V: Bonds 15: Duration.

Slides:

Advertisements

Similar presentations

V: Bonds 15: Duration. Chapter 15: Duration © Oltheten & Waspi 2012 Duration Concept Calculation Duration and Price Volatility.

Advertisements

Bond pricing theorems. Bond convexity The mathematical relationship between bond yields and prices.

Contents Method 1: –Pricing bond from its yield to maturity –Calculating yield from bond price Method 2: –Pricing bond from Duration –Pricing bond from.

Bond Price Volatility.

Chapter 11 Managing Fixed-Income Investments 11-2 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Managing Fixed Income Securities: Basic Strategies.

Hossein Abdoh Tabrizi Maysam Radpour June Table of Contents Bonds; risk & return tradeoff Maturity effect; interest rate volatility risk Duration.

McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Managing Bond Portfolios CHAPTER 11.

More on Duration & Convexity

1 Applying Duration A Bond Hedging Example Global Financial Management Fuqua School of Business Duke University October 1998.

V: Bonds 16: Immunization. Chapter 16: Immunization © Oltheten & Waspi 2012 Immunization  Concept  The sad story of John Q. Investor  How to immunize.

Chapter 4 Bond Price Volatility.

Fixed Income Derivatives MGT 4850 Spring 2008 University of Lethbridge.

Method 3: Pricing of Coupon Bond Pricing of coupon bond without knowing the yield to maturity.

Managing Bond Portfolios

Pricing Fixed-Income Securities. The Mathematics of Interest Rates Future Value & Present Value: Single Payment Terms Present Value = PV  The value today.

Managing Bond Portfolios

Managing Bond Portfolios

Pricing Fixed-Income Securities

Yields & Prices: Continued

Copyright 2014 by Diane S. Docking1 Duration & Convexity.

©2009, The McGraw-Hill Companies, All Rights Reserved 3-1 McGraw-Hill/Irwin Chapter Three Interest Rates and Security Valuation.

Copyright 2015 by Diane S. Docking 1 Bond Valuation.

FINC4101 Investment Analysis

V: Debt Markets 12: Prices and Yields. Chapter 12: Prices and Yields Time Value of Money © Oltheten & Waspi 2012.

Managing Bond Portfolios

Managing Bond Portfolio

Valuing risky debt The story teller makes no choice, soon you will not hear his voice. His job is to shed light and not to master. – Garcia, Hunter.

Chapter 11 Managing Fixed-Income Investments Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Managing Fixed Income Securities: Basic Strategies.

1 FIN 2802, Spring 08 - Tang Chapter 16: Managing Bond Portfolios Fina2802: Investments and Portfolio Analysis Spring, 2008 Dragon Tang Lecture 12 Managing.

BOND PRICE VOLATILITY. PRICE YIELD PRICE YIELD RELATIONSHIP CONVEX SHAPE.

Duration and Convexity

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 1 Chapter 10.

Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Chapter Three Interest Rates and Security Valuation.

BOND VALUATION All bonds have the following characteristics: 1. A maturity date- typically years. 2. A coupon rate- the rate of interest that the.

©2009, The McGraw-Hill Companies, All Rights Reserved 3-1 McGraw-Hill/Irwin Chapter Three Interest Rates and Security Valuation.

Chapter 8 Jones, Investments: Analysis and Management

1 Bond Portfolio Management Term Structure Yield Curve Expected return versus forward rate Term structure theories Managing bond portfolios Duration Convexity.

Chapter 5 part 2 FIN Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2.

CHAPTER ELEVEN Bond Yields and Prices CHAPTER ELEVEN Bond Yields and Prices Cleary / Jones Investments: Analysis and Management.

V: Bonds 13: Buying and Selling Bonds. Chapter 13: Buying and Selling Bonds © Oltheten & Waspi 2012 Buying and Selling Bonds  Treasury Notes & Bonds.

CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin.

