Bond Strategies

FNCE 455Class Session #11Lloyd KurtzSanta Clara University

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The Strategies

• Interest Rate Anticipation

• Cash Flow Matching

• Duration Management

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Interest Rate Anticipation

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An important feature

“Prices of long-term bonds tend to be more sensitive to interest rate changes than the prices of short-term bonds.”

- BK&M

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Factors influencing rates

• The supply of funds from savers, primarily households.

• The demand for funds from businesses to be used to finance

physical investments in plant, equipments, and inventories.

• The government’s net supply and/or demand for funds as

modified by actions of the Federal Reserve Bank.

• The expected rate of inflation.

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Source: BK&M

However…

“Unfortunately, forecasting interest rates is one of the most notoriously difficult parts of applied macroeconomics.”

- BK&M

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U.S. long-term rates: 1880-2012

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Data Source: Robert Shiller, Yale University

U.S. long-term rates: 1980-2012

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Data Source: Robert Shiller, Yale University

Cash Flow Matching

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Cash Flow Matching: Ex. #1

A company knows it will have to pay a large legal

settlement in three years. It investments a zero-

coupon bond (a ‘bullet’) that matures in three years to

fund this obligation.

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Cash Flow Matching: Ex #2

A family knows it will have to start paying college tuition

bills in four years. They purchase zero coupon bonds with

maturities around the dates they know tuition bills will be

due.

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Cash Flow Matching: Ex. #3

A pension fund has two large groups of retirees – one will

retire in the next three years, the other will not retire for

more than 20 years. The manager ‘barbells’ the portfolio,

buying short-maturity issues to fund the near-term

obligations, and long-term issues to fund the distant ones.

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Goal of Cash Flow Matching

Have the net cash flow for every date in the future = 0.

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Cash Flow Matching

• Advantages• Simple• Intuitive• Effective

• Disadvantages• Not well-suited to complex situations• Market may not be liquid enough to accommodate

need for certain types of bonds• May be expensive

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Duration Management

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Duration

A measure of the effective maturity of a bond...

• It is the weighted average of the times until each

payment is received, where weights are proportional to

the present value of the payment

• Duration is shorter than maturity for all bonds except

zero coupon bonds

• Duration is equal to maturity for zero coupon bonds

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Duration Calculation

8%Bond

Timeyears

Payment PV of CF(10%)

Weight C1 XC4

1 80 72.727 .0765 .0765

2 80 66.116 .0690 .1392

Sum

3 1080 811.420

950.263

.8539

1.0000

2.5617

2.7774

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The weight is 72.727 divided by 950.263...

What Duration Does

• Duration measures how much of the value of a bond is attributable to near-term vs. longer-term cash flows.

• A bond with most cash flows coming in the near-term, will have a shorter duration.

• A bond with most cash flows coming a long time from now will have a higher duration.

• A zero-coupon bond has only one cash flow – the return of principal at maturity – that is why its duration exactly equals its maturity.

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Cash Flows of 8-yr Bond with 9% annual coupon and 10% YTM

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Pop Quiz

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What would be the duration of this bond if payments 1 through 7 were eliminated?

Duration vs. Maturity

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Immunization

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Imagine you are running two discounted cash flow models side-by-side. One estimates the present value of your liability (in this case the single payment obligation). The other estimates the present value of your assets (in this case, the bond). The goal of immunization is to find an asset that is a close match for the liability, both in terms of the present value, and the shape of the value/rate curve.

Uses of Duration

• Summary measure of length or effective maturity for a portfolio

• Immunization of interest rate risk (passive management)• Net worth immunization• Target date immunization

• Measure of price sensitivity for changes in interest rate

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