Interest Rate Swaps

October, 2007
Primary Analyst: Jason Stipanov
(212)-761-2983
jason.stipanov@morganstanley.com

The Primary Analyst(s) identified above certify that the views expressed in this report accurately reflect his/her/their personal views about the subject securities/instruments/issuers, and no
part of his/her/their compensation was, is or will be directly or indirectly related to the specific views or recommendations contained herein.

This report has been prepared in accordance with our conflict management policy. The policy describes our organizational and administrative arrangements for the avoidance,
management and disclosure of conflicts of interest. The policy is available at www.morganstanley.com/institutional/research.

Please see additional important disclosures at the end of this report.

Interest Rate Swaps
The Structure of a Swap

See additional important disclosures at the end of this report.

2
What is a Swap?
Spot-Starting 5-Year Fixed/Floating Swap ($100MM Notional)

Fixed Payments
5.05% Semiannually on 30/360-Day Count
Party A Party B
3-Month LIBOR Quarterly on Act/360-Day Count

Floating Payments

• Swap: Contractual agreement to exchange fixed for floating cash flows over a
specified period of time
• Floating rate reference: USD LIBOR
• LIBOR: British Banker Association’s (BBA) fixing of the London Inter-Bank Offered
Rate. A contributor bank contributes the rate at which it could borrow funds, if it
were to do so by asking for and accepting inter-bank offers in reasonable market
size just prior to 11 AM London time. 16 banks contribute, the top and bottom 4
fixings are eliminated, and the remaining 8 fixings are averaged.

See additional important disclosures at the end of this report.

3
A Cashflow Example
Swap rate = average of expected LIBOR settings
Suppose You Pay Fixed on a 2-year Swap at a Rate of 4.83%

Floating Leg Fixed Leg

3M LIBOR = 5.21% (Quarterly, Actual/360)

3M LIBOR in 3 months 4.83% (Semi, 30/360)

3M LIBOR in 6 months

3M LIBOR in 9 months 4.83% (Semi, 30/360)

3M LIBOR in 1 year

3M LIBOR in 1YR 3M 4.83% (Semi, 30/360)

3M LIBOR in 1YR 6M

3M LIBOR in 1YR 9M 4.83% (Semi, 30/360)

See additional important disclosures at the end of this report.

4
A Swap is Similar to a Leveraged Bond
Similar to a leveraged bond transaction
Swap Transaction Is Similar to a Bond Transaction
Combined with 3-Month Financing

Receive Fixed on a Swap

You

Pay LIBOR

UST Rate (buy bonds)

You
Pay Repo

See additional important disclosures at the end of this report.

5
A Swap Is Different from a AA Bank Bond
An interest rate swap has different characteristics compared to a AA bank bond

• Differences between a swap contract and a AA bank bond

− Swap: No risk of principal loss or default
− Swap: Less risk of downgrade (if a bank is downgraded, it will be thrown
out of the LIBOR panel)
− Swap: Majority of trades are collateralized, thus reducing counterparty risk
• Result: Swap rates trade richer than AA bank credits
Components of Corporate Bond Treasury Spread

Swap Spread =
Systemic Risk

Company
Specific Risk

See additional important disclosures at the end of this report.

6
Determining Future Expectations of LIBOR

• How Do We Determine Expectations of Future 3M LIBOR

Settings?
• Out to 5 years, we use Eurodollar contracts:
− Forward contracts on 3M LIBOR
− Liquidity exists out to 5 years
− Convexity issue

• Beyond 5 years, expected 3M LIBOR settings are implied

from the swap rates.

See additional important disclosures at the end of this report.

7
Generating the Swap Curve
From the Eurodollar Futures and Market Traded Swap Rates, a Swap
Curve Is Generated
The swap curve is smooth and continuous, unlike government bond curves
0.058
0.056
0.054
0.052 Swap spread
0.05
0.048
0.046
Swap Rate
0.044
Tsys
0.042
0.04
October 5, March 27, September March 9, August 30, February August 12,
2007 2013 17, 2018 2024 2029 20, 2035 2040

Source: Morgan Stanley

See additional important disclosures at the end of this report.

