Description
Describes concept of interest rate swaps, uses of an interest rate swap, various risks associated with interest rate risk.
INTEREST RATE SWAPS ---- GROUP 4
What are Interest Rate Swaps?
?
?
An agreement between two parties (known as counterparties) where one stream of future interest payments is exchanged for another based on a specified principal amount. Interest rate swaps often exchange a fixed payment for a floating payment that is linked to an interest rate (most often the LIBOR).
The global OTC derivative market
Source: BIS
A “Plain Vanilla” Interest Rate Swap
?
An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million.
Cash Flows to Microsoft
---------Millions of Dollars--------LIBOR FLOATING Date Rate FIXED Net Cash Flow Cash Flow Cash Flow +2.10 –2.50 –0.40
Mar.5, 2004
Sept. 5, 2004
4.2%
4.8%
Mar.5, 2005
Sept. 5, 2005 Mar.5, 2006
5.3%
5.5% 5.6%
+2.40
+2.65 +2.75
–2.50
–2.50 –2.50
–0.10
+0.15 +0.25
Sept. 5, 2006
Mar.5, 2007
5.9%
6.4%
+2.80
+2.95
–2.50
–2.50
+0.30
+0.45
Uses of an Interest Rate Swap
?
Portfolio management: Interest rate swaps allow portfolio managers to add or subtract duration, adjust interest rate exposure, and offset the risks posed by interest rate volatility. Speculation: Because swaps require little capital up front, they give fixed-income traders a way to speculate on movements in interest rates while potentially avoiding the cost of long and short positions in Treasuries. Risk Management: The bulk of fixed and floating interest rate exposures typically cancel each other out, but any remaining interest rate risk can be offset with interest rate swaps. Rate-locks on bond issuance: When corporations decide to issue fixed-rate bonds, they usually lock in the current interest rate by entering into swap contracts. That gives them time to go out and find investors for the bonds.
?
?
?
Intel and Microsoft transform a Liability
• MS has a $100m loan @ LIBOR+10bps • Intel has a 3 year $100m loan @ 5.2%
5%
5.2%
Intel
LIBOR
Cash flows to Intel •Pays 5.2% to lenders •Pays LIBOR to MS •Receives 5% from MS
MS
LIBOR+0.1%
Cash flows to Microsoft •Pays LIBOR+0.1% to lenders •Pays 5% to Intel •Receives LIBOR from Intel
Intel and Microsoft transform an Asset
• MS owns $100m in bonds providing interest @ 4.7% for the next 3 years • Intel has an investment of $100m yielding LIBOR minus 20bps
5%
4.7%
Intel
LIBOR-0.2% LIBOR
MS
Cash flows to Intel Cash flows to Microsoft •Receives LIBOR – 0.2% on investment •Receives 4.7% fixed on investment •Pays LIBOR under swap terms to MS •Pays 5% under swap terms to Intel •Receives 5% fixed under swap terms •Receives LIBOR under swap terms
Role of Financial Intermediaries
Financial Institution earns about 3-4 bps on a pair of offsetting transactions 4.985% 5.2% Intel LIBOR 4.985% Intel LIBOR – 0.2% LIBOR Financia l Instituti on Financial Institution LIBOR 5.015% MS 4.7% LIBOR 5.015% MS
LIBOR + 0.1%
Spread earned by Financial Intermediary compensates partially for default risk
Comparative Advantage
?
Comparative advantage brings out the benefits of relative advantages of borrowing from 2 different markets.
FIXED FLOATING
Company A 4.0%
LIBOR+3bps
Company B 5.2% LIBOR+100bps
• Company A has comparative advantage in fixed rate markets • Company B has comparative advantage in floating rate markets
Comparative Advantage: Illustration
4% COMPANY A LIBO R 3.95% COMPANY B LIBOR+1% Cash Flows to Company A • Pays 4% p.a. to lenders • Receives 3.95% p.a. from B • Pays LIBOR to B Cash Flows to Company B • Pays LIBOR+1% p.a. to lenders • Receives LIBOR from A • Pays 3.95% p.a. to A
•Effectively, Company A pays LIBOR+0.05% p.a., as opposed to LIBOR+0.3% ea •Effectively, Company B pays 4.95% p.a., as opposed to 5.2% earlier. •Total gains from comparative advantage theory = 1.2% - 0.7%= 50 bps!!