Chapter 18 - The Analysis and Valuation of Bonds.

Fundamentals of Corporate Finance Chapter 6 Valuing Bonds Topics Covered The Bond Market Interest Rates and Bond Prices Current Yield and Yield to Maturity.

Problems Consider the following Bond Structure Face ValueInterest Rate (%) Maturity (Years) Current Price

Chapter 11 Managing Bond Portfolios. Interest Rate Sensitivity (Duration we will cover in Finc420) The concept: Any security that gives an investor more.

1 Not To Be Naïve about Duration 1.The duration D we have been discussing also known as Macaulay duration. 2.First derivative of price-yield curve is and.

Comm W. Suo Slide 1. comm W. Suo Slide 2  Active strategy Trade on interest rate predictions Trade on market inefficiencies  Passive.

Bond Price Volatility Chapter 4.

Fundamentals of Corporate Finance Chapter 6 Valuing Bonds Topics Covered The Bond Market Interest Rates and Bond Prices Current Yield and Yield to Maturity.

Fixed Income Kuliah 8.

Fixed Income portfolio management: - quantifying & measuring interest rate risk Finance 30233, Fall 2010 S. Mann Interest rate risk measures: Duration.

McGraw-Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. Managing Bond Portfolios CHAPTE R 10.

Chapter 11 Managing Bond Portfolios 1. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest Rate Risk A change in market.

Interest Rates and Bond Valuation Chapter Seven. Problem Set - Bonds 1.You want to purchase a 182 day Treasury Bill with a $500,000 face value. If the.

FIXED INCOME MANAGEMENT1 MEASURING YIELD. FIXED INCOME MANAGEMENT2.

McGraw-Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. Managing Bond Portfolios CHAPTER 10.

Intermediate Investments F3031 Duration Duration is an empirical method of measuring the true life of a bond portfolio –Comes into play in determining.

Assignment tips.

Managing Bond Portfolios

Copyright © 1999 Addison Wesley Longman

13: Buying and Selling Bonds

Managing Bond Portfolios

Duration and convexity for Fixed-Income Securities

14: Term Structure of Interest Rates

III: Money Market 10: Money Market I.

Managing Bond Portfolios

V: Debt Markets 12: Prices and Yields.

Bonds and Their Valuation Supplement

IV. Fixed-Income Securities

Presentation transcript:

V: Bonds 15: Duration

Duration Concept Calculation Duration and Price Volatility

Fundamental Risk Reinvestment Risk: Price Risk: The risk that coupons, paid out of the bond, cannot be reinvested at the same YTM. Price Risk: The risk that the price of the bond will fall Note that this is a risk only if we sell the bond before it matures. There is no price risk if we hold the bond to maturity.

Duration Duration: Weighted by Net Present Value average term to maturity. Duration can be calculated on any cash flow structure.

A Tale of Two Bonds $1000 5% Annual Coupon $50 Price: $918.00 $1000 $90 Price: $1,082.00 © Oltheten & Waspi 2012

A Tale of Two Bonds Capital Gain -1.56% Capital Gain 1.73% Income Yield: 8.32% Income Yield: 5.45% 5 year capital gain = - 7.58% Annual capital gain = - 1.56% 5 year capital gain = 8.93% Annual capital gain = 1.73% Yield to Maturity: 7.00% Yield to Maturity: 7.00% © Oltheten & Waspi 2012

How much of my investment faces a reinvestment risk every year? A Tale of Two Bonds How much of my investment faces a reinvestment risk every year? $50 $1050 $90 $1090 © Oltheten & Waspi 2012

Calculating Duration I 5 year 5% Annual Coupon Bond at 7% T Cash Flow NPV NPV/P 1 year $50 $46.73 5.09% 2 years $43.67 4.76% 3 years $40.81 4.45% 4 years $38.14 4.16% 5 years $1050 $748.64 81.55% Total NPV =$918.00 100.00% © Oltheten & Waspi 2012