8
The Duration and Convexity of a Swap
• DV01 (for a bond) - The change in the price of the bond for a 1bp change in
yield. To calculate shift the bond yield by 1 bp and compute the price change.
• DV01 (for a swap) - The change in PV (present value) of the swap for a 1 bp
parallel shift in the swap curve.
• PV01 - The present value of a 1bp annuity with a maturity equal to the swap
maturity.
• Note that for a par swap, DV01 ≈ PV01. For a swap that is not at par DV01
must be used.
• The market convention is typically to only quote the duration of the fixed leg of
the swap.
• Stub risk - The duration of the floating leg of the swap, arises because once
LIBOR is set it becomes a 3M fixed rate. Typically managed separately, but
can be meaningful when LIBOR is volatile.
• Convexity – Change in DV01 of a swap for a 1 bp parallel shift in the swap
curve.

See additional important disclosures at the end of this report.

9
Who Uses Swaps and Why?
The Major Players in the Swap Market

See additional important disclosures at the end of this report.

10
Who Uses the Swaps Market?
New Issue Asset Swaps Asset/Liability Loan Originations Asset Swaps
Hedging Management Hedging (Prepays)

Eurodollar Exchange
OAS
Corporates ABS/CMBS

Volatility

Global Mortgages
Rate/FX/Credit (Residential) Asset
Arbitrage Swap Market Swaps

Convexity
Hedging

Discount
Repo Agencies Notes
Treasuries

Specials On-the-Run Off-the-Run Bullets Callables Mortgage

GC Market

See additional important disclosures at the end of this report.

11
Corporation – To Hedge New or Existing Issuances
Rate Lock Asset/Liability Management Swap
Before New Issuance After existing Issuance

UST + Swap Spread UST + Swap Spread

Swap Swap
Corporate Corporate
Dealer Dealer
LIBOR LIBOR

UST +
Credit Spread
Investor

Swap Spreads Widen Swap Spreads Tighten

• Corporates pay fixed to hedge • Corporates receive fixed to achieve

future debt issuance floating rate exposure

See additional important disclosures at the end of this report.

12
Dealers – To Hedge Inventory

UST + Swap Spread

Bond Trading
Desk Swap Trading Desk
LIBOR
UST + Credit Spread

Corporate Bond
Issuer Swap Spreads Widen

• Active users: Hedge funds, pension funds, banks, and

insurance companies
• Asset swap strategy: Valuing fixed-rate assets relative to
LIBOR curve

See additional important disclosures at the end of this report.

13
Mortgage Holders
Convexity Hedging
– To Hedgein the US
Convexity
Duration Profile

New
Interest Swap
Rates Mortgage
Increase Portfolio Swap
Mortgage Swap
Portfolio Hedge Hedge

– OR –

Interest
Rates Unwind
Mortgage Swap Decrease Swap
Portfolio Hedge Swap
Mortgage
Portfolio Hedge

See additional important disclosures at the end of this report.

14
Money Managers – To Manage Portfolio
Exposure

Treasury Bonds

Agency Bonds
Money Manager Swap Market
Mortgages
Pay or receive fixed in the swap market
Corporate Bonds

• Money Manager Transacts with the Swap Market to:

− Increase and reduce spread exposure
− Lengthen or shorten duration

See additional important disclosures at the end of this report.

15
Interest Rate Swaps
The Swap Spread

See additional important disclosures at the end of this report.

16
The Swap Spread
• Swap spread: The difference between the yield on a government
security (such as a US Treasury) and the fixed rate of a floating swap
(with the same maturity as the Treasury).

• What drives the swap spread?

− Fundamental Factors:
• Carry & Funding
• Systematic risk

− Technical factors
• Treasury-specific factors
• Supply/demand effect

See additional important disclosures at the end of this report.

