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FINS 2624 Study Notes Compressed - Cheryl Mew FINS2624...

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Cheryl Mew FINS2624 Portfolio Management Semester 1, 2011 1 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 15 th of every month. A zero coupon bond is a bond with no coupons. The important information of a bond: 1. Transaction date: T 2. Settlement date:T+2 3. Coupon payment dates 4. Maturity date 5. YTM 6. Coupon rate Cum-interest or Ex-interest? 1. If<=7 days to the next coupon payment-----> ex-interest 2. 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
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Cheryl Mew FINS2624 Portfolio Management Semester 1, 2011 2 P = 𝑃 1+ 𝑟 𝑓 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! P 0 = ( 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. Find fraction of period before coupon payment = f = (coupon settlement date) / total days in period 3. Discount P’ to find the Price as at settlement date = P
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Cheryl Mew FINS2624 Portfolio Management Semester 1, 2011 3 P adj = 𝑃 + 𝐶𝑃𝑃 . 𝑓 P = 𝑃 + 𝐶𝑃𝑃 1+ 𝑟 𝑓 P adj = 𝑃
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