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Title: **Bond** **pricing** **theorems** Author: Cole Computer Centre Last modified by: Cole Computer Centre Created Date: 12/1/2001 5:20:57 PM Document presentation format

**BOND** VALUATION Dr. Rana Singh Associate Professor www.ranasingh.org CONTENTS Introduction **Bond** Returns coupon rate current yield spot interest rate yield to maturity yield to call **Bond** Prices **Bond** **Pricing** **Theorems** **Bond** Risks **Bond** Duration INTRODUCTION Bonds are Long-term fixed income securities.

... **THEOREMS** 5 **BOND** **PRICING** **THEOREMS** for a typical **bond** making periodic coupon payments and a terminal principal payment **BOND** **PRICING** **THEOREMS** 5 **BOND** **PRICING** **THEOREMS** THEOREM 1 If a **bond**’s market price increases then its yield must decrease conversely if a **bond**’s market price decreases ...

**Bond** Price Sensitivity to YTM Interest Rate Risk and Time to Maturity (Figure 7.2) **Bond** **Pricing** **Theorems** The following statements about **bond** **pricing** are always true. 1. **Bond** prices and market interest rates move in opposite directions. 2.

... YTM with Annual Coupons YTM with Semiannual Coupons Table 7.1, pg. 199 Current Yield vs. Yield to Maturity **Bond** **Pricing** **Theorems** Differences Between Debt and Equity The **Bond** Indenture **Bond** Classifications **Bond** Characteristics and Required Returns **Bond** Ratings ...

... Interest Rate Risk Figure 7.2 **Bond** **Pricing** **Theorems** **Bond** Classifications **Bond** Characteristics and Required Returns **Bond** Ratings – Investment Quality **Bond** Ratings - Speculative Government Bonds **Bond** Markets Treasury Quotations Clean vs. Dirty Prices ...

... to Maturity YTM with Annual Coupons YTM with Semiannual Coupons Table 7.1 Current Yield vs. Yield to Maturity **Bond** **Pricing** **Theorems** **Bond** Prices with a Spreadsheet Differences Between Debt and Equity The **Bond** Indenture **Bond** Classifications **Bond** Characteristics and Required Returns ...

Chapter 9 Debt Instruments Quantitative Issues Learning Objectives **Bond** Valuation Yield Measures Duration Managing **Bond** Portfolios Term Structure Factors affecting Prices/Yields Five **Bond** **Pricing** **Theorems** **Bond** prices move inversely to changes in interest rates The longer the maturity of a **bond** ...

... bonds that have more frequent trading will generally have lower required returns **Bond** **Pricing** **Theorems** Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, ...

... Relationship Between Coupon and Yield The **Bond** **Pricing** Equation Interest Rate Risk Figure 7.2 Computing Yield to Maturity YTM with Semiannual Coupons Current Yield vs. Yield to Maturity **Bond** **Pricing** **Theorems** Differences Between Debt and Equity The **Bond** Indenture **Bond** ...

The Interest Rate Risk of Bonds **Bond** **pricing** **Theorems** Implicit Interest on a Zero-coupon Solution Inflation and Returns Reading the Wall Street Journal Treasury Bonds Inflation and Returns Inflation and Returns, concluded ...

... (Treasury bonds and bills) are risky Treasury bonds are called ‘risk-free’ because they are not subject to default **Bond** **Pricing** **Theorems** Prices and yields move in opposite directions Holding other things constant ...

T8 **Bond** Price Sensitivity to YTM T9 Interest Rate Risk and Time to Maturity T10 **Bond** **Pricing** **Theorems** The following statements about **bond** **pricing** are always true. 1. **Bond** prices and market interest rates move in opposite directions. 2. When a ...

Interest Rate Risk – **Bond** **Pricing** **Theorems** Low coupon **bond** prices are more sensitive to i-rate changes than high coupon **bond** prices ex. A B Coupon ($) ...

