The document discusses using Eurodollar futures and interest rate swaps to hedge interest rate risk for loans with variable interest rates. It provides examples of how a borrower could use these instruments to create synthetic fixed rate loans and protect against rising interest rates. By entering offsetting positions in the futures market, the borrower can lock in rates and reduce uncertainty, while the lender can better manage its own interest rate risk exposure.

1. Eurodollar Futures and TED spread
Trading
Training Workshop
François Choquet
Advanced Application Specialist
July 2011

2. Motivations and Applications
• Speculation on views on interest rates.
• Hedge against fluctuations in Interest Rates.
1. Convert fixed rate loans into floating rate loans.
2. Convert Floating rate loans into fixed rate loans.
3. Hedging using a stack of Eurodollar Contracts
4. Hedging using a strip of Eurodollar Contracts

3. Motivations and Applications
• Speculation on views on interest rates.
• Hedge against fluctuations in Interest Rates.
1. Convert fixed rate loans into floating rate loans.
2. Convert Floating rate loans into fixed rate loans.
3. Hedging using a stack of Eurodollar Contracts
4. Hedging using a strip of Eurodollar Contracts

4. Speculating with IR Futures
• Trading by holding an outright positions i.e.
long or short or trading a spread
• The long trader bets that interest rate will fall
so the price of the futures will rise
• The short trader bets that interest rate will
rise so the price of the futures will fall.
• The spread trader bets that interest rate curve
will steepen or flatten.

5. Outright Position
• (1) The trader believes that short term rates will rise and execute the
following trade:
Date Futures Market
5/16/2011 Sell one SEP 11 ED Futures at 99.685
8/14/2011 Buy one SEP 11 ED Futures at 99.505
Profit=18 basis points
Total Gain=18 x 25 x 1 =450
• To profit from rising rates, the trader must be short IR futures. Accordingly
the trader sells one SEP11 contracts at 99.30. Five days later IR have risen
and the futures contract trades at 99.12.
• The trader gains 18 basis points. As each basis point is worth $25, the total
profit is $450.

6. Spreads
• Intracommodity spread: Speculation on the changing shape of the IR
curve. E.g. spread between a nearby and more distant futures contract.
• Intercommodity spread: Shifting risk from two different instruments:
Libor-OIS spread.
• Today, a trader considers the following Libor rates and futures yields:
Time to mty Libor Spot Futures Contract Ticker Futures Futures
Rates Yield Price
3m 0.264 SEP 11 - 4.4 months EDU1 comdty 0.32 99.68
6m 0.27485 DEC 11 - 7.4 months EDZ1 comdty 0.415 99.585
9m 0.30915 MAR 12 - 10.4 months EDH2 comdty 0.575 99.425
1y 0.35741
• The yield curve is upward sloping with a spread between 12 month and 3
month showing 9 basis points.
• The futures yields are consistent with the forward rates implied from the
Eurodollar curve.

7. Spread Curve Trade
• (2) The trader speculates that the curve will flatten within the next 6
months and decides to execute the following trade:
Date Futures
11-May-11 Buy the MAR12 ED contract at 99.425
Sell the DEC11 ED contract at 99.585
30-Jul-11 Buy the DEC11 ED contract at 99.635
Sell the MAR12 ED contract at 99.525
Profit=5 basis points
Total Gain=$125
• By buying the more distant MAR12 contract and selling the DEC11
contract today , the trader bets that the yield differential of 16 bps of will
narrow.
• On July 30th, the yield spread diff. between MAR12 and DEC11 is 11 bps.
• No matter whether rates rise or falls, this spread strategy will produce a
profit.

8. FRA/OIS Spread
• Speculating on changing risk structure of interest rates.
• E.g. risk of widespread default triggers widening of
spread between OIS and Libor reflecting the changing
perception of the risk involved in holding Eurodollar
deposits in the face of potentially very large loan
losses.
• Assume the spread between the 3 month IMM OIS and
FRA is 17bps.
• The banks’ riskiness is perceived to increase, we might
expect the spread to widen. (This would be the case
whether interest rates are rising or falling).

