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
1
The NOB Spread


The NOB spread is “notes over bonds”
Traders who use NOB spreads are
speculating on shifts in the yield curve
–
2
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 Tnote futures contracts and buy T-bond futures
Trading Spreads
3
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)
–
4
If you think the spread will widen, buy the
spread (buy T-bill, sell ED)
Pricing Interest Rate Futures
Contracts

Interest rate futures prices come from the
implications of cost of carry:
Ft  S (1  C0,t )
where
Ft  futures price for delivery at time t
C0 , t
5
S  spot commodity price
 cost of carry from time zero to time t
Computation

Cost of carry is the net cost of carrying the
commodity forward in time (the carry return
minus the carry charges)
–

6
If you can borrow money at the same rate that a
Treasury bond pays, your cost of carry is zero
Solving for C in the futures pricing equation
yields the implied repo rate (implied
financing rate)
Implied Repo or Financing rate
7
Arbitrage With T-Bill Futures

If an arbitrageur can discover a disparity
between the implied financing rate and the
available repo rate, there is an opportunity
for riskless profit
–
8
If the implied financing rate is greater than
the borrowing rate (overpriced futures), then
he/she could borrow, buy T-bills, and sell
futures
Chapter 12
Futures Contracts
and Portfolio
Management
9
© 2004 South-Western Publishing
Outline



10
The concept of immunization
Altering portfolio duration with futures
Duration as a convex function as opposed
to market risk measure beta
Introduction

An immunized bond portfolio is largely
protected from fluctuations in market
interest rates
–
–
–
11
Seldom possible to eliminate interest rate risk
completely
A portfolio’s immunization can wear out, requiring
managerial action to reinstate the portfolio
Continually immunizing a fixed-income portfolio can
be time-consuming and technical
Bond Risks

A fixed income investor faces three primary
sources of risk:
–
–
–
12
Credit risk
Interest rate risk
Reinvestment rate risk
Bond Risks (cont’d)

13
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
– Lower bond ratings mean higher
expected returns but with more risk of
default
– Investors choose the level of credit risk
that they wish to assume
Bond Risks (cont’d)

Interest rate risk is a consequence of the
inverse relationship between bond prices
and interest rates
–
14
Duration is the most widely used measure of a
bond’s interest rate risk
Bond Risks (cont’d)

15
Reinvestment rate risk is the uncertainty
associated with not knowing at what rate
money can be put back to work after the
receipt of an interest check
– The reinvestment rate will be the
prevailing interest rate at the time of
reinvestment, not some rate determined
in the past
Duration Matching


16
Bullet immunization
Change of portfolio duration with interest
rate futures
Introduction

Duration matching selects a level of
duration that minimizes the combined
effects of reinvestment rate and interest
rate risk

Two versions of duration matching:
–
–
17
Bullet immunization
Bank immunization
Bullet Immunization

18
Seeks to ensure that a predetermined
sum of money is available at a specific
time in the future regardless of
interest rate movements
Bullet Immunization (cont’d)