* Note that the assumed starting date is January 2009. This, however, provides a good beginning point for illustrating **bond** **pricing** in ... Computing Yield to Maturity YTM with Annual Coupons YTM with Semiannual Coupons Current Yield vs. Yield to Maturity **Bond** **Pricing** **Theorems** Zero ...

FIVE **BOND** **PRICING** **THEOREMS**. **Bond** prices move inversely to changes in interest rates. The longer the maturity of a **bond**, the more price sensitive the **bond**. The price sensitivity of bonds to changes in interest rates increases as maturity increases, but at a decreasing rate.

... on the belief that the market is not so efficient some investors have the opportunity to earn above-average returns **BOND** **PRICING** **THEOREMS** 5 **BOND** **PRICING** **THEOREMS** The **theorems** deal with how **bond** prices move in response to changes in the bonds’ yields-to-maturity. for a typical **bond** ...

**Bond** **Pricing** **Theorems** The following statements about **bond** **pricing** are always true. **Bond** prices and market interest rates move in opposite directions When a **bond**’s coupon rate is (greater than / equal to / less than) the market’s required return, ...

Solve the **bond** **pricing** equation for the interest rate (i) such that price paid for the **bond** equals PV of remaining payments due under the **bond**. Computing yield to maturity, ... **Bond** **theorems** **Bond** prices are inversely related to **bond** yields.

Note also that the spreads widen as maturity increases. Malkiel’s **Bond** **Pricing** **Theorems** In 1961, Burton Malkiel published a paper where he proved five important **bond** **pricing** **theorems**: ...

Remember that increasing the rate decreases the **bond** value. **Bond** **Pricing** **Theorems** Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, ...

YTM = 4%*2 = 8% Table 7.1 **Bond** **Pricing** **Theorems** Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, ...

**Bond** Price Volatility Outline Price/Yield Relationship for Option Free Bonds **Bond** Price **Theorems** Price Volatility of Option Free Bonds Measures of **Bond** Price **Theorems** **Bond** Duration **Bond** Convexity Price/Yield Relationship A fundamental property of an option free **bond** is that the price of the **bond** ...

... .35 = 8%, which the same YTM computed earlier * **Bond** **Pricing** **Theorems**** Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, ...

**Bond** **Pricing** **Theorems** LO3 Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, you can estimate its YTM and use that to find the price of the second **bond**

Table 7.1 **Bond** **Pricing** **Theorems** Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, ...

... .35 = 8%, which the same YTM computed earlier **Bond** **Pricing** **Theorems** Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, ...

The Mechanics of **Bond** **Pricing** A fixed-rate **bond** is a contract detailing the par value, the coupon rate, and maturity date. ... **Bond** **Theorems** **Bond** yields vary inversely with changes in **bond** prices. **Bond** price volatility increases as maturity increases.

**Bond** Prices and Yields **Bond** Prices and Yields Our goal in this chapter is to understand the relationship between **bond** prices and yields. In addition, we will examine some fundamental tools that fixed-income portfolio managers use when they assess **bond** risk.

YTM = 4%*2 = 8% Table 7.1 – Summary of **Bond** Valuation **Bond** **Pricing** **Theorems** Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, ...

* Note that the assumed starting date is January 2008. This, however, provides a good beginning point for illustrating **bond** **pricing** in ... Computing Yield to Maturity YTM with Annual Coupons YTM with Semiannual Coupons Current Yield vs. Yield to Maturity **Bond** **Pricing** **Theorems** **Bond** ...

In general, from the **bond** **pricing** **theorems**, the longer the term-to-maturity and the lower the coupon rate, the greater the percentage price change for a given change in yield.

... .35 = 8%, which the same YTM computed earlier **Bond** **Pricing** **Theorems** Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, ...

... -to-maturity YTM with Annual Coupons YTM with Semiannual Coupons Table 7.1 Current Yield vs. Yield to Maturity **Bond** **Pricing** **Theorems** **Bond** Prices with a Spreadsheet Differences Between Debt and Equity The **Bond** Indenture **Bond** Classifications **Bond** Characteristics and Required ...

