SS15 Fixed-Income: Basic Concepts SS15 Fixed-Income: Analysis of Risk

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1 SS15 Fixed-Income: Basic Concepts SS15 Fixed-Income: Analysis of Risk SS 15 R52 FI Securities: Defining Elements R53 FI Markets: Issuance, Trading, and Funding R54 Introduction to FI Valuation SS 16 R55 Understanding FI Risk and Return R56 Fundamentals of Credit Analysis

2 Framework for Fixed Income Basic Concepts Valuation Return Risk Slide 2 Securities Markets Yield Measures Yield Spreads Interest Rate Risk Credit Risk Liquidity Risk

3 Contents for Sept. 14 Overview of a Fixed-Income Security Bonds with Contingency Provisions Callable Bonds Putable Bonds Convertible Bonds Fixed-Income Valuation Pricing Bond with a Market Discount Rate Pricing Bond with Spot Rates Relationships Between Bond Price and Bond Characteristics Flat Price, Accrued Interest, and Full Price Sources of Return Interest Rate Risk Slide 3

4 Overview of a Fixed-Income Security Fixed-Income Security An instrument that allows governments, companies, and other types of issuers to borrow money from investors. A financial obligation of an entity that promises to pay a specified sum of money at a specified future dates. FI Security Issuers - Borrowers FI Security Holders/Investors Lenders Slide 4

5 Overview of a Fixed-Income Security Basic Features of a Bond Issuer Maturity Par value Coupon rate and frequency Currency denomination Slide 5

6 Callable Bonds Callable bond = option-free bond call option Options for issuers The right to redeem all or part of the bond before the specified maturity date. Protect issuers against a decline in interest rate. Market interest rates fall. Issuer s credit quality improves. Obligations for investors Higher level of reinvestment risk Higher yield and lower price Slide 6 Call Callable Bond

7 Putable Bonds Putable bond = option-free bond + put option Options for bondholders The right to sell back bond to the issuer before maturity. Increasing int. rate decreasing bond price benefit bondholders because of the predetermined price Increasing int. rate higher reinvestment income Obligations for issuers Higher price and lower yield Slide 7 Putable Bond Put

8 Convertible Bond Convertible bond = straight bond + embedded equity call option Option for bondholders to convert bond into a specified number of the issuer s shares. Advantages for bondholders Downside protection & equity upside potential Advantages for issuers Reduced interest expense Eliminating debt once converted Especially attractive for newer companies Disadvantages for existing shareholders Dilution of interests Slide 8

9 Convertible Bond Conversion price The price at which the convertible bond can be converted into shares. Conversion ratio The number of common shares that each bond can be converted into. = par value conversion price Slide 9

10 Convertible Bond Conversion value = current share price conversion ratio Conversion premium = convertible bond price - conversion value Conversion parity Parity: conversion value = convertible bond s price Below parity: conversion value < bond price Above parity: V conversion > P bond value/parity value Slide 10

11 Convertible Bond Example: Convertible Bond A convertible bond with the par value of $1,000 is trading at $900 now. It could be converted into common shares at the price of $50 per share. Now the market price of the common share is $60 per share. Conversion price = $50 Conversion ratio = $1000 $50 = 20 Conversion value = $60 20 = $1,200 Conversion premium = $900 - $1,200 = -$300 Conversion parity: above parity Slide 11

12 Pricing Bond with a Market Discount Rate Cash flows Coupon payments & Principal repayment Discount Rate Mkt. discount rate/required yield/required Rate of Return Valuation PV = present value/price of the bond PMT = coupon payment per period FV = future value paid at maturity/par value r = mkt. discount rate/required rate of return N = number of periods to maturity Slide 12 PV N i PMT FV i 1 (1 r) (1 r) N

13 Pricing Bond with a Market Discount Rate Example 1: Annual-Payment Bond Valuation The coupon rate on a bond is 4% and the payment is made once a year. If the time-to-maturity is five years and the market discount rate is 6%, calculate the price of the bond per 100 of par value. Cash flows Coupons Principal Discount Discount periods Discount rate Slide 13 Cash Flows 2 ND FV N=5 I/Y=6% PMT=4 FV=100 CPT PV= Discounting Factor 4 (1+6%) 4 (1+6%) 2 4 (1+6%) 3 4 (1+6%) (1+6%) 5

14 Pricing Bond with a Market Discount Rate Coupon rate Indicate interests given by issuers. Mkt. discount rate Reflect interest required by investors to pay full par value for the bond. Relationship Coupon rate = mkt. discount rate Price = Par Value Coupon rate < mkt. discount rate Price < Par Value (discount) Coupon rate > mkt. discount rate Price > Par Value (premium) Slide 14