Criticisms of the Theory
?
?
?
In floating rate markets, there is the possibility of adjusting the spread over LIBOR as per risk assessment. Spread between 5 year rates is greater than the spread between 6 month rates. Advantage is correlated to the conditionality that the floating market loan rate(liability) shall not be revised upwards.
Swap Curve
The Swap curve and the Treasury yield curve
Source: Federal Reserve
• Plot of swap rates across all available maturities is called the Swap curve. • The Swap curve incorporates forward expectations for LIBOR and the market’s perception of credit quality of these AA-rated banks. •“Swap spread” at any given maturity, mostly reflects the incremental credit risk associated with the banks that provide swaps compared to Treasuries, which are viewed as risk-free.
Risk associated with Swaps
?
?
Interest rate risk: Because actual interest rate movements do not always match expectations, swaps entail interest-rate risk. Put simply, a receiver (the counterparty receiving a fixed-rate payment stream) profits if interest rates fall and loses if interest rates rise. Conversely, the payer (the counterparty paying fixed) profits if rates rise and loses if rates fall. Counterparty risk: the chance that the other party in the contract will default on its responsibility. Although this risk is very low – banks that deal in LIBOR and interest rate swaps generally have very high credit ratings of double-A or above – it is still higher than that of a risk-free U.S. Treasury bond.
Swap Rate and its calculation
Maturity 2 year 3 year 4 year 5 year 10 year Bid 6.03 6.20 6.45 6.70 6.90 Offer 6.06 6.24 6.49 6.74 6.96 Swap Rate 6.045 6.22 6.47 6.72 6.93
Swap Rate : Average of fixed rate that a swap market maker is prepared to pay in exchange for receiving LIBOR (bid rate) and fixed rate it is prepared to receive in exchange for paying LIBOR (offer rate) For Example: Swap rate for maturity 2 years = (6.03+6.06)/2 = 6.045
Valuation of a Swap
?
?
Method 1: Valuation in terms of Bond prices Method 2: Valuation in terms of FRA (Forward Rate Agreement)
Valuation in terms of Bond Prices
LIBOR Infosys(Floating Rate Payer) 5%
Wipro (Fixed Rate Payer)
Floating rate payer 1. Long position in fixed interest rate 2. Short position in floating interest rate
Plain Vanilla Interest Rate Swap Bond with Fixed coupon Bond with Floating coupon
Value of Swap = B fix-B fl
Value of Fixed Rate Bond Underlying the swap Value of Floating Rate Bond underlying the swap
Method 1: Illustration
Infosys (Floating Rate Payer) Swap Agreement 1. Agreed to pay Fixed rate of 8% p.a( compounded semiannually) 2. Receive 6 month LIBOR Current situation: Time to maturity: 1.25 year Present Value of Floating rate Bond =(L+K)e -rt L - Notional Principal K - Floating payment(made in time t) R- LIBOR/Swap Zero Rate for maturity of t Present Value of Fixed rate Bond = ?C* Discount factor + P* Discount factor 1. C-Coupon Payment 2. P- Notional principal payment at the end of the maturity of swap
Method 1: Table
Year B fl (Cash flow) 105.1 B fix (Cash flow) 4 4 104 LIBO R Discoun P.V. t Factor (B fl ) P.V. (B fix)
0.25 0.75 1.25 Total
10% 10.5% 11%
0.9753 0.9243 0.8715
102.50 5
3.901 3.697 90.640
102.50 5 Swap value Table illustrating the calculation of Swap value
98.238 4.267
Valuation in terms of FRAs
