adms 4504 - lecture 1, part 1

7/25/2019 ADMS 4504 - Lecture 1, Part 1

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Week 1 (Part I)

Features of DebtSecurities


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Plan of the lecture

Some basic features of a bond

Coupon rate structures

Floating rate securities

Accrued interest

Options embedded in a bond Borrow funds to purchase bonds (repo)


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Basic features of a bond

Bonds can have anypar value The market practice is to quote the price of a

bond as a percentageof its par value

Example: Suppose a bond has a par value of$1,000

If the bond sells at $1,000, the bond price isquoted as 100, i.e., 100% of par value

If the bond price is $950, the bond is said to beselling at 95,i.e., 95% of par value

And if the bond price is $1,050, the bond is tradingat 105, i.e., 105% of par value


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A bond is said to be trading at adiscountif it sells belowits par value, e.g., at 95

A bond is trading at parif it sells atits parvalue, i.e., at 100

A bond is said to be trading at a premiumif it sells aboveits par value, e.g., at 105

A bond sells above or below its par valuedepending on the levels of interest rates


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In the United States, when computing thedollar price of a bond, we first compute theprice per US$1 of par value, which is thenmultiplied by the bond par valueto get thedollar priceof the bond

Quoted price Price per US$1 of par value Par value Dollar price

(1) (2) (3) (4) = (2) (3)86 1/4 0.86250 $50,000 $43,125

110 3/8 1.10375 $200,000 $220,750


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Couponis the annualinterestpayment made to abondholder

Coupon rate(also known as nominal rate) is anannualrate

The coupon rate is specified for a bond, along with itsmaturity date Example: 5s of 12/16/2015 means the coupon rate is 5%

In both Canada and the U.S., bonds typically pay coupons in

two equal semiannualinstallments

125$500,2$%5

500,2$%,5

coupon

valueparratecoupon:Example

valueparratecouponCoupon


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Step up notes (continued) Multiple step up note: where there are

multiple (i.e., more than one) increases in thecoupon rate

Example: A three year bond has the followingcoupon schedule

5% from 1/1/2012 to 12/31/2012

5.25% from 1/1/2013 to 12/31/2013

5.60% from 1/1/2014 to 12/31/2014


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Deferred coupon bonds

Bonds whose interest payments are deferredfor several years, i.e., nointerest paymentduring the deferred period

At the end of the deferred period, the issuerpays higher periodic interests (than that

would otherwise have been paid) to thebondholder as a compensation


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The quoted marginis the additionalamount paid above the reference rate

Example: The coupon formula is

A basis pointis 0.01% or 0.0001 So 100 basis points = 1%, 120 basis points = 1.2%

etc.

Suppose the U.S. Treasury bill rate is 4%, thenthe coupon rate = 4% + 1.2% = 5.2%

Coupon rate = U.S. Treasury bill rate + 120 basispoints


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The quoted margin could be a negativevalue


Suppose the U.S. AAA rate is 5%, then the

coupon rate = 5% - 0.6% = 4.4%

Coupon rate = U.S. AAA rate -60 basispoints


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Capsand floors A capis the maximumcoupon rate paid on a

floater


and the cap is 10%

Suppose the reference rate is 8.5%, then thecoupon rate is 10%, not10.5% (= 8.5% + 2%)

Coupon rate = reference rate + 200 basis points


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Caps and floors (continued) A flooris the minimumcoupon rate paid on a

floater


and the floor is 3%

Suppose the reference rate is 3.25%, then thecoupon rate is 3%, not2.75% (= 3.25% - 0.5%)

Coupon rate = reference rate -50 basis points


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In-class exercise 1 Fill in the table below. The coupon

formula is: reference rate + 60 basis pointswith a capof 5.50%

Reference rate Coupon rate

First reset date 4.50% ?

Second reset date 5.00% ?

Third reset date 4.85% ?


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In-class exercise 2 Fill in the table below. The coupon

formula is: reference rate + 25 basis pointswith a floorof 2.75%

Reference rate Coupon rateFirst reset date 3.00% ?Second reset date 2.80% ?

Third reset date 2.25% ?


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Inverse floater(or reverse floater) Floating rate securities where the coupon rate

moves in the oppositedirection from thereference rate

The coupon formula is:

where Kand Lare fixed values

Example: Suppose Kis 25%, Lis 2.5, the reference

rate is 8%, then the coupon rate is 25% - 2.5 8% =5%

A cap and/or floor can be imposed on an inversefloater

Coupon rate = KL (reference rate)


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Accrued interest

Accrued interestis the interest earned by thebond seller between the last coupon paymentdateand the bond settlement date

Lastcouponpayment

date

(A)

Settlement date(B)

Nextcoupon

paymentdate

(C)

Accrued interest earnedby the seller

Interest earned by the buyer


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Embedded options

Options beneficial to issuers include: The right to call(i.e., repurchase) a bond at a

specified call price Call risk

Theright to prepayprincipal above thescheduled principal payment on, e.g., mortgagebacked securities Prepayment risk

And the capon a floater

Bondholders do notlike these options. Sowhat would happen to the bond price?


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Embedded options

Options beneficialto lendersinclude: The right to put(i.e., sell back) a bond at a

specified put price

The right to convertor exchangea bond for anumber of common shares

Convertible bonds

And the flooron a floater

Embedded options can significantly impactthe bond prices, as we will see in laterchapters


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Borrow funds to

purchase bonds

The investor(A)

Sellssecurities

Receives

cash

Buys back thesame securities

Pays (a higher)

repurchase priceincluding reporate

Time 0 Time 1

Repurchase agreement(repo)

The

Buyer(B)

The

Buyer(B)


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Repo

Repo is a collateralizedloanbetween theinvestor (A) and the buyer (B): A effectivelyuses securities as collateralto borrowfunds from B to finance her purchase of

some other assets Overnight repo: the term of the loan is one

day

Term repo: the term of the loan is more thanone day

The interest rate on the loan is called therepo rate


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Repo

General collateral repo rate

Special repo rate

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Repo

Repo (from the investor (A)s perspective):agrees to sell the securities and buy themback, i.e., borrow funds

Reverse repo (from the buyer (B)sperspective): agrees to buy the securitiesfirst and sell them back later, i.e., make aloan

Repo is primarily for institutional investorsto meet their short term financing needs


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Repo

Example: How much does a mutual fundneed to pay back an investment bank on a

14 day $94.8 million 3% repo loan?

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million9106.94$)360

14%31(million8.94$

adms 4504 - lecture 1, part 1

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