Duration
MGT 4850
Spring 2008
University of Lethbridge
Fixed Income Securities
• Bonds and Pricing
• Term Structure of Interest Rates
• Risk
– Credit
– Interest rate
• Price
• Reinvestment Risk
• Measuring and Hedging Interest rate Risk
Pricing of Treasury Bonds
Bond Pricing Example (cont’d)
$30
$1,030
P0 

 $1,002.71
0.5
1.0
(1.0573)
(1.0580)
This corresponds to a newspaper price of about 100 8/32nds.
3
Interest Rate Term Structure
• http://www.smartmoney.com/onebond/index.cfm?story=yieldcurve
Bootstraping and Forward rates
• Non-arbitrage in Interest rate futures
• Trading the Yield curve
• Trading Spreads
http://www.cbot.com/cbot/pub/cont_detail/0,3206,1070+12541,00.html
The NOB Spread
• The NOB spread is “notes over bonds”
• Traders who use NOB spreads are
speculating on shifts in the yield curve
– If you feel the gap between long-term rates
and short-term rates is going to narrow (
yield curve slope decreases or flattens),
you could sell T-note futures contracts and
buy T-bond futures
NOB spread (trading the yield
curve)
slope increases (long term R increases more than
short term or short term even decreases) buy notes
sell bonds
TED spread (different yield
curves)
• The TED spread is the difference
between the price of the U.S. T-bill
futures contract and the eurodollar
futures contract, where both futures
contracts have the same delivery
month (T-bill yield<ED yield)
– If you think the spread will widen, buy the
spread (buy T-bill, sell ED)
Trading Spreads
Bond Risks
• Credit risk is the likelihood that a
borrower will be unable or unwilling to
repay a loan as agreed
– Rating agencies measure this risk with
bond ratings
• Interest rate risk is a consequence of
the inverse relationship between bond
prices and interest rates
– Duration is the most widely used measure
of a bond’s interest rate risk
10
Sensitivity to interest rate changes
Coupon
Lower
Higher
Lower
Ambiguous
Lower
Higher
Higher
Ambiguous
Maturity
11
Definition
• Measure of the sensitivity of the price of a
bond to changes in the interest rate at
which bond is discounted
• Macauley duration measure
• Basic Duration Calculation
Using Excel Formula
• Settlement (purchase date)
• Maturity (bond’s maturity date)
• Coupon
• Yield (to maturity)
• Frequency (# coupons per year)
• Basis (day count)
0 30/360
1 act/actual
2 act/360
3 act/365
4 Eur 30/360
Duration Matching
• Duration matching selects a level of
duration that minimizes the combined
effects of reinvestment rate and
interest rate risk
• Bullet immunization
• Bank immunization
14
Bullet Immunization
• When we want to ensure that the
money invested in bonds will grow at a
target compound rate over the next
target period years we need to find a
bond with current YTM matching our
expected yield and duration equal to
the target period.
Meaning of Duration
• Weighted Average of the bond’s payments
• Bond’s price elasticity with respect to its
discount rate
• Discount factor elasticity
• Price volatility
Babcock’s Formula
• Weighted average of “current yield” and
PVIF
Duration Patterns
• Maturity
Duration Patterns
• Coupon