9. • (3) To take advantage of this view, the trader could sell the SEP IMM FRA
buy the SEP IMM OIS contract.
Date Futures
Today Sell $1mm SEP IMM 3MO FRA at a rate of 0.32%
Buy $1mm SEP IMM OIS at a rate of 0.16%
August Sell $1mm SEP IMM OIS at a rate of 0.17%
15th Buy one SEP IMM 3MO FRA at a rate of 0.40%
Profit = 7 basis points
Total Gain = 7 x 25 = $175
• On August 15 the spread between the two contracts has widened by 16
basis points, in line with the trader’s expectations which produces a profit
of $400.
• The futures prices already embed the expectation of higher rates and
spread between Eurodollar and OIS. Thus, by engaging into this
strategy, the trader speculates AGAINST the rest of the market.
• It is not enough to expect yield spreads to widen, but the trader must
expect them to widen MORE than the market EXPECTS.

10. Motivations and Applications
• Speculation on views on interest rates.
• Hedge against fluctuations in Interest Rates.
1. Convert fixed rate loans into floating rate loans.
2. Convert Floating rate loans into fixed rate loans.
3. Hedging using a stack of Eurodollar Contracts
4. Hedging using a strip of Eurodollar Contracts

11. Creating a Synthetic Fixed Rate Loan
• A construction firm plan a project that will take
six months to complete. It is worth $100 million.
The bank provides funds for 6 months at a single
rate, that is 200 bps above the 90- day Libor.
• The rate for the second quarter is 200 bps above
the 90 day Libor rate that prevails at that date.
• The company must pay interest at the end of 3
month and interest plus principal at the end of
the 6 month period.

12. Schedule
Cash Market Futures Market
June 20th, 2011 Borrow $100 m at 2.316% Sell 100 Sept. Eurodollar
for three months from the Futures Contracts at 99.66
bank who commit to extend which corresponds to a
the loan for 3 additional 0.34% yield.
months at 200 bps above 3
month Libor.
September 20th, 2011 The company pays interest Offset 100 Sept. contracts
of $591,886.67. The 3 Mo at 99.06 reflecting a 0.84%
Libor is now at 0.84% so the yield. The trade produces
company borrows for a profit of $125,000.
another 3 months at 2.84%. (50*25*100)
December 20th, 2011 Pay interest of $717,888.89 Futures Profit: $125,000.
and repay principal of
$100m. Total interest
expense $1,309,755.56
Net Interest Expense after Hedging: $1,184,755.56

13. Synthetic Floating Rate Loan
• The bank decides to let the company borrowing at a fixed
rate.
• The bank’s cost of funds is 90 day Libor and expect to pay
0.316% this quarter and 0.34% next quarter, so an average of
0.328% over 6 months.
• Therefore the bank decides to make a fixed rate 6 month loan
to the construction company at 2.328%.
• The bank’s expected profit is the 200 basis points between the
lending rate and the bank’s Libor based cost of funds.
• If Libor rises by 50 bps to .% for the second quarter, the bank
will have to pay an additional $125,000 in interest. To avoid
that the bank will transact as follows:

14. Schedule
Cash Market Futures Market
June 20th, 2011 Borrow principal of $100m Sell 100 September
at 0.316% and lend it for 6 Eurodollar contracts at
months at 2.316% to the 99.66 (.34% yield)
construction company.
September 20th, 2011 Pay Interest of $80,755.56 Offset the 100 Sept.
Libor is now at .84% so the contracts at 99.16
bank borrows $100m @ reflecting the .84% yield. It
.84%. produces a profit of
$125,000.00
March 20th, 2011 Pay interest of $212,333.33
and repay principal of
$100m.
Total Expense=$293,088.89 Profit=$125,000
Net interest expense after hedging: $168,088.89

15. Multi-Period Funding
• In the previous example, the interest risk focuses on a single date. Often
the period of the loans comes at a number of different dates at which the
rate might be reset.
• The company makes a more realistic assessment of the completion date of
the project: 1 year.
• The bank insists on making a floating rate loan for 3 months at a rate of
200 basis points above the 90 day Libor rate prevailing at the time.
– 3 month Libor: 0.316%
– SEP Eurodollar: 0.34%
– DEC Eurodollar: 0.416%
– MAR Eurodollar: 0.595%
• The cost of funds is then 2.316%, 2.34%, 2.416% and 2.595% or @100m @
an average rate of 2.41675%.
• In a stack hedge, all of the futures contracts are concentrated or stacked in
a single futures expiration date.

