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Chapter2 - FIXED-INCOME SECURITIES Chapter 2 Bond Prices...

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Chapter 2 Bond Prices and Yields FIXED-INCOME SECURITIES
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Outline Bond Pricing Time-Value of Money Present Value Formula Interest Rates Frequency Continuous Compounding Coupon Rate Current Yield Yield-to-Maturity Bank Discount Rate Forward Rates
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Bond Pricing Bond pricing is a 2 steps process Step 1: find the cash-flows the bondholder is entitled to Step 2: find the bond price as the discounted value of the cash-flows Step 1 - Example Government of Canada bond issued in the domestic market pays one-half of its coupon rate times its principal value every six months up to and including the maturity date Thus, a bond with an 8% coupon and $5,000 face value maturing on December 1, 2005 will make future coupon payments of 4% of principal value every 6 months That is $200 on each June 1 and December 1 between the purchase date and the maturity date
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Bond Pricing Step 2 is discounting = + = T t t t r F P 1 0 ) 1 ( Does it make sense to discount all cash-flows with same discount rate? Notion of the term structure of interest rates – see next chapter Rationale behind discounting: time value of money
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Time-Value of Money Would you prefer to receive $1 now or $1 in a year from now? Chances are that you would go for money now First, you might have a consumption need sooner rather than later That shouldn’t matter: that’s what fixed-income markets are for You may as well borrow today against this future income, and consume now In the presence of money market, the only reason why one would prefer receiving $1 as opposed to $1 in a year from now is because of time-value of money
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Present Value Formula If you receive $1 today Invest it in the money market (say buy a one-year T-Bill) Obtain some interest r on it Better off as long as r strictly positive: 1+r>1 iif r>0 How much is worth a piece of paper (contract, bond) promising $1 in 1 year? Since you are not willing to exchange $1 now for $1 in a year from now, it must be that the present value of $1 in a year from now is less than $1 Now, how much exactly is worth this $1 received in a year from now? Would you be willing to pay 90, 80, 20, 10 cents to acquire this dollar paid in a year from now? Answer is 1/(1+r) : the exact amount of money that allows you to get $ 1 in 1 year Chicken is the rate, egg is the value
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Interest Rates Specifying the rate is not enough One should also specify Maturity Frequency of interest payments Date of interest rates payment (beginning or end of periods) Basic formula After 1 period, capital is C 1 = C 0 (1+ r ) After n period, capital is C n = C 0 (1+ r ) n Interests : I = C n - C 0 Example Invest $10,000 for 3 years at 6% with annual compounding Obtain $11,910 = 10,000 x (1+ .06) 3 at the end of the 3 years Interests: $1,910
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