Zvi Wiener

Fall-02

Term Structure of Interest Rates

BKM Ch 15

Zvi Wiener tel: 02-588-3049 mswiener@mscc.huji.ac.il

http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

Investments

Yields

Yield Curves

BKM Ch 15

Upward

Sloping

Flat

Downward

Sloping

Maturity slide 2 Zvi Wiener

Expected Interest Rates in Coming Years (Table 15.1)

Zvi Wiener

Expected One-Year Rates in Coming Years

1

2

3

Year

0 (today)

Interest Rate

8%

10%

11%

11%

BKM Ch 15 slide 3

Pricing of Bonds using forward Rates

Zvi Wiener

PV n



( 1

 r

1

)( 1



1 r

2

)...( 1

 r n

)

PV n

= Present Value of $1 in n periods r

1

= One-year rate for period 1 r

2

= One-year rate for period 2 r n

= One-year rate for period n

BKM Ch 15 slide 4

Forward Rates y

1

=8% y

2

=8.995% y

3

=9.660% y

4

=9.993%

1

1 .

08995

2



1

1 .

08



1 .

1 r

1

=8% r

2

=10% r

3

=11% r

4

=11%

1

1 .

0966

3



1

1 .

08



1 .

1



1 .

11 slide 5 Zvi Wiener BKM Ch 15

Zvi Wiener

Forward Rates from

Observed Long-Term Rates

( 1

 f n

)



( 1

( 1





) n y n y n



1

) n



1 f n

= one-year forward rate for period n y n

= yield for a security with a maturity of n

( 1

 y n

) n 

( 1

 y n



1

) n



1

( 1

 f n

)

BKM Ch 15 slide 6

Forward rates y ( S , T )

 r ( T ) T

T



 r ( S ) S

S

Take a forward loan at S of 1 and repay it at T

0



1

 e

 r ( S ) S  x

 e

 r ( T ) T x

 e r ( T ) T

 r ( S ) S

Zvi Wiener BKM Ch 15 slide 7

Zvi Wiener

Instantaneous forward rates y ( S , T )

 r ( T ) T

T



 r ( S ) S

S f ( S )

 r ( S )



S



 r ( S )



S

B ( T )

 exp







T



0 f ( s ) ds





BKM Ch 15 slide 8



Example of Forward Rates using Table 15.2 Numbers

Zvi Wiener

4 yr = 9.993

3yr = 9.660

fn = ?

(1.0993) 4 = (1.0966) 3 (1+f n

)

(1.46373) / (1.31870) = (1+f n

) f n

= .10998 or 11%

Note: this is expected rate that was used in the prior example.

BKM Ch 15 slide 11

Zvi Wiener

Downward Sloping

Spot Yield Curve

Zero-Coupon Rates Bond Maturity

12% 1

11.75%

11.25%

2

3

10.00%

9.25%

4

5


Forward Rates for

Downward Sloping Yield Curve

1yr Forward Rates

1yr [(1.1175) 2 / 1.12] - 1 = 0.115006

2yrs [(1.1125) 3 / (1.1175) 2 ] - 1 = 0.102567

3yrs [(1.1) 4 / (1.1125) 3 ] - 1 = 0.063336

4yrs [(1.0925) 5 / (1.1) 4 ] - 1 = 0.063008


Theories of Term Structure

Expectations

Liquidity Preference

Upward bias over expectations

Market Segmentation

Preferred Habitat


Expectations Theory

Observed long-term rate is a function of today’s short-term rate and expected future short-term rates.

Long-term and short-term securities are perfect substitutes.

Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term rates.


Liquidity Premium Theory

Long-term bonds are more risky.

Investors will demand a premium for the risk associated with long-term bonds.

The yield curve has an upward bias built into the long-term rates because of the risk premium.

Forward rates contain a liquidity premium and are not equal to expected future short-term rates.


Yields

Liquidity Premiums and Yield Curves

Observed Yield

Curve

Forward Rates

Liquidity

Premium

Maturity slide 17 Zvi Wiener BKM Ch 15

Yields

Liquidity Premiums and Yield Curves

BKM Ch 15

Observed Yield

Curve

Forward Rates

Liquidity

Premium

Maturity slide 18 Zvi Wiener

Market Segmentation and Preferred Habitat

Short- and long-term bonds are traded in distinct markets.

Trading in the distinct segments determines the various rates.

Observed rates are not directly influenced by expectations.

Preferred Habitat:

Modification of market segmentation

Investors will switch out of preferred maturity segments if premiums are adequate.

slide 19 Zvi Wiener BKM Ch 15

Using Spot Rates to Price

Coupon Bonds

A coupon bond can be viewed as a series of zero coupon bonds.

To find the value each payment is discount at the zero coupon rate.

Once the bond value is found, one can solve for the yield.

It’s the reason that similar maturity and default risk bonds sell at different yields to maturity.