17
The Four Swap Spread Drivers
• Carry/Funding effect: if the difference between GC repo and 3mL were
to permanently remain fixed at 25bp, the swap spread would also be
25bp. This effect is more pronounced in the short term.

• Systematic Risk factor: a market-wide credit squeeze would drive up

3mL, which would drive up the fixed rate on a swap and increase the
swap spread.

• Treasury-specific factors: some individual Treasury bonds can be

scarce and thus be funded at levels below GC repo.

• Supply/Demand effect: swaps are often a better hedging tool than Tsys
as they also include systematic market risk. In times of crisis, for
instance, the Treasury curve decouples from other assets since it is risk-
free by definition.

See additional important disclosures at the end of this report.

18
Funding Spreads Example –
The Term Structure of Turmoil
3m Libor / Fed Funds Fwd Spreads
120
• Stress in the asset-backed 100

commercial paper market has 80

3m

pushed the 3M Libor / fed

6m
60 9m

funds spread significantly 40 1y

wider 20

• The basis swap market is -20

implying the spread will stay

7
7

7
/0

/0

/0

/0

/0

/0
9/

6/

3/
11

25

23

20

17

/1
7/

8/

9/

10
6/

6/

7/

8/

9/
wide for the next 6-12
months. 2y and 10y Swap Spreads

• This has affected swap

spread carry dramatically and
has caused swap spreads to
widen, especially 2y spreads

See additional important disclosures at the end of this report.

19
Supply / Demand Factor –
Dealers
Mortgage– To Hedge Inventory
Convexity Hedging
Convexity Hedging Needs Swap Spreads vs. Durations
40
90
Incremental Convexity Hedging Needs ($ billion

30 Sell-Off Rally 80 10Y Spds vs TBA

10Y Swap Spreads

20
Index
70
in 10-year Swap Equiv)

10 60 Oct-11 Close
50
0
40
-10 2
30
R = 0.6212
-20
20
2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50
-30
180 160 140 120 100 80 60 40 20 0 -20 -40 -60 -80
Mortgage Index Duration
Interest Rate Scenario (parallel shift, bp)

• Since mortgage durations are volatile and the mortgage market is large,
mortgage hedging needs are typically the most important driver of 10-
year swap spreads.

See additional important disclosures at the end of this report.

20
Roll and Carry Considerations

See additional important disclosures at the end of this report.

21
Roll-Down & Carry – Definitions and Concepts
• Roll-Down & Carry comprise the entire PnL in an unchanged market

• Especially important in an environment of low volatility or low conviction

• Profit/Loss = Capital Gains + Interest Income

= Δ(Price) from Market Volatility + Roll-Down + Pull-to-Par + Coupon - Funding

≈ Δ(Price) from Market Volatility + Roll-Down + Yield - Funding

≈ Δ(Price) from Market Volatility + Roll-Down + Carry

See additional important disclosures at the end of this report.

22
Roll-Down & Carry – Calculations
Roll-Down
• Fully realized in a stable yield curve environment

• Example: 6M roll-down on a 10Y swap:

Leveraged Perspective = 10Y Rate – 9.5Y Rate

Total Return ≈ (10Y Rate – 9.5Y Rate) * (PV01 of a 9.5Y Swap)

Carry
• Can be locked in on trade date
• Example: 6M carry on a 10Y swap:

Leveraged Perspective ≈ (10Y Rate)*(180/360) - (6M LIBOR)*(Act/360)

(PV01 of a 9.5y Swap)
Total Return = (10Y Rate)*(180/360) - (6M LIBOR)*(Act/360)

• Note that in a forward-starting swap, there is no carry (only roll-down)

See additional important disclosures at the end of this report.

23
Quick Carry Estimations
• Carry on spot rates (and hence forward rates) can be estimated very quickly
using simple arithmetic:
Example
Using only spot rates, what is the 3M carry on a duration neutral 2s10s flattener?

