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

Y = Y + I + P

• maturity U.S. Treasury yield.
• n r where Y n is the nominal yield, Y r is the real yield - yield on U.S. Treasury inflation-indexed bonds (see WSJ), I is the expected inflation rate over the life of the bond - regular Treasury yield minus inflation-indexed yield, P is the risk premium - bond yield minus same

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 Inflation

Note: 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 BONDS

General 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 & LOCAL

QUESTION: How do you know if its best to buy tax exempt or taxable bonds?

Y T = Taxable yield

TE

Y

= Tax exempt yield

T = Tax rate

Y TE = Y T (1 - T) or, Y = Y / (1 - T)

T TE

=> T = 1 - (Y TE / Y T )

If we know Y TE and Y T we can estimate the "indifferent" T implicit marginal buyer's tax rate



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

Y AT = Y T (1 - T p )

Therefore, if your T p >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: Y AT = .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 maturity assumes coupons reinvested at YTM rate.

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

B C k C k C k Par k n n n n = + + + + + + + 1 2 2 1 1 1 1 ( ) ( ) ( ) ( )

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



BOND PRICING

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

B E C k E C k E C k E Par k n n n n = + + + + + + + ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 1 1 1 1

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

REALIZED YIELD - CALCULATED AFTER THE FACT

Assume you sell after 2 periods - find k in

B C k C k B k p s = + + + + + 1 2 2 2 1 1 1 ( ) ( )

B p = Purchase Price B s = Sales Price

This assumes coupons reinvested at k

CURRENT YIELD

Y C P c m = = coupon current market price




BOND VALUATION

      + +       + -= n n k Par k k k Coupon B ) 1 ( 1 ) 1 ( 1 1

= Coupon[PVA k,n ] + Par[PV k,n ]

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

    + -= n n k k k k PVA ) 1 ( 1 1 ,

compute a present value annuity factor  

    + = n n k k PV ) 1 ( 1 ,

  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




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 market with 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, semiannually, 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 3 years maturity and you hold it for three years are you sure to earn 20%?

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

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[PV k,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)[PV k,3 ] = 1630.5[PV k,3 ]

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




Suppose you buy a20 percent coupon bond at par; and immediately after you the market yield falls to5 to hold the bond until maturity, your realized falls because reinvested coupons earn less. buy, plan yield




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.