgages to hedge? $50B


• What tenor? 5-year (mortgage average life)


• Fixed or pay fixed? Pay fixed, receive floating (converts fixed mortgages to floating)

Step 2: Get pricing

• Contact swap dealer (usually JPMorgan, Goldman Sachs, etc.)


• "We want to pay fixed, receive SOFR on $50B, 5-year"


• Dealer quotes bid/ask: "I bid 4.65%, I offer 4.67%"


• This means dealer will receive fixed at 4.65%, pay fixed at 4.67%


• Bank chooses: Bank pays 4.67% and receives SOFR (using dealer's offer)

Step 3: Trade execution

• Terms confirmed


• Confirmation sent (legal document detailing all terms)


• Trade settles in 2 business days (T+2)

Step 4: Mark-to-market

• Daily valuation of swap


• Monthly reporting of gains/losses


• Quarterly rebalancing based on changing balance sheet

Swap Basis and Hedging Effectiveness

Swaps are priced off SOFR. But mortgages don't directly price off SOFR; they price off retail competition and market conditions.

Basis risk example:

• Mortgage rate: Prime rate (Wall Street Journal prime, based on Fed Funds) + spread


• Swap: SOFR-based


• When Fed Funds and SOFR diverge (unlikely but possible), the hedge becomes imperfect

Bases are usually tight (<5bps), but exist.

Real Example: Quarterly Swap Rebalancing

Q1 Swap Position:

• Pay fixed 4.5% on $50B swaps (5-year tenor)


• Monthly mark-to-market: Rates fall 20bps (swaps gain value)


• Cumulative MTM gain: $5M


• Hedge effectiveness: 75% (earnings hedged by 75%)

Q2 Balance sheet change:

• $5B mortgages prepaid (customer refinanced)


• $3B new mortgages originated (higher rate environment)


• New mortgage rate: 4.8% (higher than Q1's 4.5%)


• Need to reduce swap by $2B (net $3B - $5B prepaid)

Q2 Rebalancing:

• Unwind $2B of old swaps (pay fixed 4.5%)


• Current swap rate: 4.6% (rates have risen)


• Unwind gain: Bank unwinds at 4.6% vs. locked at 4.5% (loss of $200K = $2B * 0.1%)


• New swap: Execute $3B pay-fixed at 4.6%


• Total position: $51B pay-fixed (mix of 4.5% and 4.6%)

Cost of rebalancing:

• Bid-ask spread on unwind: $200K


• Bid-ask spread on new trade: $100K


• Total cost: $300K


• Purpose: Rebalance to match new mortgage portfolio


• Worth it? Depends on size of new mortgages and expected duration of position