(short) (long)

2yr leg 10yr leg

+ rate 4.852% 5.305%
- 3ML 5.214% 5.214%
= 1Y carry - 36.4 bp 9.1 bp
→ 3M carry - 9.1bps 2.23 bps
≈ Duration 1.887 7.735
Bp running - 4.822 bps running 0.288 bps running

carry
bp running =
swap duration
•Thus the approximate carry on a 2s10s flattener would be: 0.288 - (-4.822) = 5.11 bps running.

See additional important disclosures at the end of this report.

24
Forward-Starting Swaps

See additional important disclosures at the end of this report.

25
What Does the Forward Rate Represent?
• The forward rate/yields represents the breakeven future rate/yield on the bond
versus investing in the short rate

• Example:
− Spot 10-year Treasury yield = 4.6%
− 3-month forward yield = 4.75%
− Thus, if you buy the 10-year note rather than invest in 3-month cash, you will break
even on the position (relative to the cash alternative) if the 10-year yield increases by
15 bp over the next three months

• Given that the LIBOR curve has a constant financing rate and is not impacted
by idiosyncratic bond risk, it is easier to judge the shape of the forward curve in
the swap market

See additional important disclosures at the end of this report.

26
Expressing Views Using Forward Starting Swaps
• If an investor has a time horizon that is greater than one day, he/she
should be concerned with what is priced into the forward swap market
rather than the spot market.

• For example:

• Suppose an investor believes that the 2-year swap rate is likely to

decrease by 50 bp over the next year.

• Receiving on a 2-year swap does not express this view as the swap will be
an 1-year instrument in one year’s time.

• Thus, the investor needs to consider the 2-year rate one year forward.

• Note that if this rate is trading 100 bp lower than the spot 2-year rate, then
the investor may in fact wish to pay on the forward rate - despite the fact
he/she believes that 2-year rates will fall.

See additional important disclosures at the end of this report.

27
Forward-Starting Swaps: Cash Flows
A forward-starting swap = Combination of two spot-starting swaps

For example…

A 2-year swap 5-years forward is a combination of receiving on a 7-year swap and

paying on a 5-year swap with equal notional amount

Receive fixed on $100 mm

of a 7-year swap
0y 1y 2y 3y 4y 5y 6y 7y
Pay fixed on $100mm
of a 5-year swap

Net actual cash flows

Net exposure:
Receive 5y2y fixed 0y 1y 2y 3y 4y 5y 6y 7y

Note: floating rate components cancel each other out for the first five years

See additional important disclosures at the end of this report.

28
Forward-Starting Swaps: Embedded Exposures
• As combinations of two spot starting swaps, forward-starting swaps have
embedded exposures that should be considered.

• For example, receiving on a 5y5y forward swap is equivalent to receiving

the spot 10-year rate, while paying on the spot 5-year rate on equal
notionals. This means the trade has both an outright exposure to the spot
10-year rate, but also has an embedded 5s/10s flattener
Breaking down a 5y5y forward starting swap Receive Pay
10-year fixed 5-year fixed
Forward Starting Swap
Notional 100 100
PV01 Risk 7.73 4.38

Forward Starting Swap

Broken Down

Duration Neutral Flattener Notional 56.66 100

PV01 Risk 4.38 4.38

Outright Long Notional 43.34

PV01 Risk 3.35

See additional important disclosures at the end of this report.

29
Forward-Starting Swaps: Embedded Exposures
In general, forward rates move with the outright level of the market…

• The usual curve dynamics of bull steepening and bear flattening result in
offsetting influences on forward rates: in a rally, forward rates fall with the
spot rates, but the steepening puts upward pressure on the forward rates;
vice-versa in a sell-off.

• These offsetting factors mean that we need to look at correlations between

spot and forward rates to see how the exposures affect the forward rate:
Correlations since 1990 Correlations since 2006
Rate 1 Rate 2 Beta Correlation Rate 1 Rate 2 Beta Correlation
10y 5y5y 0.95 89.93% 10y 5y5y 0.78 86.65% For each 10 bp move in the
30-year rate, we expect
2y 1y1y 1.03 96.28% 2y 1y1y 0.78 94.59% around 9 bp of movement
5y 2y3y 0.95 91.24% 5y 2y3y 0.81 90.71% from the 10y20y rate (based
20y 10y10y 0.97 87.69% 20y 10y10y 0.87 93.10% on data from the past year)
30y 15y15y 0.73 81.32% 30y 15y15y 0.92 97.53%
30y 10y20y 0.87 88.64% 30y 10y20y 0.90 96.27%

See additional important disclosures at the end of this report.

