Essay on Fixed Income

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3/16/11

Lecture 5 Swaps

What is Swaps? • Agreement to exchange cash flows • Example: Switching apartments and payments

Interest Rate Swaps • Exchange the cash flows of two bonds • Typically between a fixed coupon and a floater

Ownership

Ownership

1

3/16/11

Currency Swaps

• Exchange the cash flow of two bonds nominated in different currency • Example: Dollar nominated US T-­‐Bill and Euro nominated German government bond • May also include interest rate swap

Gain and Loss from Swaps 6m L + 1%

4% annual

Home Depot s Swap Gain/Loss star[ng Jan 2010 per $100 face value bond Date

6m LIBOR

Fixed Received

Floa5ng Paid

Net Cash Flow

June 2010

1.0%

$2.00

-­‐$2.00

$0.00

Jan 2011

1.5%

$2.00

-­‐$2.50

-­‐$0.50

June 2011

0.5%

$2.00

-­‐$1.50

$0.50

Jan 2012

0.5%

$2.00

-­‐$1.50

$0.50

Jun 2012

2.0%

$2.00

-­‐$3.00

-­‐$1.00

Jan 2013

2.5%

$2.00

-­‐$3.50

-­‐$1.50

Swap Valua[on

Vswap = B fix − B float
Vswap = B float − B fixed

If you are a fixed receiver

If you are a floating receiver

• A bond value is the sum of discounted cash flows • A swap value is the difference in the sum of discounted cash flows • We use term structure of interest rates to calculate the value

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Interest Rate Swap Valua[on Example I

• Receive 10% fixed and pay 1 year LIBOR + 1% for next 3 years • Equivalent to switching a floater with fixed coupon rate bond • $100 million principal – Swap no[onal value • Current term structure: Year

LIBOR Spot Rates

1

5%

2

6%

3

7%

4

8%

Interest Rate Swap Valua[on Example II

5%

Current

6%

Next Year

7%

Two Years

Three Years

Four Years

• Receive 10% fixed and pay 1 year LIBOR + 1% for next 3 years • Receive $10 million each year and pay:

Interest Rate Swap Example III

• Suppose we can use LIBOR spot rates to discount the cash flows of the swap • Then the swap value is the discounted value of the cash flows • Typically, two par[es set the ini[al value of the swap as zero-­‐value transac[on Year

Fixed

1

$10 mil

Floa5ng

Difference

Discount 1/(1.05)

2

$10 mil

1/(1.06)2

3

$10 mil

Present Value

1/(1.07)3

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Swap Valua[on and Interest Rate Change

• Receive 10% fixed and pay 1 year LIBOR + 1% • Now, suppose LIBOR spot rate drops 1% each
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