1 bond price, yields, and returns different bond types bond price bond yield bond returns bond risk...
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1
Bond Price, Yields, and Returns
Different Bond Types Bond Price Bond Yield Bond Returns Bond Risk Structure
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Face or par value Coupon rate
Zero coupon bond Compounding and payments
Accrued Interest Indenture
Bond Characteristics
3
Accrued Interest
periodcouponinDays
periodAIinDayscoupondollarannualAI
___
___
2
__
Example on page 447
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Different Issuers of Bonds
U.S. Treasury Notes and Bonds
Corporations Municipalities International Governments and Corporations Innovative Bonds
Floaters and Inverse Floaters Asset-Backed Catastrophe
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Figure 14.2 Corporate Bond Listings
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Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking funds
Provisions of Bonds
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Principal and Interest Payments for TIPS
The above is index bond.
See pages 451-452.
Compute real returns in year 1, 2, 3
8
)1()1(1 rParValue
rCP T
T
T
tt
tB
PB = Price of the bond
Ct = interest or coupon payments
T = number of periods to maturity
y = semi-annual discount rate or the semi-annual yield to maturity
Bond Pricing
Accrued interest: page 459
9
Ct = 40 (SA)P = 1000T = 20 periodsr = 3% (SA)
Price: 10-yr, 8% Coupon, Face = $1,000
77.148,1$
)03.1(
1000
03.1
140
20
20
1
P
Pt
t
10
Prices and Yields (required rates of return) have an inverse relationship
When yields get very high the value of the bond will be very low.
When yields approach zero, the value of the bond approaches the sum of the cash flows.
Bond Prices and Yields
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Inverse Relation Between Prices and Yields
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Yield to Maturity
Interest rate that makes the present value of the bond’s payments equal to its price.
Solve the bond formula for r
)1()1(1 rParValue
rCP T
T
T
tt
tB
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Yield Measures
Bond Equivalent Yield
7.72% = 3.86% x 2
Effective Annual Yield
(1.0386)2 - 1 = 7.88%
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Current Yield
Annual Interest / Market Price
$70 / $950 = 7.37 %
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Yield to Call
For callable bonds See example on page 454
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Holding Period Return versus YTM
Reinvestment Assumptions Holding Period Return
Changes in rates affects returns Reinvestment of coupon payments Change in price of the bond
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Figure 14.6 Prices over Time of 30-Year Maturity, 6.5% Coupon Bonds
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Holding-Period Return: Single Period
HPR = [ I + ( P0 - P1 )] / P0
where
I = interest payment
P1 = price in one period
P0 = purchase price
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Example (Single period analysis)
CR = 8%
YTM = 10%
N=10 years
Semiannual Compounding
What is HPR when the rate falls to 7% in six months?
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Horizon Analysis (multiple period)
Example 14.6 – page 456
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Mortgage Example
Say you are interested in buying a 2-bedroom condo in Boston. The price is $300,000. You have a 30-year 3.5% APR mortgage with 20% down payment.
(1)What would be the monthly mortgage payment?
(2)What if you have 15-year mortgage with the same APR?
(3)Suppose you could rent the place out and the rent you collect will cover your mortgage payment. What would be the annual return of your investment if the condo value stays constant.
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Zero-coupon Bonds and Treasury Strips Zero coupon bonds – page 459
Short term treasuries Long term zero coupons Treasury may strip payments from treasury coupon
bonds -- STRIPS
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The Price of a 30-Year Zero-Coupon Bond over Time at a Yield to Maturity of 10%
After-tax return – see page 478.
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Rating companies (P 461) Moody’s Investor Service Standard & Poor’s Fitch
Rating Categories Investment grade Speculative grade Page 462
Default Risk and Ratings
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Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt
Factors Used by Rating Companies
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Sinking funds Subordination of future debt Dividend restrictions Collateral
Protection Against Default
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Yields on Long-Term Bonds, 1954 – 2006
Understand default premium – page 473-474
28Chapter 1: Overview
14-28
Credit Default Swaps
A credit default swap (CDS) acts like an insurance policy on the default risk of a corporate bond or loan.
CDS buyer pays annual premiums. CDS issuer agrees to buy the bond in a default or pay
the difference between par and market values to the CDS buyer.
29Chapter 1: Overview
14-29
Credit Default Swaps
Institutional bondholders, e.g. banks, used CDS to enhance creditworthiness of their loan portfolios, to manufacture AAA debt.
CDS can also be used to speculate that bond prices will fall.
This means there can be more CDS outstanding than there are bonds to insure!
30Chapter 1: Overview
14-30
Figure 14.12 Prices of Credit Default Swaps
3114-31
Credit Risk and Collateralized Debt Obligations (CDOs)
Major mechanism to reallocate credit risk in the fixed-income markets Structured Investment Vehicle (SIV) often
used to create the CDO Loans are pooled together and split into
tranches with different levels of default risk.
Mortgage-backed CDOs were an investment disaster in 2007
3214-32
Figure 14.13 Collateralized Debt Obligations