FIN 440 Flashcards
chapter 1 bond
notes from PPT
Bonds
Bond Characteristics
Bond
Security that obligates issuer to make payments to holder over time
Face Value, Par Value
Payment to bondholder at maturity of bond
Coupon Rate
Bondβs annual interest payment per dollar of par value
Zero-Coupon Bond
Pays no coupons, sells at discount, provides only payment of par value at maturity
U.S. Treasury Quotes: Treasury note and bond data are representative over-the-counter quotations as of 3pm Eastern time.
Treasury Bonds and Notes
Accrued interest and quoted bond prices
Quoted prices do not include interest accruing between payment dates
Accrued interest =[(π¨πππππ ππππππ πππππππ)/π]Γ(π«πππ πππππ ππππ ππππππ πππππππ)/(π«πππ ππππππππππ ππππππ ππππππππ)
Example: Consider a bond with the following characteristics: Semi-annual payments, coupon rate of 6%, $1,000 par value. If 45 days have passed since the last coupon payment, what is the accrued interest?
A.I = 45/182 x 30 = 7.42
Corporate Bonds
Call provisions on corporate bonds
Callable bonds: May be repurchased by issuer at specified call price during call period
Convertible bonds
Allow bondholder to exchange bond for specified number of common stock shares
Corporate Bonds
Puttable bonds
Holder may choose to exchange for par value or to extend for given number of years
Floating-rate bonds
Coupon rates periodically reset according to specified market date
Preferred Stock
Commonly pays fixed dividend
Floating-rate preferred stock becoming more popular
Dividends not normally tax-deductible
Corporations that purchase other corporationsβ preferred stock are taxed on only 30% of dividends received
Other Domestic Issuers State, local governments (municipal bonds) Federal Home Loan Bank Board Farm Credit agencies Ginnie Mae, Fannie Mae, Freddie Mac
International Bonds
Foreign bonds
Issued by borrower in different country than where bond sold, denominated in currency of market country
Eurobonds
Denominated in currency (usually that of issuing country) different than that of market
Innovation in the Bond Market
Indexed bonds
Payments tied to general price index/price of particular commodity
Treasury Inflation Protected Securities (TIPS): Par value of bond increases with consumer price index
Nominal return=(πΌππ‘ππππ π‘+πππππ πππππππππ‘πππ)/(πΌπππ‘πππ πππππ)
Real return=(1+πππππππ πππ‘π’ππ)/(1+πΌπππππ‘πππ)β1
Bond Pricing
Prices fall as market interest rate rises
Interest rate fluctuations are primary source of bond market risk
Bonds with longer maturities more sensitive to fluctuations in interest rate
Bond Yields
Yield to Maturity
Discount rate that makes present value of bondβs payments equal to price.
Current Yield
Annual coupon divided by bond price
Premium Bonds
Bonds selling above par value
Discount Bonds
Bonds selling below par value
Bond Prices Over Time
Yield to Maturity versus Holding Period Return (HPR)
Yield to maturity measures average RoR if investment held until bond matures
HPR is RoR over particular investment period; depends on market price at end of period
Yield to Call
Calculated like yield to maturity
Time until call replaces time until maturity; call price replaces par value
Premium bonds more likely to be called than discount bonds
Price Paths of Coupon Bonds in Case of Constant Market Interest Rates
Zero-Coupon Bonds and Treasury STRIPS
Zero-coupon bond: Carries no coupons, provides all return in form of price appreciation
Separate Trading of Registered Interest and Principal of Securities (STRIPS): Oversees creation of zero-coupon bonds from coupon-bearing notes and bonds
Investment grade bond
Rated BBB and above by S&P or Baa and above by Moodyβs
Speculative grade or junk bond
Rated BB or lower by S&P, Ba or lower by Moodyβs, or unrated
Default Risk and Bond Pricing
Determinants of Bond Safety
Coverage ratios: Company earnings to fixed costs
Leverage ratio: Debt to equity
Liquidity ratios
Current: Current assets to current liabilities
Quick: Assets excluding inventories to liabilities
Profitability ratios: Measures of RoR on assets or equity
Cash flow-to-debt ratio: Total cash flow to outstanding debt
Bond Indentures
Indenture
Defines contract between issuer and holder
Sinking fund
Indenture calling for issuer to periodically repurchase some proportion of outstanding bonds before maturity
Bond Indentures
Subordination clause
Restrictions on additional borrowing stipulating senior bondholders paid first in event of bankruptcy
Collateral
Specific asset pledged against possible default
Debenture
Bond not backed by specific collateral
chapter 1 bond part two
notes from ppt
Managing Bond Portfolios
Interest rate risk Interest rate sensitivity of bond prices Duration and its determinants Convexity Passive and active management strategies
Interest Rate Risk
Interest Rate Sensitivity
Bond prices and yields are inversely related
An increase in a bondβs yield to maturity results in a smaller price change than a decrease of equal magnitude
Long-term bonds tend to be more price sensitive than short-term bonds
As maturity increases, price sensitivity increases at a decreasing rate
Interest rate risk is inversely related to the bondβs coupon rate
Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Duration
A measure of the effective maturity of a bond
The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment
It is shorter than maturity for all bonds, and is equal to maturity for zero coupon bonds
Duration calculation:
y = YTM
Wt = [CFt/(1+y)^t]/Price
Duration = sum t x wt
Duration-Price Relationship
Price change is proportional to duration and not to maturity
Example 16.1 Duration and Interest Rate Risk
Two bonds have duration of 1.8852 years
One is a 2-year, 8% coupon bond with YTM=10%
The other bond is a zero coupon bond with maturity of 1.8852 years
Duration of both bonds is 1.8852 x 2 = 3.7704 semiannual periods
Modified D = 3.7704/1 + 0.05 = 3.591 periods
Two bonds have duration of 1.8852 years
One is a 2-year, 8% coupon bond with YTM=10%
The other bond is a zero coupon bond with maturity of 1.8852 years
Duration of both bonds is 1.8852 x 2 = 3.7704 semiannual periods
Modified D = 3.7704/1 + 0.05 = 3.591 periods
Rule 4
Holding other factors constant, the duration of a coupon bond is higher when the bondβs yield to maturity is lower
Rules 5
The duration of a level perpetuity is equal to:
(1 + y) / y
Convexity
The relationship between bond prices and yields is not linear
Duration rule is a good approximation for only small changes in bond yields
Bonds with greater convexity have more curvature in the price-yield relationship
Convexity = 1/[Px(1+y)^2]xSUM[(CFt/(1+y)^t * (t^2+t)]
correction for convexity:
Why Do Investors Like Convexity?