15 Pricing Bond with a Market Discount Rate Example 2: Annual Compounding Zero-Coupon Bond Valuation A zero coupon bond matures in 15 years. At a market discount rate of 4.5% per year and assuming annual compounding. Calculate the price of the bond per 100 of par value. Example 3: Semi-Annual-Payment Bond Valuation The coupon rate on a bond is 8% and the payments are made semiannually on 15 June and 15 December. If there are three years to maturity and the market discount rate is 3%, calculate the bond price. Example 4: Semi-Annual Compounding Zero-Coupon Bond Valuation A semi-annual pay zero coupon bond matures in 15 years. The market discount rate of 4.5% per year. Calculate the price of the bond per 100 of par value. Slide 15

16 Pricing Bonds with Spot Rates Spot Rates YTM on zero-coupon bonds Bootstrap Method Value a bond as a package of cash flows. View each cash flow as a zero-coupon bond Discount each cash flow at spot rate. No-arbitrage value Sum of PVs of zero-coupon bonds. PV PMT PMT PMT FV... (1 Z ) (1 Z ) (1 Z ) N N Slide 16

17 Pricing Bonds with Spot Rates Example: Bond Valuation with Spot Rates Calculate the price for a four-year 3% annual coupon payment bond with the par value of $100, using spot rates. And calculate the YTM for the bond. Maturity Slide 17 Spot Rates 1 year 0.39% 2 years 1.40% 3 years 2.50% 4 years 3.60% Period CFs Disc. Factor Period CFs Disc. Factor Price Calculation (1.0039) (1.0140) (1.0250) (1.0360) YTM Calculation (1 r) (1 r) (1 r) (1 r) r 3.516%

18 Relationships Between Bond Price and Bond Characteristics Four Relationships about the change in the bond price given the market discount rate change are Inverse Effect Convexity Effect Coupon Effect Maturity Effect The change in the bond price over time for a given market discount rate Constant-yield price trajectory Slide 18

19 Relationships Between Bond Price and Bond Characteristics Slide 19

20 Relationships Between Bond Price and Bond Characteristics Inverse Effect Mkt. discount rate bond price N PMT FV PV i N i 1 (1 r) (1 r) Convexity Effect The percentage price change is greater when the market discount rate goes down than when it goes up. Price appreciation > price decline for a same percentage of price change Slide 20

21 Relationships Between Bond Price and Bond Characteristics Price Option-Free Bond Par Coupon Rate Market Yield Slide 21

22 Relationships Between Bond Price and Bond Characteristics Coupon Effect Coupon rate price volatility Lower-coupon bonds have more price volatility than highercoupon bonds, other things being equal. Maturity Effect Generally, longer-term bonds have more price volatility than shorter-term bonds, other things being equal. Exceptions occur for low-coupon (but not zero-coupon), long-term bonds trading at a discount. Slide 22

23 Relationships Between Bond Price and Bond Characteristics Constant-Yield Price Trajectory/Pull to Par Bond price approaches par value as time passes. At maturity date bond value/price = par value bond selling at a premium price declines bond selling at a discount price increases bond selling at par value unchanged price Premium Slide 23 Par Discount Premium Bond Par Bond Discount Bond Maturity

24 Relationships Between Bond Price and Bond Characteristics Example: Bond Price and Bond Characteristics An investor is considering the following six annual coupon payment government bonds. Which bond will go up in price the most on a percentage basis if all yields go down from 5% to 4.9%? Which bond will go down in price the least on a percentage basis if all yields go up from 5% to 5.1%? Slide 24 Bond Coupon Rate Maturity YTM A 0% 2 years 5% B 5% 2 years 5% C 8% 2 years 5% D 0% 4 years 5% E 5% 4 years 5% F 8% 4 years 5%

25 Flat Price, Accrued Interest, and Full Price Accrued interest The interest earned by the seller but received by the buyer between the last coupon payment date and the settlement date. t AI coupon payment per period T t=days between last coupon payment and the settlement date T=number of days in the coupon period Slide 25

26 Flat Price, Accrued Interest, and Full Price Full price and Flat Price Accrued Interest T Flat Price Full Price P t C C+P Accrued interest increases every day. Flat prices are quoted to not misrepresent the daily increase in the full price as a result of interest accruals. Slide 26 P Full