Interest Rate Risk . **Bond** **Theorems**. **Bond** **theorems** are statements about the math used in **bond** **pricing**. **Bond** prices are inversely related to interest rate movements.

**Bond** Basics, II. Two basic yield measures for a **bond** are its coupon rate and its current yield. The **Bond** **Pricing** Formula Recall: ... More on Yields Calculating Yields Yield to Call Interest Rate Risk and Malkiel’s **Theorems** Promised Yield and Realized Yield Interest Rate Risk and Maturity ...

Chapter 11 **Bond** Prices and Yields Chapter outline **Bond** basics Straight **bond** prices and YTM More on yields Interest rate risk and Malkiel’s **theorems**

... bonds usually carry a wider bid-ask spread * Malkiel’s Interest Rate **Theorems** Malkiel’s interest rate **theorems** provide information about how **bond** prices change as interest rates change Any good portfolio manager knows Malkiel ... **Bond** **pricing** and returns What is meant by the ...

... .35 = 8%, which the same YTM computed earlier **Bond** **Pricing** **Theorems** Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, ...

Solve the **bond** **pricing** equation for the interest rate (i) such that price paid for the **bond** equals PV of remaining ... 2012 John Wiley & Sons, Inc. * Copyright© 2012 John Wiley & Sons, Inc. * Copyright© 2012 John Wiley & Sons, Inc. * **Bond** **theorems** **Bond** prices are inversely related to **bond** ...

Copyright© 2006 John Wiley & Sons, Inc. * **Bond** **theorems** Copyright© 2006 John Wiley & Sons, Inc. * **Bond** prices are inversely related ... **Bond** **Pricing**: What is a **bond**? Copyright© 2006 John Wiley & Sons, Inc. * A form of loan—a debt security obligating a borrower to pay a lender ...

Chapter 10 **Bond** Prices and Yields Straight **Bond** Obligates the issuer of the **bond** to pay the holder of the **bond**: A fixed sum of money (principal, par value, or face value) at the **bond**’s maturity Constant, periodic interest payments (coupons) during the life of the **bond** (Sometimes) Special ...

**Bond** **Pricing** **Theorems**. There is a specific formula for finding **bond** prices on a spreadsheet. PRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis) YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis) Settlement and maturity need to be actual dates.

Fin 221: Chapter 5 **BOND** PRICES AND INTEREST RATE RISK * * The Time Value of Money Investing—in financial assets or in real assets—means giving up consumption until later.

**Bond** **Theorems** **Bond** Prices inversely related to rates. Volatility of L-T **bond** > S-T **bond**. Volatility of low-coupon **bond** > high-coupon **bond**. Example: zero-coupon **bond** What is reinvestment rate risk? Long-term bonds: High interest rate risk, low reinvestment rate risk.

... Rate **Theorems** Definition Theorem 1 Theorem 2 Theorem 3 Theorem 4 Theorem 5 * Definition Malkiel’s interest rate **theorems** provide information about how **bond** prices change as interest rates change Any ... Bonds Book Entry Bonds **Bond** **Pricing** and Returns **Bond** **Pricing** and ...

The Mechanics of **Bond** **Pricing** A fixed-rate **bond** is a contract detailing the par value, the coupon rate, ... Review of **Bond** **Theorems** **Bond** yields vary inversely with changes in **bond** prices. **Bond** price volatility increases as maturity increases.

Chapter 12 **Bond** Prices and the Importance of Duration We cannot gamble with anything so sacred as money. - William McKinley Outline Introduction Review of **bond** principles **Bond** **pricing** and returns **Bond** risk Introduction The investment characteristics of bonds range completely across the risk ...

to accompany FUNDAMENTALS OF CORPORATE FINANCE Fifth Edition Stephen A. Ross Randolph W. Westerfield Bradford D. Jordan CLICK MOUSE OR HIT SPACEBAR TO ADVANCE

**Bond** **Pricing** **Theorems** Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one **bond**, ...