LIBOR Infosys(Floating Rate Payer) 5% Plain Vanilla Interest Rate Swap The procedure is: 1. Use the LIBOR/swap zero curve to calculate forward rate for each of LIBOR rates that will determine swap cash flows 2. Calculate swap cash flows on the assumption that the LIBOR rate will be equal to forward rates 3. Discount these swap cash flows (using LIBOR/swap zero curve ) to obtain the swap value Wipro (Fixed Rate Payer)
Method 2: Illustration
Infosys (Floating Rate Payer) Swap Agreement 1. Agreed to pay Fixed rate of 8% p.a( compounded semiannually) 2. Receive 6 month LIBOR Current situation: Time to maturity: 1.25 year
Year LIBOR rate Forward rate (semiannual)
6 month at last payment date
0.25 0.5 0.75
10.2%
10% 10.5% 11%
}
10.2%
}
11.044% 12.102%
Formula used for calculating forward rates = (R2T2-R1T1)/(T2-T1) =(0.105*0.5-0.10*0.25)/0.25 = 10.75% 10.75% in continuous compounding = 11.044% in semi annual compounding
Method 2: Table
Year Floatin g cash flow Fixed cash flow Net cash flow Discoun Presen t Factor t value of net cash flow 0.9753 0.8715 Swap value 1.073 1.407 1.787 4.267
0.25 0.75 1.25 Total
5.100 5.522 6.051
-4 -4 -4
1.100 2.051
1.1522 0.9243
Inference
1. The fixed rate in an interest rate swap zero initially. 2. Value of Forward Rate forward contract to fixed rate payer >0 <0 =0 >5% <5% =5% is chosen so that the swap is worth Value of forward contract to fixed rate payer <0 >0 =0 Forward Rate
>5% >5% =5%
From the point of Fixed rate payer
Maturit y
Interest Rate variation
Value of forward contract
Maturit y
Thank You
doc_301904560.pptx
Describes concept of interest rate swaps, uses of an interest rate swap, various risks associated with interest rate risk.
INTEREST RATE SWAPS ---- GROUP 4
What are Interest Rate Swaps?
?
?
An agreement between two parties (known as counterparties) where one stream of future interest payments is exchanged for another based on a specified principal amount. Interest rate swaps often exchange a fixed payment for a floating payment that is linked to an interest rate (most often the LIBOR).
The global OTC derivative market
Source: BIS
A “Plain Vanilla” Interest Rate Swap
?
An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million.
Cash Flows to Microsoft
---------Millions of Dollars--------LIBOR FLOATING Date Rate FIXED Net Cash Flow Cash Flow Cash Flow +2.10 –2.50 –0.40
Mar.5, 2004
Sept. 5, 2004
4.2%
4.8%
Mar.5, 2005
Sept. 5, 2005 Mar.5, 2006
5.3%
5.5% 5.6%
+2.40
+2.65 +2.75
–2.50
–2.50 –2.50
–0.10
+0.15 +0.25
Sept. 5, 2006
Mar.5, 2007
5.9%
6.4%
+2.80
+2.95
–2.50
–2.50
+0.30
+0.45
Uses of an Interest Rate Swap
?
Portfolio management: Interest rate swaps allow portfolio managers to add or subtract duration, adjust interest rate exposure, and offset the risks posed by interest rate volatility. Speculation: Because swaps require little capital up front, they give fixed-income traders a way to speculate on movements in interest rates while potentially avoiding the cost of long and short positions in Treasuries. Risk Management: The bulk of fixed and floating interest rate exposures typically cancel each other out, but any remaining interest rate risk can be offset with interest rate swaps. Rate-locks on bond issuance: When corporations decide to issue fixed-rate bonds, they usually lock in the current interest rate by entering into swap contracts. That gives them time to go out and find investors for the bonds.
?
?
?