Objective is to get the effects of interest
rate and reinvestment rate risk to offset
–
–
19
If interest rates rise, coupon proceeds can be
reinvested at a higher rate
If interest rates fall, proceeds can be reinvested
at a lower rate
Bullet Immunization (cont’d)
Bullet Immunization Example
A portfolio managers receives $93,600 to invest in
bonds and needs to ensure that the money will
grow at a 10% compound rate over the next 6 years
(it should be worth $165,818 in 6 years).
20
Bullet Immunization (cont’d)
Bullet Immunization Example (cont’d)
The portfolio manager buys $100,000 par value of a
bond selling for 93.6% with a coupon of 8.8%,
maturing in 8 years, and a yield to maturity of
10.00%.
21
Bullet Immunization (cont’d)
Bullet Immunization Example (cont’d)
Panel A: Interest Rates Remain Constant
Year 1
$8,800
Year 2
$9,680
$8,800
Year 3
$10,648
$9,680
$8,800
Year 4
$11,713
$10,648
$9,680
$8,800
Year 5
$12,884
$11,713
$10,648
$9,680
$8,800
Interest
Bond
Total
22
Year 6
$14,172
$12,884
$11,713
$10,648
$9,680
$8,800
$68,805
$97,920
$165,817
Bullet Immunization (cont’d)
Bullet Immunization Example (cont’d)
Panel B: Interest Rates Fall 1 Point in Year 3
Year 1
$8,800
Year 2
$9,680
$8,800
Year 3
$10,648
$9,680
$8,800
Year 4
$11,606
$10,551
$9,592
$8,800
Year 5
$12,651
$11,501
$10,455
$9,592
$8,800
Interest
Bond
Total
23
Year 6
$13,789
$12,536
$11,396
$10,455
$9,592
$8,800
$66,568
$99,650
$166,218
Bullet Immunization (cont’d)
Bullet Immunization Example (cont’d)
Panel C: Interest Rates Rise 1 Point in Year 3
Year 1
$8,800
Year 2
$9,680
$8,800
Year 3
$10,648
$9,680
$8,800
Year 4
$11,819
$10,745
$9,768
$8,800
Year 5
$13,119
$11,927
$10,842
$9,768
$8,800
Interest
Bond
Total
24
Year 6
$14,563
$13,239
$12,035
$10,842
$9,768
$8,800
$69,247
$96,230
$165,477
Bullet Immunization (cont’d)
Bullet Immunization Example (cont’d)
The compound rates of return in the three
scenarios are 10.10%, 10.04%, and 9.96%,
respectively.
25
Duration Shifting
26

The higher the duration, the higher the level
of interest rate risk

If interest rates are expected to rise, a bond
portfolio manager may choose to bear
some interest rate risk (duration shifting)
Duration Shifting (cont’d)



27
The shorter the maturity, the lower the
duration
The higher the coupon rate, the lower the
duration
A portfolio’s duration can be reduced by
including shorter maturity bonds or bonds
with a higher coupon rate
Duration Shifting (cont’d)
Coupon
Lower
Higher
Lower
Ambiguous
Duration
Lower
Higher
Duration
Higher
Ambiguous
Maturity
28
Hedging With Interest Rate
Futures

A financial institution can use futures
contracts to hedge interest rate risk

The hedge ratio is:
Pb Db (1  YTM ctd )
HR  CFctd 
Pf D f (1  YTM b )
29
Hedging With Interest Rate
Futures (cont’d)

The number of contracts necessary is given
by:
portfolio par value
# contracts 
 hedge ratio
$100,000
30
Hedging With Interest Rate
Futures (cont’d)
Futures Hedging Example
A bank portfolio holds $10 million face value in government
bonds with a market value of $9.7 million, and an average
YTM of 7.8%. The weighted average duration of the portfolio
is 9.0 years. The cheapest to deliver bond has a duration of
11.14 years, a YTM of 7.1%, and a CBOT correction factor of
1.1529.
An available futures contract has a market price of 90 22/32 of
par, or 0.906875. What is the hedge ratio? How many futures
contracts are needed to hedge?
31
Hedging With Interest Rate
Futures (cont’d)
Futures Hedging Example (cont’d)
The hedge ratio is:
0.97  9.0 1.071
HR  1.1529 
 0.9898
0.906875 11.14 1.078
32
Hedging With Interest Rate
Futures (cont’d)
Futures Hedging Example (cont’d)
The number of contracts needed to hedge is:
$10,000,000
# contracts 
 0.9898  98.98
$100,000
33
Summary of Immunization and
duration hedging



34
Bullet immunization (bond with target yield and
duration = target date)
Duration as a measure of sensitivity to interest
rate changes
Duration is a convex function hedge ratio does
not change linearly (BPV)
Examples for review
Spot rate is $1.33 per 1€. The US 3m T-bill rate is 2.7%
and the Forward 3m rate is 1.327011. What is the risk
free rate of the European central bank if the interest
rate parity condition determined this forward rate?
(3.6%)
The spot rate is CAD 2.2733 per 1£. If the inflation rate in
Canada is 3.4% a year and the inflation rate in UK is
2.3% per year, according to the purchasing power
parity the forward exchange rate should be……….?
(2.285838)
35