A Tale of Two Bonds How much of each bond must be reinvested after 1,2,3,4 and 5 years? © Oltheten & Waspi 2012

5 year 5% Annual Coupon Bond at 7% Calculation 5 year 5% Annual Coupon Bond at 7% T Cash Flow NPV NPV/P Duration T*NPV/P Convexity D*(T+1) 1 year $50 $46.73 5.09% .050903 .101806 2 years $43.67 4.76% .095146 .285439 3 years $40.81 4.45% .133383 .533530 4 years $38.14 4.16% .166209 .831044 5 years $1050 $748.64 81.55% 4.077553 24.465317 Total NPV =$918.00 100.00% 4.523 yrs 26.217 yrs2 © Oltheten & Waspi 2012

A Tale of Two Bonds © Oltheten & Waspi 2012

Duration & Price Risk Volatility: Change in the price of the bond due to a change in market yield.

Duration & Volatility 5% annual bond: 9% annual bond: 4.523 yrs * 1% = 4.227% 1.07 Modified Duration is 4.227 years If Yd1% then P4.227% If Yd 1% then P4.227% 9% annual bond: 4.272 yrs * 1% = 3.993% 1.07 Modified Duration is 3.993 years If Yd1% then P3.993% If Yd 1% then P3.993% © Oltheten & Waspi 2012

Price Yield Curve

Price Yield Curve 5 year 5% annual coupon 7% yield

Price Yield Curve 20 year 6% semi-annual coupon 8% yield

Calculating Duration II Calculate the duration and convexity of a semi-annual bond $10,000 6% coupon December 31, 2017 Settles March 2, 2014 102.000

Calculating Duration II Base Price: 62/180 days Accrued Interest: Invoice Price: YTM: 5.41186% $10,200.00 $103.33 $10,303.33 © Oltheten & Waspi 2012

Calculating Duration II © Oltheten & Waspi 2012

Exercise Calculate the duration and convexity of a semi-annual bond $1000 6% coupon 2.5 years to maturity Priced to yield 8%

1 1/2 year 6% Semi-Annual Coupon Bond at 8% Semi-Annual Bonds 1 1/2 year 6% Semi-Annual Coupon Bond at 8% T Cash Flow NPV NPV/P Duration T*NPV/P Convexity D*(T+1) 1 2 3 4 5 © Oltheten & Waspi 2012

Volatility Duration: First derivative of the Price Yield Curve .D = dP/dY Modified duration is the slope of the Yield Curve Convexity: Second derivative of the Price Yield Curve .C = dP2/d2Y Curvature of the Yield Curve

Volatility Taylor Expansion: Modified Duration Modified Convexity Yield at which duration was calculated Modified Duration Modified Convexity

Volatility $1000 Duration: 2.355 yrs 6% semi-annual coupon 2 ½ years to maturity Priced to Yield 8% Duration: 2.355 yrs Modified D: 2.355 =2.264 (1.04) Convexity: 6.922 yrs2 Modified C: 6.922 = 6.400 (1.04)2 © Oltheten & Waspi 2012

Δ Yield +200 basis points Duration only Convexity Correction Total -2.355 (+.02) + 1 6.922 (+.02)2 = (1.04) 2 (1.04)2 © Oltheten & Waspi 2012

Δ Yield -200 basis points Duration only Convexity Correction Total -2.355 (-.02) + 1 6.922 (-.02)2 = (1.04) 2 (1.04)2 © Oltheten & Waspi 2012

Price Yield Curve Convexity corrections are always positive Price effect is asymmetric

Volatility Yields increase by 2% - 4.5288% + 0.128% = - 4.4009% Yields decrease by 2% + 4.5288% + 0.128% = + 4.46568% Convexity corrections are always positive Price effect is asymmetric

Spreadsheet Exercise 15-1 15-2

Bonds IV © Oltheten & Waspi 2012