30
Example –
The Relationship Between Forward Rates and Carry
Suppose a client is interested in 2s/10s curve flattener - how can we quickly establish the roll-
and-carry characteristics of a duration neutral 2s/10s flattener?

For Swap Tenor We know that for the 10-year rate (for example):
In 01Y 02Y 03Y 04Y 05Y 06Y 07Y 08Y 09Y 10Y 15Y 20Y 25Y
0M 4.97 4.79 4.83 4.91 5.00 5.06 5.12 5.17 5.22 5.26 5.40 5.47 5.49 • 3m Roll-down = 10y Rate - 9.75y Rate
1M 4.89 4.76 4.82 4.90 4.99 5.06 5.12 5.17 5.22 5.27 5.40 5.47 5.49 • 3m Carry = 9.75y Rate 3m Forward - 10y Rate
3M 4.77 4.72 4.80 4.90 4.99 5.06 5.12 5.18 5.22 5.27 5.41 5.47 5.49
6M 4.63 4.69 4.80 4.92 5.01 5.08 5.14 5.19 5.24 5.29 5.42 5.48 5.50 Hence:
1Y 4.61 4.76 4.89 5.00 5.08 5.15 5.21 5.26 5.31 5.36 5.46 5.52 5.53
• 3m Roll and Carry = 10y Rate - 9.75y Rate
Expiry

2Y 4.92 5.04 5.15 5.22 5.28 5.32 5.37 5.42 5.47 5.51 5.56 5.60 5.60
3Y 5.16 5.28 5.33 5.38 5.42 5.46 5.50 5.55 5.59 5.61 5.64 5.66 5.65 + (9.75y Rate 3m Forward - 10y Rate)
4Y 5.40 5.42 5.46 5.49 5.53 5.57 5.62 5.66 5.68 5.67 5.69 5.70 5.68
5Y 5.45 5.49 5.53 5.57 5.61 5.67 5.71 5.72 5.71 5.71 5.73 5.72 5.70 = 9.75y Rate 3m Forward - 9.75y Rate
7Y 5.61 5.65 5.71 5.77 5.81 5.81 5.79 5.78 5.77 5.77 5.78 5.75 5.72 Similarly:
10Y 5.99 6.00 5.94 5.88 5.83 5.81 5.81 5.81 5.82 5.82 5.79 5.74 5.70
15Y 5.70 5.75 5.78 5.80 5.81 5.81 5.80 5.79 5.77 5.76 5.69 5.64 5.60 10y Rate 3m Forward - 10y Spot Rate
20Y 5.80 5.76 5.73 5.70 5.68 5.66 5.65 5.63 5.62 5.60 5.54 5.50 5.48 = Roll and Carry on 10.25Rate

So: 3m Forward 2s/10s curve - Spot 2s/10s curve = (10y Rate 3m Fwd - 2y Rate 3m Fwd) - (Spot 10y Rate - Spot 2y Rate)
= (10y Rate 3m Fwd - Spot 10y Rate) - (2y Rate 3m Fwd - Spot 2y Rate)
= Roll and Carry on 10.25 Rate - Roll and Carry on 2.25 Rate
= Roll and Carry on a Duration Neutral 2.25y/10.25y Flattener
≈ Roll and Carry on a Duration Neutral 2s/10s Flattener

See additional important disclosures at the end of this report.

31
Approximation Can be Used to Understand Roll and
Carry
Such valuation techniques can be used to look at roll and carry over history...