16. Scenario 1: Parallel Shift
• Shortly after the company enters the
hedge, Libor rates jump by 50 basis points.
The borrowing rate for the next 3 quarters are
then:
– September 11 – December 11 : 0.84%
– December 11– March 12: 0.916%
– March 12 – June 12: 1.095%
• Hedge $100 m with 300 September Eurodollar
Futures contracts.

17. Eurodollar Stack Hedge
Cash Market Futures Market
Jun 20th, 2011 Borrow $100 m at 2.316% for 3 months and Sell 300 Dec Eurodollar futures contracts
commit to roll over the loan for 3 quarters @ 99.66 which corresponds to a yield of
at 200 basis points over the prevailing Libor 0.34%.
rate.
Sep 20th, 2011 Co pays interest of $591,866.67. Libor is Offset 300 Dec Eurodollar contracts @
now 0.84% so the co borrows $100m @ 99.16 which reflects the yield of 0.84%.
2.84%. The trade produces a profit of
50*25*300=$375,000.
Dec 20th, 2011 Co pays interest of $717,888.89. and
borrows $100 m for 3 months @ 2.916%.
Mar 20th, 2012 Co pays interest of $737,100.00 and
borrows $100m for 3 months @ 3.095%.
June 20th, 2012 Co pays interest of $790,044.44 and repays
principal of $100m.
Total interest expense: @$2,837,800.00 Futures profit : $375,000
Total interest expense net of hedging: $2,462,800.00
Initial cost without 50 basis point increase: $2,457,029.17 (2.41675%*100m*366/360)

18. Scenario 2: Steepening Curve
• Shortly after the company enters the hedge, Libor rates jump unevenly across the
Libor curve. The borrowing rate for the next 3 quarters are then:
– September 11 – December 11 : 0.43% (+9bps)
– December 11– March 12: 0.93% (+51bps)
– March 12 – June 12: 1.5% (+55 bps)
• Hedge $100 m with 300 September Eurodollar Futures contracts.
• With this changes the company will suffer an increase in borrowing costs as
follows:
New rate Days in Cost for the period
period
June – September: 2.32% 92 591,866.67
September-December: 2.43% 91 614,250.00
December-March 2.93% 91 740,638.89
March-June 3.50% 92 894,444.44
$ 2,841,200.00
• This change in rates produces an increase in costs of $348,171.00 from the initially
expected level of $2,457,029.17 to $2,841,200.00
• Here the DEC contract produces only a gain of which is equal to:
0.09/0.005*12.5=$67,500. It isn’t sufficient to cover the increase in cost.

19. Interest Rate Curve Scenarios
1.60%
1.40%
1.20%
1.00%
expected cost of funding today
0.80%
Cost of funding (+50 bps parallel shift)
Cost of funding (steepening)
0.60%
0.40%
0.20%
0.00%
today (June 20th 2011) Sep 11-Dec 11 Dec 11-Mar 12 Mar 12-June 12

20. A Strip Hedge
• Unlike a stack hedge which concentrates the position on a single
expiration date, a strip hedge uses an EQUAL number of contracts for each
futures expiration over the hedging horizon.
• For a $100 mln financing requirements at risk for three quarters, the co
sells 100 ED contracts each of the SEP, DEC and MAR futures instead of the
300 contracts on SEP futures.
• With the hedge in place, each quarter of the coming year is hedged
against shifts in IR for that quarter.
• (see next table) Timing of the futures hedge to that of the market risk
exposure: The performance of the strip hedge results from the alignment
of the futures market hedges with the actual risk exposure of the firm.
• Performance depends on the horizon and the liquidity of the most distant
contracts.