27 Flat Price, Accrued Interest, and Full Price Full price and Flat Price PV Full PMT PMT PMT FV... 1 t/ T 2 t/ T N t/ T (1 r) (1 r) (1 r) Full PV PV (1 r) t/ T Flat Full PV PV Accrued Interst Slide 27

28 Flat Price, Accrued Interest, and Full Price Example: Full Price, Accrued Interest, and Flat Price Bond G, described in the exhibit below, is sold for settlement on 16 June Annual Coupon 5% Coupon Pmt Frequency Semiannual Interest Payment Dates 10 April and 10 Oct. Maturity Date 10 Oct Day Count Convention 30/360 Annual YTM 4% Calculate Full Price, Accrued Interst, and Clean Price on the settlement date of 16 June Slide 28

29 Flat Price, Accrued Interest, and Full Price T P t C C+P P Full N=5 I/Y=2% PMT=2.5 FV=100 PV= T=180 t=66 PV Full =PV (1+r) 66/180 = (1+2%) 66/180 = Accrued Interest=PMT (t/t)=2.5 (66/180)=0.92 PV Flat =PV Full Accrued Interest= = Slide 29

30 Sources of Return Receipt of promised coupon and principal payments on the scheduled dates. Reinvestment of coupon payments Amortization of discount or premium as the bond s carrying value pulls to par Potential capital gains or losses on the sale of the bond prior to maturity Slide 30

31 Sources of Return Constant-Yield Price Trajectory:the relationship between bond price and time based on the YTM when the bond is purchased Carrying Value Amortization of Discount Slide 31

32 Sources of Return Carrying Value The price implied by any point on the constant-yield price trajectory. Carrying value = purchase price + amortization of discount Carrying value = purchase price - amortization of premium Amortization of Discount/Premium The change in price between two points on the trajectory. Capital Gain/Loss Return associated with a change in the value of a bond as indicated by a change in the YTM Capital gain = sale price carrying value Capital loss = carrying value sale price Slide 32

33 Return Calculation Total Return Coupon payments Coupon reinvestment income Redemption of principal on maturity date / sale price prior to maturity Horizon Yield Realized Rate of Return Internal rate of return (IRR) between the total return and the purchase price Annualized holding-period rate of return Slide 33

34 Return Calculation Example: An investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. After the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after five years. Assume that interest rates remain unchanged at 8% over the five-year holding period. Please calculate: a) Coupon and coupon reinvestment income. b) Capital gain/loss per 100 of par value from the sale of the bond at the end of five-year holding period. c) Total return for five-year holding period. d) Horizon yield for five-year holding period. Slide 34

35 Return Calculation a) coupon=7 reinvestment rate=8% no. of coupons=5 7 (1+8%) 4 +7 (1+8%) (1+8%) 2 +7=41.07 b)issuing at par carrying value=100 N=4 I/Y=8% PMT=7 FV=100 market price=96.69 capital loss= =-3.31 c)total return = coupon & coupon reinvestment income + sale price = = d)purchase Price=Total Return/(1+Horizon Yield) N 100 = /(1+r) 5 r=6.62% Slide 35

36 Return Calculation Example: An investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. After the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after 8 years. Assume that interest rates remain unchanged at 8% over the 8-year holding period. Please calculate: a) Coupon and coupon reinvestment income. b) Capital gain/loss per 100 of par value from the sale of the bond at the end of five-year holding period. c) Total return for 8-year holding period. d) Horizon yield for 8-year holding period. Slide 36

37 Return Calculation a) coupon=7 reinvestment rate=8% no. of coupons=8 7 (1+8%) 7 +7 (1+8%) (1+8%) 5 +7= b)issuing at par carrying value=100 N=1 I/Y=8% PMT=7 FV=100 market price=99.07 capital loss= =-0.93 c)total return = coupon & coupon reinvestment income + sale price = = d)purchase Price=Total Return/(1+Horizon Yield) N 100 = /(1+r) 8 r=7.13% Slide 37

38 Interest Rate Risk Interest Rate Risk Coupon Reinvestment Risk Market Price Risk offset each other When int. rate reinvestment & capital loss When int. rate reinvestment & capital gain coupon reinvestment risk dominates when the investor has a long-term horizon relative to the time-tomaturity (e.g. a buy-and-hold investor) market price risk dominates when the investor has a short-term horizon relative to the time-tomaturity Investment Horizon is important for the analysis of interest rate risk. Slide 38

39 Interest Rate Risk Interest Rate Risk The risk that interest rate will change (from the initial market discount rate), which affects the reinvestment of coupon payments and the market price if the bond is sold prior to maturity. Slide 39

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