Bonds with greater curvature gain more in price when yields fall than they lose when yields rise
The more volatile interest rates, the more attractive this asymmetry
Bonds with greater convexity tend to have higher prices and/or lower yields, all else equal
Duration and Convexity Callable Bonds As rates fall, there is a ceiling on the bondβs market price, which cannot rise above the call price Negative convexity Use effective duration:
Mortgage-Backed Securities (MBS)
The number of outstanding callable corporate bonds has declined, but the MBS market has grown rapidly
MBS are based on a portfolio of callable amortizing loans
Homeowners have the right to repay their loans at any time
MBS have negative convexity
Often sell for more than their principal balance
Homeowners do not refinance as soon as rates drop, so implicit call price is not a firm ceiling on MBS value
Tranches β the underlying mortgage pool is divided into a set of derivative securities
Passive Management
Bond Index Funds
Bond indexes contain thousands of issues, many of which are infrequently traded
Bond indexes turn over more than stock indexes as the bonds mature
Therefore, bond index funds hold only a representative sample of the bonds in the actual index
Immunization
A way to control interest rate risk that is widely used by pension funds, insurance companies, and banks
In a portfolio, the interest rate exposure of assets and liabilities are matched
Match the duration of the assets and liabilities
Price risk and reinvestment rate risk exactly cancel out
As a result, value of assets will track the value of liabilities whether rates rise or fall
Cash Flow Matching and Dedication
Cash flow matching = Automatic immunization
Cash flow matching is a dedication strategy
Not widely used because of constraints associated with bond choices
Active Management Swapping Strategies Substitution swap Intermarket spread swap Rate anticipation swap Pure yield pickup swap Tax swap
Horizon Analysis
Select a particular holding period and predict the yield curve at end of the period
Given a bondβs time to maturity at the end of the holding period its yield can be read from the predicted yield curve and the end-of-period price can be calculated
High-quality vehicles can accompany you for a long time, whether itβs sunny or stormy.
15
A coupon bond that pays interest of $100 annually has a par value of $1,000, matures in five years, and is selling today at a $72 discount from par value. The yield to maturity on this bond is
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A coupon bond that pays interest semi-annually has a par value of $1,000, matures in five years, and has a yield to maturity of 10%. The intrinsic value of the bond today will be __________ if the coupon rate is 8%.
922.78
Consider a bond with the following characteristics: Quarterly payments, coupon rate of 8%, $1,000 par value. If 45 days have passed since the last coupon payment, what is the accrued interest? (Assume 364 days in a year)
1000x8%/4x45/(364/4) = 9.89
Consider a bond with the following characteristics: Monthly payments, coupon rate of 8%, $1,000 par value. If 18 days have passed since the last coupon payment, what is the accrued interest?
1000x8%/12x18/(364/12) = 3.96
An upward sloping yield curve is a(n) _______ yield curve
normal
humped
inverted
flat
normal
A 10%, 14-year bond has a yield to maturity of 12.9% and duration of 11.4 years. If the market yield changes by 31 basis points, how much change will there be in the bondβs price?
- 11.4x0.0031/(1+12.9%) = -3.13%
- duration*base point changes/(1+YTM)
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A 21-year corporate bond with a 11% rate has a yield of 8.7%. The Macaulay duration for the bond is 11.8 years. What is the bonds modified duration?
modified duration = macaulay duration/(1+ytm)
= 11.8/(1+8.7%) = 10.86
There is a bond selling with a modified duration of 14.3 years and convexity of 248. What would a 2.6% decrease in yield change the percentage price change according to the duration-with-convexity rule?
Modified duration D = 14.3 Convexity C = 248 change in yield dy = -2.6% change in price dP price P
dP = -DPdy + (1/2)CPdy^2
dP / P = -Ddy + (1/2)Cdy^2
= - 14.6*(-2.6%) + (1/2) * 248 *(-2.6%)^2 = 46.34%
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In your own words, name three things that affect bond price. A complete answer will not only mention the three effects, but also describe how it affects a bond. For example, what happens when a market interest rates go up?
The interest rates, inflation (or time to maturity), and credit rating affect the bond price.
Changes in interest rates affect bond prices by affecting the discount rate. Inflation generates higher interest rates, which in turn requires a higher discount rate, which reduces bond prices.
In this case, the price of bonds with longer maturities will fall sharply because these bonds are exposed to inflation and interest rate risks for a longer period of time, thereby increasing the discount rate required to estimate future cash flows. At the same time, the decline in interest rates led to a decline in bond yields, thereby increasing bond prices.
Credit risk also affects bond prices. Bonds are rated by independent credit rating agencies such as Moodyβs and Fitch to rank the default risk of bonds. Bonds with higher risk and lower credit ratings are considered speculation Bonds have higher yields and lower prices. If a credit rating agency lowers the rating of a particular bond to reflect more risks, the bondβs yield must increase and the price should fall.