21. Eurodollar Strip Hedge
Cash Market Futures Market
Jun 20th, 2011 Borrow $100 m at 2.316% for 3 Sell 100 for each of Sept, Dec and
months and commit to roll over Mar @ 99.66, 99.584, 99.405
the loan for 3 quarters at 200 basis respectively.
points over the prevailing Libor
rate.
Sep 20th, 2011 Co pays interest of $591,866.67. Offset 100 Sep contracts @ 99.57.
Libor is now 0.43% so the co Profit=$22,500.00
borrows $100m @ 2.43%.
Dec 20th, 2011 Co pays interest of $614,250.00 Offset 100 Dec contracts @ 99.07.
and borrows $100 m for 3 months Profit=$128,500.00
@ 2.93%.
Mar 20th, 2012 Co pays interest of $740,638.89 Offset 100 Mar contracts @ 98.5.
and borrows $100m for 3 months Profit=$226,250.00
@ 3.5%.
June 20th, 2012 Co pays interest of $894,444.44
and repays principal of $100m.
Total interest expense: Total Profit = $377,250.00
$2,841,200.00
Total interest expense net of hedging: $2,463,950.00

22. Arbitraging and Hedging Treasuries against Eurodollars.
TED SPREAD

23. Speculating with IR Futures
• Trading by holding an outright positions i.e. long
or short or trading a spread
• The long trader bets that interest rate will fall so
the price of the futures will rise
• The short trader bets that interest rate will rise so
the price of the futures will fall.
• The spread trader bets that:
– Interest rate curve will steepen or flatten.
– The correlation between the ED futures rates and
yield on Treasuries will change over time (TED).

24. G7 Macro Situation Today
Events with Significant Impact
• Strong recovery of the global economy in 2010 to 1st
quarter 2011 but outlook for growth tilted on the downside
amid weaker consumer sentiment.
• Price risk is rising but expectations remain anchored to
central banks’ objective of keeping inflation close to 2%.
• Expectations for higher policy rates from ECB & BOE.
• Severe stress in the bond markets reflecting the on-going
sovereign crisis in the Euro-zone. Downgrades of Greece
and Portugal.
• Large exposure of G7 banks to Greece, Ireland, Portugal
and Spain.
• Geopolitical tensions and North African and the middle
east.

25. -40
-30
-20
-10
-12
-10
-8
-6
-4
-2
10
20
30
40
0
0
2
4
8
6
Mar-04 Dec-98
Jul-04 Aug-99
Nov-04
Apr-00
Mar-05
Dec-00
Jul-05
U.S.
Aug-01 U.S.
Nov-05
Mar-06 Apr-02
Jul-06 Dec-02
Nov-06 Aug-03
Eurozone
Mar-07
Apr-04
Eurozone
Jul-07
Dec-04
Nov-07
Aug-05
Mar-08
U.K.
Jul-08 Apr-06
U.K.
Nov-08 Dec-06
Mar-09 Aug-07
Japan
Jul-09 Apr-08
Industrial Production YoY %
Japan
Nov-09
Dec-08
Mar-10
Aug-09
Real Output Growth YoY changes %
Jul-10
Nov-10 Apr-10
Mar-11 Dec-10
-60
-40
-20
40
60
0
20
10
20
30
40
50
60
70
0
Dec-96
Mar-04
Jul-97
Feb-98 Aug-04
Sep-98 Jan-05
Apr-99
Jun-05
U.S.
Nov-99
Jun-00 Nov-05
Jan-01
Apr-06
Aug-01
Mar-02 Sep-06
Oct-02 Feb-07
Eurozone
May-03
Dec-03 Jul-07
Jul-04 Dec-07
Feb-05
May-08
U.K.
Sep-05
Exports YoY %
Apr-06 Oct-08
Nov-06
Mar-09
Jun-07
Jan-08 Aug-09
Japan
PMI Composite
Aug-08 Jan-10
Mar-09
Global Purchasing Manager Index
Jun-10
Oct-09
May-10 Nov-10
Dec-10
Apr-11

26. Inflation Rates YoY changes % Global Commodity Indices
U.S. Eurozone U.K. Japan Agriculture Metal Energy
6 450
5 400
4 350
3 300
2 250
1 200
0 150
-1 100
-2 50
-3 0
May-09
May-10
May-11
Nov-09
Nov-10
Jul-09
Sep-09
Jul-10
Sep-10
Jan-09
Mar-09
Jan-10
Mar-10
Jan-11
Mar-11
Aug-99
Apr-00
Aug-01
Apr-02
Aug-03
Apr-04
Aug-05
Apr-06
Aug-07
Apr-08
Aug-09
Apr-10
Dec-98
Dec-00
Dec-02
Dec-04
Dec-06
Dec-08
Dec-10
Public Debt / GDP % Budget Deficit (-) %
160 10
140 Greece, 144 5
120 0
Italy, 118.1 Italy, -4.6
-5
100 Spain, -9.2
Ireland, 94.2 -10
80 Portugal, 83.2 Portugal, -9.1
-15 Greece, -10.5
60 Spain, 63.4
-20
40 -25
20 -30
Ireland, -32.4
0 -35
2003 2004 2005 2006 2007 2008 2009 2010 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

