BOND MARKETS

CHARACTERISTICS

• yields• coupon• maturity• tax features• liquidity• risk• ratings• callability• indenture restrictions• subordination• convertability

MONEY MARKET INSTRUMENTS - LIQUID ASSETS

Also called “cash” assets

• T-bills • Commercial Paper• Bankers Acceptances• Eurodollar deposit • short term tax-exempts• money market funds and accounts (check writing -

insured)

BONDS AND NOTES

• Bonds 5-40 years maturity

• Notes 1-7 years maturity

Types include treasury, corporate, gov. agency, municipal.

Look at quotes - see websites – Investinginbonds.com, Tradebonds.com, Bonds-online.com

YIELD SPREADS

Yn = Yr + I + P

where Yn is the nominal yield,

Yr is the real yield - yield on U.S. Treasury inflation-indexed bonds (see WSJ),

I is the expected inflation rate over the lifeof the bond - regular Treasury yield minus inflation-indexed yield,

P is the risk premium - bond yield minus same maturity U.S. Treasury yield.

P widens during recession and narrows in expansion. It can be measured by the difference (spread) between the yield on a risky bond and a risk-free bond (U.S. Treasury).

Spreads Due to InflationNote: The terms “yields” and “rates” (like interest rates) are used interchangeably.

ANALYSIS OF CORPORATE BONDS•Economic significance (cyclicality) of company &

industry/ quality of management/ performance in recession - e.g. Chrysler wants cash cushion.

•Financial resources of the company (liquidity, asset protection, capital structure).

•Indenture provisions include collateral / sinking fund / call provisions / creation of additional debt / working capital & dividend restriction

•Ratings - below Baa or BBB not investment quality

SPREADS DATA – economagic.com, riskmetrics.com

Spreads Due to Risk Differences

Mortgage Yield Spread

ANALYSIS OF MUNICIPAL BONDSGeneral Obligations

• Rating• Economic Strength of Community• Revenue Raising Potential• Relative Magnitude of fixed charges• Attitude and Fiscal discipline of Officials

Revenue Bonds

analyze financial prospects of the project supporting payment only revenues support payments

TAX EXEMPT YIELDS -STATE & LOCALQUESTION: How do you know if its best to buy tax

exempt or taxable bonds?

YT = Taxable yieldYTE = Tax exempt yieldT = Tax rate

YTE = YT (1 - T)or, YT = YTE / (1 - T)

=> T = 1 - (YTE / YT)

If we know YTE and YT we can estimate the "indifferent" T - implicit marginal buyer's tax rate

If your personal tax rate is Tp then your after tax yield on a taxable bond is

YAT = YT (1 - Tp)

Therefore, if your Tp >T, then buy Tax Exempt Bond(only approximate for bonds trading above or below par because capital gains are taxable)

QUESTION: If the taxable bond yield is 8 percent, the tax exempt yield is 6 percent and your tax rate is 30 percent, which bonds should you buy?

ANS: YAT = .08(1 - .30) = .056 => buy tax exempts

QUESTION: Investor expects a Democrat to win the presidential election- expect tax rates will rise - what should happen to municipal yields? - fall

QUESTION: What happens if we get a flat tax at 17%? - taxable yields fall and tax exempts rise

• COLLATERALIZED OBLIGATIONS

• mortgage

• car loans

• credit card debt

• David Bowie royalties

BOND VALUATION AND YIELDS

PROMISED YIELD TO MATURITY

assumes bond held to maturityassumes coupons reinvested at YTM rate.

Find k given bond price, Bn , coupons, C, maturity, n, and par value, Par.

if all payments are made we get the promised yield, k, if we pay price Bn. Otherwise, we need to substitute the expected coupon and par payment rather than the promised payments and then find k.

BC

k

C

k

C

k

Par

knn

n n

1 221 1 1 1( ) ( ) ( ) ( )

BOND PRICING

Find and estimate of Bn given expected coupons and Par, E(C) and E(Par), and k.