Chapter 15 Weblinks http://www.smartmoney.com/bonds/

This site contains a good source for current rates, the current and past yield curves, and explanations of how the shape of the yield curve can affect economic performance. It also has a summary of current economic factors that are influencing rates. http://www.bondresources.com/

The site listed above has price and yield curve information and the ability to chart Treasury securities over time.

http://www.bloomberg.com/markets


http://www.investinginbonds.com


http://www.stls.frb.org/

Historical information on interest rates and other economic factors are available in the Federal

Reserve Economic Data Base (FRED) at the address shown above. Data in FRED can be downloaded in a spreadsheet format.


Summary

Term structure of interest rates

Zero-coupon

Government or LIBOR-Swap

Spread for risky bonds

OAS for bonds with embedded options

Forward rates

Expectation, Liquidity, Segmentation

Impact of taxation


Home

At www.mhhe.com/bkm you can download

SPOTYA.XLS file that demonstrates the bootstrapping technique used for derivation of zero coupon curve from coupon bonds.


Home Assignment

Required:

• problems 3, 5, 9, 13, 17 (3 rd ed).

• problems 4, 6, 12, 17, 22 (5 th ed).

• closely follow financial news!

Recommended:

• read ML publication on world bond markets

• visit recommended web links


Treasuries

Par

Investment grade Swap

Speculative grade 144A

Strips, zeros Yield

Volatility Callable

LIBOR

Spread

Puttable

CP, CD

TIPS Floater

Securitization GNMA, MBA

Convertible Default risk


End


Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

Default Risk and Ratings

Rating companies

Moody’s Investor Service

Standard & Poor’s

Duff and Phelps

Fitch

Rating Categories

Investment grade

Speculative grade slide 27 Zvi Wiener BKM Ch 15

Zvi Wiener

Straight bond

Floater


How to treat Floaters

Floater is similar to a constantly renewed loan with fixed spread (!).

Thus the yield of a floater is equal to the yield on the basis plus the spread.

Note that some of the Israeli government bonds have funny linkage to other bonds.


Reverse (Inverse) Floater

USD 5 year interest rates are 5%, however short term interest rates are Libor =2%.

Libor = London Interbank offered rate on Bloomberg see FWCV + currency

One can construct so-called reverse floater: slide 30 Zvi Wiener BKM Ch 15

1

2

3

4

5

Years

0

5

5

5 bond

-100

5

105

Reverse Floater loan

+100

-L

0

-L

1

-L

2

-L

3

-100- L

4

5

5

5 bond

-100

5

105

Reverse Fl.

-100

8

10-L

1

10-L

2

10-L

3

110- L

4 slide 31 Zvi Wiener BKM Ch 15

Features of Corporate Bonds

(indentures)

Corporate trustee

– represents bondholders

Term bonds – maturity

Under 10 years – notes

Some bonds have specific collateral

Others are debentures

Guaranteed bonds (third party’s guarantees)


SEC rule 144A

Allows to trade private placements among qualified institutions.


Medium Term Notes (MTN)

Notes are registered with the SEC under Rule

415 (the shelf registration) and are offered continuously to investors by an agent of the issuer.

Maturities vary from 9 months to 30 years.

Can be either fixed or floating.

Very flexible way to raise debt!


Primary Market (MTN)

Issuer posts spreads over Treasuries for a variety of maturities.

Then an agent tries to find an investor.

Minimal size is between $1M and $25M.

The schedule can be changed at any time!

Often structured MTNs are used (caps, floors, etc.) = structured notes.


Structured Notes

Many institutional investors can use swaps and structured notes to participate in markets that were prohibited.

Another use of structured notes is in risk management.

Financial Engineering is used to create securities satisfying the needs of investors.


Commercial Papers

Short term debt issued with less documentation typically by large and stable corporations for up to 270 days.

Much cheaper borrowing than banks.

Bridge financing.

Rollover Risk

An alternative to CD.


Commercial Papers

Short term unsecured promissory note

An alternative to short term bank borrowing

A typical round-lot transaction is $100,000

In the USA maturity is up to 270 days

Requires less paperwork

Those with maturity up to 90 days can be used as collateral for FED discount window.


Commercial Papers

Typically rolled over

Rollover risk is backed by an unused bank credit line

In order to issue CP one need either a high rating or good collateral

Sometimes credit enhancement is used (LOC)

CP issued in the USA by foreigners are called

Yankee CP slide 39 Zvi Wiener BKM Ch 15

Commercial Papers

Between 71 an 89 there was one default on CP.

3 defaults occurred in 89 and 4 in 90

Direct paper is sold without an agent

Secondary market is thin

There is a special rating for CP, P-1,3, A-1,3 discount instruments, used by money market


Bankruptcy and Creditor Rights liquidation (Chapter 7) - all assets will be distributed reorganization (Chapter 11) - a new corporate entity will result a company that files for protection becomes a debtor in possession and continues to operate under the supervision of the court


Bankruptcy and Credit Rights

Absolute priority rule - senior creditors are paid in full before junior creditors are paid anything.

Works in liquidation but often does not work in reorganization.


$

Merton’s model firm equity debt

Zvi Wiener

D

BKM Ch 15

V slide 43

Government Sponsored Enterprises

Federal Home Loan Bank System

Federal National Mortgage Association

Federal Home Loan Mortgage Corporation

Federal Farm Credit Bank System


Zvi Wiener

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