27. Tensions in the Government Bond
Markets
Government Bond Spreads in 2010 and 2011
1400
1200 Greece, 1209.4
1000
Spreads in bps
800
Ireland, 709.7
600
Portugal, 547.6
400
200 Spain, 193.1
Italy, 121.7
0

28. Deterioration in perceived debt
sustainability of “PIGS”
Five Year CDS spreads
1600
1400
greece cds usd sr
1200 5y, 1248.397
1000
800 portug cds usd sr 5y, 606.5
600
400
200 spain cds usd sr 5y, 232.248
0

29. Banks Exposure to “PIGS”
End of Q3 2010; in billion of US dollars – Source BIS
Germany France Italy Other Euro Area UK Japan U.S. R.O.W
Total exposure $2.512 trillion Germany, 685.6
France, 632.5
UK, 609.3
Germany, 570.7
523.7
UK, 421.2
U.S., 426.7
287.5
France, 247.3
193 Germany, 137.1
Germany, 179.2
France, 200.8 151.7
France, 128.5
112.3 111.5
97.3 93.2 UK, 92.8 98.7 82.8
UK, 55.8 64.1 66 63.8
17.7 26.1 20.5 15.7
5.9 8
Greece Ireland Portugal Spain

30. Counterparty Risk
3 Month Libor OIS Spreads
50
45
40
35
OIS GBP, 27.94
Spreads in bps
30
OIS EUR, 26
25
20
15
OIS USD, 15.95
10
5
0

31. AXE
• Less accommodative monetary policy resulting in
an increase in interbank rates.
• Growing concerns about PIGS’ sustainability of
public finances and fiscal outlook. Talks amongst
EU leaders about debt restructuring for Greece.
• Large exposure of banks to “PIGS”.
• Flight to safety resulting in a decrease in AAA
rated government bond yields.
– > BUY TREASURY, SELL EURODOLLARS/EURO FUTURES

32. TED Spread
Speculative trades on TED are executed in anticipation of a change in the
spread between Treasury and Eurodollar deposits based on the assumption
that the correlation between returns of the two instruments will change
overtime.
• Long position in TSY and a short position in a strip of euro-dollar contracts
with similar maturity.
• Position is established when the spread is narrow. The spread between
the two yields is constantly changing as it is affected by the turmoil or
uncertainty in the international markets and banks’ overall liquidity
position.
• A manager takes a position on the on-the-run 2 year TSY when the spread
is at 16 basis points.
• The manager anticipates that the spread will widen to 26 basis points
allowing him to exit the trade at a profit…(see next slide)

33. Trade Example Bond position
5/12/2011 6/13/2011
Principal : 100,142,000.00 99,953,125
Position Established on 5/12/2011 (T+1)
Accrued: 22,078.80 76,426.63
Bought 100mm of 0 5/8 13@100.142 (YTM 0.552%) Total: 100,164,078 100,029,551.63
Sold 2 year Eurodollar bundle i.e. first 8 quarterly CME Profit (Loss): ($134,526.37)
Eurodollar contracts.
Futures Strip Position:
Last Price Rate # Contracts
Profit: 803*20*25=$401,500
Front Stub 99.80097 0.19903125 36
EDM1 Comdty 99.735 0.265 101
EDU1 Comdty 99.69 0.31 101 Total Gain: $266,973.63
EDZ1 Comdty 99.595 0.405 101
EDH2 Comdty 99.455 0.545 101
Margin per Contract ($650)
EDM2 Comdty 99.22 0.78 101
EDU2 Comdty 98.925 1.075 100 Capital employed (803 contracts x $650 – 0% haircut)=$521,950
EDZ2 Comdty 98.615 1.385 99
EDH3 Comdty 98.34 1.66 99 Total Return on Capital for 32 days: 51.15%
Position reviewed on 6/13/2011
Sell 100mm of 0 5/8 13 @ 99.951 (YTM 0.651% up 10 bps)
Buy 2 year Eurodollar bundle at following prices (implying
a 20 basis point increase in rates):
# Contracts:
Price Rate P&L
Front Stub 99.60097 0.399031 0
EDM1 Comdty 99.535 0.465 50500 Face value x (days in contract/360) x discount factor strip
EDU1 Comdty 99.49 0.51 50500 --------------------------------------------------------------------------
EDZ1 Comdty 99.395 0.605 50500 Risk of ED Futures x 10,000
EDH2 Comdty 99.255 0.745 50500
EDM2 Comdty 99.02 0.98 50500
EDU2 Comdty 98.725 1.275 50000 The rate used in calculating the discount factor is the ED rate.
EDZ2 Comdty 98.415 1.585 49500 (the TED spread can be subtracted from it).
EDH3 Comdty 98.14 1.86 49500
$401,500