Intel and Microsoft transform a Liability
• MS has a $100m loan @ LIBOR+10bps • Intel has a 3 year $100m loan @ 5.2%
5%
5.2%
Intel
LIBOR
Cash flows to Intel •Pays 5.2% to lenders •Pays LIBOR to MS •Receives 5% from MS
MS
LIBOR+0.1%
Cash flows to Microsoft •Pays LIBOR+0.1% to lenders •Pays 5% to Intel •Receives LIBOR from Intel
Intel and Microsoft transform an Asset
• MS owns $100m in bonds providing interest @ 4.7% for the next 3 years • Intel has an investment of $100m yielding LIBOR minus 20bps
5%
4.7%
Intel
LIBOR-0.2% LIBOR
MS
Cash flows to Intel Cash flows to Microsoft •Receives LIBOR – 0.2% on investment •Receives 4.7% fixed on investment •Pays LIBOR under swap terms to MS •Pays 5% under swap terms to Intel •Receives 5% fixed under swap terms •Receives LIBOR under swap terms
Role of Financial Intermediaries
Financial Institution earns about 3-4 bps on a pair of offsetting transactions 4.985% 5.2% Intel LIBOR 4.985% Intel LIBOR – 0.2% LIBOR Financia l Instituti on Financial Institution LIBOR 5.015% MS 4.7% LIBOR 5.015% MS
LIBOR + 0.1%
Spread earned by Financial Intermediary compensates partially for default risk
Comparative Advantage
?
Comparative advantage brings out the benefits of relative advantages of borrowing from 2 different markets.
FIXED FLOATING
Company A 4.0%
LIBOR+3bps
Company B 5.2% LIBOR+100bps
• Company A has comparative advantage in fixed rate markets • Company B has comparative advantage in floating rate markets
Comparative Advantage: Illustration
4% COMPANY A LIBO R 3.95% COMPANY B LIBOR+1% Cash Flows to Company A • Pays 4% p.a. to lenders • Receives 3.95% p.a. from B • Pays LIBOR to B Cash Flows to Company B • Pays LIBOR+1% p.a. to lenders • Receives LIBOR from A • Pays 3.95% p.a. to A
•Effectively, Company A pays LIBOR+0.05% p.a., as opposed to LIBOR+0.3% ea •Effectively, Company B pays 4.95% p.a., as opposed to 5.2% earlier. •Total gains from comparative advantage theory = 1.2% - 0.7%= 50 bps!!
Criticisms of the Theory
?
?
?
In floating rate markets, there is the possibility of adjusting the spread over LIBOR as per risk assessment. Spread between 5 year rates is greater than the spread between 6 month rates. Advantage is correlated to the conditionality that the floating market loan rate(liability) shall not be revised upwards.
Swap Curve
The Swap curve and the Treasury yield curve
Source: Federal Reserve
• Plot of swap rates across all available maturities is called the Swap curve. • The Swap curve incorporates forward expectations for LIBOR and the market’s perception of credit quality of these AA-rated banks. •“Swap spread” at any given maturity, mostly reflects the incremental credit risk associated with the banks that provide swaps compared to Treasuries, which are viewed as risk-free.
Risk associated with Swaps
?
?
Interest rate risk: Because actual interest rate movements do not always match expectations, swaps entail interest-rate risk. Put simply, a receiver (the counterparty receiving a fixed-rate payment stream) profits if interest rates fall and loses if interest rates rise. Conversely, the payer (the counterparty paying fixed) profits if rates rise and loses if rates fall. Counterparty risk: the chance that the other party in the contract will default on its responsibility. Although this risk is very low – banks that deal in LIBOR and interest rate swaps generally have very high credit ratings of double-A or above – it is still higher than that of a risk-free U.S. Treasury bond.