QUESTION: What happens if k increases? B decreases What happens if k decreases? B increases

BE C

k

E C

k

E C

k

E Par

knn

n n

( )

( )

( )

( )

( )

( )

( )

( )1 2

21 1 1 1

REALIZED YIELD - CALCULATED AFTER THE FACT

Assume you sell after 2 periods - find k in

Bp = Purchase PriceBs = Sales Price

This assumes coupons reinvested at k

CURRENT YIELD

BC

k

C

k

B

kps

1 2

2 21 1 1( ) ( )

YC

Pcm

coupon

current market price

BOND VALUATION

n

nkk

PV)1(

1,

= Coupon[PVAk,n] + Par[PVk,n]

To get the bond price you can use a financial calculator or you can

compute a present value annuity factor

nn k

Parkkk

CouponB)1(

1

)1(

11

n

nkkkk

PVA)1(

11,

And a present value factor for one cash flow

And plug them into the formula above

Using the equation above

PROBLEM: Suppose a bond offers a 10% coupon, on $1000 par, for 3 years and the expected inflation rate is 2%, the real rate is 3% and the bond’s risk premium is 1%. What is its price?

B = 100[PVA .06, 3] + 1000[PV .06, 3]= 100(2.673) + 1000(.84)= 1107

1000 (PVk,8)

100 (PVA k,8)

par payment is a single cash flow

coupon payments are an annuity

Valuing a 10 percent coupon, 1000 par value bond.

1000

QUESTION: If the company only agrees to pay $1000 at maturity, won’t those who buy this bond lose $107 at maturity?

QUESTION: Would you buy this bond? Why? - greater coupon than par bonds.

A par bond would cost $1000 but only pay a $60 coupon. The present value of the difference in coupons

(100 - 60)(2.673) = 107

which is the difference in price between this bond and a par bond. Alternatively, a bond that offered a 2% coupon when rates are 6% will have a price of

B = 20[PVA.06, 3] + 1000[PV.06, 3] = 893 or $107 less than the par bond.

FINDING THE YIELD TO MATURITY

PROBLEM: Suppose you observe a bond in the marketwith a price of $803 that pays a coupon of 10% till maturity in 5 years. What is its implied yield to maturity?

Try 16%

803 = 100(PVA?,5) + 1000(PV?,5) = 100(3.274) + 1000(.476)

= 803

PRICING WITH SEMI-ANNUAL COUPONS

PROBLEM: Suppose a bond pays 10% coupon, semi-annually, has 10 years till maturity and has a required return (or YTM) of 8%. What is its price?

B = 50(PVA.04,20) + 1000(PV.04,20)

= 50(13.59) + 1000(.456)

= 1135.5

FINDING THE REALIZED YIELD

QUESTION: If you buy a 20% coupon, par bond, with 3years maturity and you hold it for three years are you sure to earn 20%?

ANSWER: No because the calculation of YTM assumesthat the coupons are reinvested at 20%, if rateschange your realized yield will change because you'll earn more or less than 20% on the reinvestedcoupons.

For example, when you bought the bond YTM was 20%. But suppose rates fell to 5% the day after you bought and stay there for three years.

Your realized yield will be implied in:

use PV = FV[PVk,n] = FV[1/(1+k)]n . .

Solve for k to get “realized” yield, the true yield which depends upon how much you initially invest (PV = present value) and how much you accumulate by the time that you sell in the future (FV = future value).

1000 = (200(1+.05)2 + 200(1+.05) + 1200)[PVk,3]= 1630.5[PVk,3]

=> 1000/1630.5 = [PVk,3] = [1/(1+k)]3 = .6133=> k = 17.7% realized yield falls because

reinvestment rate falls

Suppose you buy a 20 percent coupon bond at par, andimmediately after you buy, the market yield falls to 5

percent. If you plan to hold the bond until maturity, yourrealized yield falls because reinvested coupons earn less.

0 Period 1st Period 2nd Period 3rd Period

0 Period 1st Period 2nd Period 3rd Period

200 (FVA.05 ,3) = 630.4

200 (FVA.20 ,3) = 728

QUESTION: Then how can you truly lock-in a rate?

ANSWER: Buy a bond with no coupons - called zero coupon bonds.

QUESTION: Some find this attractive but is there a problem with being locked-in?

ANSWER: Yes. How about if rates rise. You lose out on earning extra interest on reinvested coupons.

QUESTION: Suppose you are asked to value a zero coupon bond. How do you set it up?

ANSWER: Only use the second term in the valuation formula given above.

QUESTION: Which bonds will appreciate assuming capital gains tax is reduced?

ANSWER: Discount bonds.