34. Futures Table
Eurodollar Contract Table
Period Ticker Last Price Rate Exp. Month Exp. Date Deposit Deposit No. days in
Period Start Period ends period
1 Front Stub* 99.8024 0.1976 5/12/2011 5/16/2011 6/15/2011 30
2 EDM1 Comdty 99.7350 0.2650 May-11 6/15/2011 6/17/2011 9/16/2011 91
3 EDU1 Comdty 99.6900 0.3100 Jun-11 9/21/2011 9/23/2011 12/23/2011 91
4 EDZ1 Comdty 99.6000 0.4000 Jul-11 12/21/2011 12/23/2011 3/23/2012 91
5 EDH2 Comdty 99.4550 0.5450 Aug-11 3/21/2012 3/23/2012 6/22/2012 91
6 EDM2 Comdty 99.2200 0.7800 Sep-11 6/20/2012 6/22/2012 9/21/2012 91
7 EDU2 Comdty 98.9300 1.0700 Oct-11 9/19/2012 9/21/2012 12/21/2012 91
8 EDZ2 Comdty 98.6300 1.3700 Dec-11 12/19/2012 12/21/2012 3/21/2013 90
9 EDH3 Comdty 98.3600 1.6400 Mar-12 3/20/2013 3/22/2013 6/21/2013 91
10 EDM3 Comdty 98.0950 1.9050 Jun-12 6/19/2013 6/21/2013 9/20/2013 91
11 EDU3 Comdty 97.8450 2.1550 Sep-12 9/18/2013 9/20/2013 12/20/2013 91
* Libor Rates
Libor Tenor Periodicity Expiration Rate
US0002W index 2 W 5/30/2011 0.17975
US0001M index 1 M 6/16/2011 0.19875
US0002M index 2 M 7/18/2011 0.232

35. How is the TED spread
calculated? 3 methods.
1. Implied Yield:
The stub Libor and ED rates are used
to find the par coupon of a swap
whose cash flows correspond to that
of the treasury note. The TSY yield is
subtracted from this par coupon to
produced the spread.
2. Spread
It represents the bps that must be
subtracted from the stub Libor and 1 – Implied Yield TED: Par Coupon on a
Eurodollar futures contract rates to set swap: Not tradable
the PV of the TSY notes cash flows to 2 – Spread: Subtracting basis points
its full market price (dirty). Act/360
money market basis points. from Futures
3 – Implied Price: PV of cash flows
3. Implied Price. (best).
Method used in the next slide. The TSY
notes cash flows are discounted at the
stub Libor and Eurodollar futures
rates. The implied yield resulting from
the PV is subtracted from the TSY
notes yield (S/A bond equivalent basis
points).