Swap Rate and its calculation
Maturity 2 year 3 year 4 year 5 year 10 year Bid 6.03 6.20 6.45 6.70 6.90 Offer 6.06 6.24 6.49 6.74 6.96 Swap Rate 6.045 6.22 6.47 6.72 6.93
Swap Rate : Average of fixed rate that a swap market maker is prepared to pay in exchange for receiving LIBOR (bid rate) and fixed rate it is prepared to receive in exchange for paying LIBOR (offer rate) For Example: Swap rate for maturity 2 years = (6.03+6.06)/2 = 6.045
Valuation of a Swap
?
?
Method 1: Valuation in terms of Bond prices Method 2: Valuation in terms of FRA (Forward Rate Agreement)
Valuation in terms of Bond Prices
LIBOR Infosys(Floating Rate Payer) 5%
Wipro (Fixed Rate Payer)
Floating rate payer 1. Long position in fixed interest rate 2. Short position in floating interest rate
Plain Vanilla Interest Rate Swap Bond with Fixed coupon Bond with Floating coupon
Value of Swap = B fix-B fl
Value of Fixed Rate Bond Underlying the swap Value of Floating Rate Bond underlying the swap
Method 1: Illustration
Infosys (Floating Rate Payer) Swap Agreement 1. Agreed to pay Fixed rate of 8% p.a( compounded semiannually) 2. Receive 6 month LIBOR Current situation: Time to maturity: 1.25 year Present Value of Floating rate Bond =(L+K)e -rt L - Notional Principal K - Floating payment(made in time t) R- LIBOR/Swap Zero Rate for maturity of t Present Value of Fixed rate Bond = ?C* Discount factor + P* Discount factor 1. C-Coupon Payment 2. P- Notional principal payment at the end of the maturity of swap
Method 1: Table
Year B fl (Cash flow) 105.1 B fix (Cash flow) 4 4 104 LIBO R Discoun P.V. t Factor (B fl ) P.V. (B fix)
0.25 0.75 1.25 Total
10% 10.5% 11%
0.9753 0.9243 0.8715
102.50 5
3.901 3.697 90.640
102.50 5 Swap value Table illustrating the calculation of Swap value
98.238 4.267
Valuation in terms of FRAs
LIBOR Infosys(Floating Rate Payer) 5% Plain Vanilla Interest Rate Swap The procedure is: 1. Use the LIBOR/swap zero curve to calculate forward rate for each of LIBOR rates that will determine swap cash flows 2. Calculate swap cash flows on the assumption that the LIBOR rate will be equal to forward rates 3. Discount these swap cash flows (using LIBOR/swap zero curve ) to obtain the swap value Wipro (Fixed Rate Payer)
Method 2: Illustration
Infosys (Floating Rate Payer) Swap Agreement 1. Agreed to pay Fixed rate of 8% p.a( compounded semiannually) 2. Receive 6 month LIBOR Current situation: Time to maturity: 1.25 year
Year LIBOR rate Forward rate (semiannual)
6 month at last payment date
0.25 0.5 0.75
10.2%
10% 10.5% 11%
}
10.2%
}
11.044% 12.102%
Formula used for calculating forward rates = (R2T2-R1T1)/(T2-T1) =(0.105*0.5-0.10*0.25)/0.25 = 10.75% 10.75% in continuous compounding = 11.044% in semi annual compounding
Method 2: Table
Year Floatin g cash flow Fixed cash flow Net cash flow Discoun Presen t Factor t value of net cash flow 0.9753 0.8715 Swap value 1.073 1.407 1.787 4.267
0.25 0.75 1.25 Total
5.100 5.522 6.051
-4 -4 -4
1.100 2.051
1.1522 0.9243
Inference
1. The fixed rate in an interest rate swap zero initially. 2. Value of Forward Rate forward contract to fixed rate payer >0 <0 =0 >5% <5% =5% is chosen so that the swap is worth Value of forward contract to fixed rate payer <0 >0 =0 Forward Rate
>5% >5% =5%
From the point of Fixed rate payer
Maturit y
Interest Rate variation
Value of forward contract
Maturit y
Thank You
doc_301904560.pptx