FINS2624 – Portfolio Management

Semester 1, 2011

LECTURE 1 – BOND PRICING

WHAT IS A BOND?

A bond is a claim on some fixed future cash flows. A commonwealth government bond (CGB) is a bond which pays semi-annual coupons, in which the maturity date/ coupon payment date is on the 15th of every month. A zero coupon bond is a bond with no coupons. The important information of a bond: 1. 2. 3. 4. 5. 6. • 1. 2. Transaction date: T Settlement date:T+2 Coupon payment dates Maturity date YTM Coupon rate Cum-interest or Ex-interest? If ex-interest If> 7 days to the next coupon payment-----> cum-interest

YIELD TO MATURITY

The Yield to Maturity (YTM) of a bond is: Interest rate that makes the present value of the bond’s payments equal to its price. Determined by the market, reflecting annual rate of return required by market.

The Relationship between YTM and Bond Price: YTM = Price AND Price Sensitivity YTM = Price AND Price Sensitivity When YTM = C = 10%, P = FV = $100 o C = YTM, P = FV – Par Bond o C < YTM, P < FV – Discount Bond o C > YTM, P > FV – Premium Bond

NO ARBITRAGE PRINCIPLE

An arbitrage is a set of trades that generate zero cash flows in the future, but a positive and risk free cash flow today. This is done through the violation of law of one price. An arbitrage trade is done by selling the real instrument, and buying a synthetic instrument (replicating strategies or portfolios). By constructing a synthetic bond and buy the under-priced real bond and selling 1

Cheryl Mew

FINS2624 – Portfolio Management

Semester 1, 2011

overpriced synthetic bond, an arbitrage opportunity exists, where people can earn money, whilst not incurring any risk. In Fins 2624, we employ the No Arbitrage Principle – i.e. same bonds will have the price.

BOND PRICING

The value of a bond (like any financial security) is the present value of all future cash flows. A bond produces two different cash flows: Coupon payments Face value (paid at maturity)

Thus all we have to do is find the present value of all coupon payments and the face value!

P0 = (

1

1+

)+

1+

C = Coupon r = required rate of return (YTM) t = time periods Make sure that you use the correct periodic required rate of return and periods e.g. A 5 year CGB bond that pays coupons on a semi-annual basis, has an annual required rate of return of 20%. “t” in this case will be 10 *5 x 2+ and “r” in this case will be 10% *20%/2+ since payments are made semiannually!!!

EX-INTEREST BONDS

CBG Bonds are ex-interest if the settlement date (2 days after transaction date) is within 7 days of the next coupon payment. CALCULATING THE PRICE OF AN EX-INTEREST BOND

1.

Calculate the Value of the Bond as at Coupon Date = P’

P’ =

(

1

1+

)+

1+

2. 3.

Find fraction of period before coupon payment = Discount P’ to find the Price as at settlement date = P

f = (coupon– settlement date) / total days in period

������′ 1+������ ������

P=

2

Cheryl Mew

FINS2624 – Portfolio Management

Semester 1, 2011

QUOTED PRICE OF EX-INTEREST BOND By convention, the market does not quote the settlement price P. This is because, if we were the buyer, and the interest was continuous, we would get some of the interest, even though it’s ex-interest. Hence, the market price = Padj

Padj = ������ + ������������������. ������ CUM-INTEREST BONDS

CBG Bonds are cum-interest if the settlement date (2 days after transaction date) is more 7 days until the next coupon payment. CALCULATING THE PRICE OF A CUM-INTEREST BOND

1.

Calculate the Value of the Bond as at Coupon Date = P’

P’ =

(

1

1+

)+

1+

2. 3.

Find fraction of period before coupon payment =

f = (coupon– settlement date) / total days in period

������′ +������������������ 1+������ ������

Discount P’ + the next coupon to find the Price as at settlement date = P

P=

QUOTED PRICE OF EX-INTEREST BOND By...