36. Calculate the TED spread Step 1 – Match the cash flows of the treasury note with the Eurodollar deposit periods.
Step 2 – Find the interpolated Eurodollar discount function.
On-the-run Treasury 2 year note
Df 9/16/2011 = [1+0.00197632*30/360]-1
Coupon 0.625 percent
Maturity 4/30/2013 *[1+0.00265*91/360]-1
Settlement 5/16/2011 =0.99166031
Accrued Interest 0.0220788 percent
Clean Price 100.1523438 Df 12/23/2011 = [1+0.00197632*30/360]-1
Full price 100.1744226 *[1+0.00265*91/360]-1
Yield 0.5465946 percent *[1+0.0031*91/360] -1
Face Amount $1,000,000.00
*[1+0.004*91/360]-1
Cash Flows =0.998383686
Present We interpolate the discount factors for 10/31/2011,the payment date of the note.
Date Interest Principal Df Value Rather than using the actual values, we use the natural log of these values (which
10/31/2011 3125 0 0.9987791 3121.19 flattens or smoothen the curvature of the ED forward curve).
4/30/2012 3125 0 0.9967968 3114.99
10/31/2012 3125 0 0.9928456 3102.64
LN(Df9/16/2011)=LN(0.99166031)=-0.00083
4/30/2013 3125 1000000 0.9861227 989204.3
Total PV= 998,543.1 LN(Df12/23/2011)=LN(0.998383686)=-0.00162
Dirty Price 99.85431 As 10/31/2011 is 45 days into the Sep – Dec 11 period, the discount factor should
reflect 45/91 day change for the period.
Clean px 99.83223
Df 10/31/2011=-0.00083+(45/91)*(-0.00162-(-0.00083)=-0.00122
Yield 0.711475
Using e ln(x) =x, where e is the base of the natural logarithm, we have e-
0.00122=0.998779081
TED 16.48806 (0.711475-0.5465946)
The discount factors for the 2nd, 3rd and 4th terms are solved similarly. All the values
are show in the cash flow table.

37. Appendix:
How to create an ED strip
• The first step is to construct a forward strip that begins with the soonest-
to-expire, front futures.
• It ends with the contract whose deposit contains the maturity of the
contiguous swap.
• A cash libor deposit that spans the period from settlement to the front
contract’s expiration is added to the front of the strip: The ‘front stub’.
• The resulting structure is a synthetic, long term, Libor quality deposit that
begins at settlement and terminates at the end of the final contract’s
deposit period.
• The rates in the chain determine the future value to which a present value
would grow if invested during the sequence of deposits that makes up the
strip.
• In other words, the chain also determines the PV of a future payment
occurring at the final maturity of the strip.

38. Appendix:
Pricing a Eurodollar Strip
PV FV * [ 1 r /( t / 360)] 1
A eurodollar strip is composedof n depositperiods - each with a uniqueinterest rate (ri )
and term (ni ). So, we can write : PVi FVi * [ 1 ri ( t i / 360)] 1 ; PVi present value
at the start of the ith depositperiod.
FVi future value at the end of the ith deposit;ri interest rate for the ith depositperiod
i number of the depositperiod, i 1,2,3...,n
Solving for the PV of a sequenceof investments starting from n to n-1 :
The strip is a sequenceof investments : The proceeds at the terminatio n of one
depositare fully and immediatel y reinvested in the next depositperiod as a sequence.
So, the present value for a given period is the future value of the preceding period.
FVi 1 PVi . Applying this equation to, say, the third depositperiod :
1
PV3 FV3 * [ 1 r3 * ( t 3 / 360)]
to find the present value of this deposit,we must discountit over the secondperiod :
1
PV2 FV2 * [ 1 r2 * ( t 2 / 360)]
1
PV2 PV3 * [ 1 r2 * ( t 2 / 360)]
or PV2 FV3 * [ 1 r3 * ( t 3 / 360)] 1 * [ 1 r2 * ( t 2 / 360)] 1

39. Solving for the PV of a sequence of investments from n to today and
Discount Function
We arrive at the present value of the cash flow at the sart of the
depositperiod - that is, today - by discountin it over the firstperiod,
g
1
PV1 FV3 * [ 1 r3 * ( t 3 / 360)]
1
* [ 1 r2 * ( t 2 / 360)]
1
* [ 1 r1 * ( t 3 / 360)]
The quantity [ 1 ri * ( t i / 360)] 1 is the discountfactor, dfi , for period i
over any depositperiods n over which FVn is discounted. The discountfactor
determines , in present value - at the start of period, i of a sumpaid at the end of period i .
1
di [ 1 ri * ( t i / 360)]
We can then express the PV as :
PV FVn * ( df1 * df2 * df3 ... * dfn )
The right most term between the parentheses is the productof the n discountfactors
that composethe strip.It is called the discountfunctionand is written as :
DFn ( df1 * df2 * df3 ... * dfn )
where dfi discountfactor for period i
DFn discountfunctioncomposedof the productof the n - period discountfactors.
It gives PV FV * DFn .