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Chapter 1 Tuckman Lecture - CHAPTER 1 TUCKMAN BOND PRICES...

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CHAPTER 1 TUCKMAN BOND PRICES, DISCOUNT FACTORS, AND ARBITRAGE We’ll start off dealing with Treasury securities. Key assumptions: T-securities are default free in which any and all promised payments will be made Securities other than T-securities, such as from financially weak firms, may default on their obligations to pay. Here is regarded as credit risk. Whether a security is default free or not will affect its pricing TREASURY BOND QUOTATIONS The cash flows from most T-bonds are completely defined by: face or par value coupon rate maturity date For T-bonds, the interest is paid semi-annually. See Figure 1.1 on page 5. An investor purchasing a T-bond on a particular date must usually pay for the bond on the flowing business day. The seller of the bond on that date must usually deliver the bond on the following business day. The practice of delivery or settlement one day after a transaction is T + 1 settle . See Table 1.1 on page 5. Table 1.1 gives: coupon rate maturity date price of bond = prices expressed as a percent of face value The numbers after the hyphens denote 32nds, often called ticks. DISCOUNT FACTORS
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The discount factor for a particular term gives the value today, or the PV of one unit of currency to be received at the end of that term. Discount factor for t years is written d(t). EXAMPLE: If d(.5) = .97557, the PV of $1 to be received in 6 months is 97.557¢ The PV of $105 to be received in 6 month is .97557 X $105 = $102.43 To calculate the FV = $1/d(t). EXAMPLE: If $1 invested today grows to $1/d(.5) or $1 / .97557 = $1.025 in 6 months. Therefore, $1/d(.5) = FV of $1 invested for 6 months. To calculate the discount factor from a T-bond price if bond matures in 6 months: The first bond in Table 1.1. Step 1: 7 7/8% ÷ 2 = 3.9375 Step 2: 100 + 3.9375 = 103.9375 = FV Step 3: 101 + 12.75/32 = 101.3984 = PV Step 4: 101.3984 = 103.9375d (.5) Step 5: 101.3984/103.9375 = d (.5) = .97557 = The discount factor 101.3984 is the PV of the T-bond. 103.9375 is the FV of the T-bond. To calculate the discount factor from a T-bond price if bond matures in 1 year: The second bond in Table 1.1.
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