(3m Fwd - Spot) 2s10s Curve

3m Forward 2s10s Spot 2s10s (3m Fwd - Spot) 2s10s Curve • Plotting the historical
difference between the
3.5 20
2s/10s curve 3 months
3
10 forward and the spot
2.5 2s/10s curve gives an idea
0
C u r v e le v e l

2 of the level of roll-and-

1.5 -10 carry offered in the past.
1
-20 • Recent steepening of the
0.5 forward curve has led to
0
-30 relatively high levels of
11-Aug-87 7-May-90 31-Jan-93 28-Oct-95 24-Jul-98 19-Apr-01 14-Jan-04 10-Oct-06 6-Jul-09 roll-and-carry for
-0.5 -40
flattening trades.
Date

See additional important disclosures at the end of this report.

32
Convexity Issues (I)
When looking further out on the forward curve, convexity issues need to be kept
in mind...
For Swap Tenor 2s10s
In 01Y 02Y 03Y 04Y 05Y 06Y 07Y 08Y 09Y 10Y 15Y 20Y 25Y bps
0M 4.97 4.79 4.83 4.91 5.00 5.06 5.12 5.17 5.22 5.26 5.40 5.47 5.49 47.1
1M 4.89 4.76 4.82 4.90 4.99 5.06 5.12 5.17 5.22 5.27 5.40 5.47 5.49 50.6
3M 4.77 4.72 4.80 4.90 4.99 5.06 5.12 5.18 5.22 5.27 5.41 5.47 5.49 55.3
6M 4.63 4.69 4.80 4.92 5.01 5.08 5.14 5.19 5.24 5.29 5.42 5.48 5.50 60.2
1Y 4.61 4.76 4.89 5.00 5.08 5.15 5.21 5.26 5.31 5.36 5.46 5.52 5.53 60.0
Expiry

2Y 4.92 5.04 5.15 5.22 5.28 5.32 5.37 5.42 5.47 5.51 5.56 5.60 5.60 47.2
3Y 5.16 5.28 5.33 5.38 5.42 5.46 5.50 5.55 5.59 5.61 5.64 5.66 5.65 33.5
4Y 5.40 5.42 5.46 5.49 5.53 5.57 5.62 5.66 5.68 5.67 5.69 5.70 5.68 25.3
5Y 5.45 5.49 5.53 5.57 5.61 5.67 5.71 5.72 5.71 5.71 5.73 5.72 5.70 21.4
7Y 5.61 5.65 5.71 5.77 5.81 5.81 5.79 5.78 5.77 5.77 5.78 5.75 5.72 11.7
10Y 5.99 6.00 5.94 5.88 5.83 5.81 5.81 5.81 5.82 5.82 5.79 5.74 5.70 -17.6
15Y 5.70 5.75 5.78 5.80 5.81 5.81 5.80 5.79 5.77 5.76 5.69 5.64 5.60 0.9
20Y 5.80 5.76 5.73 5.70 5.68 5.66 5.65 5.63 5.62 5.60 5.54 5.50 5.48 -16.1
• Is the market really pricing inversion of the 10s/30s curve in 7 years’ time?
• No: the curve has greater convexity in the 30-year sector...

See additional important disclosures at the end of this report.

33
Convexity Issues (II)
• Consider a duration neutral 10s/30s flattener 10 years forward.
•Differences in convexity mean that as the market moves, re-hedging is required to remain duration neutral...

Rate (%) PV01 Notional (mm) Risk Initially, the trade is set up to be duration neutral.
Pay 10y10y 5.75 4.85 190.91 9.26
Receive 10y30y 5.60 9.26 100 9.26

Market rallies - yield curve falls 100 bp in parallel As the market rallies, higher convexity means the duration on
Rate (%) PV01 Notional (mm) Risk the 10y30y rate increases more, leaving the trade needing re-
Pay 10y10y 4.75 5.64 190.91 10.77 hedging to make it market directional again. The investor
Receive 10y30y 4.60 11.57 100 11.57 therefore has to pay on around $ 7 mm 10y30y at 4.60%

Market sells-off - yield curve rises 200 bp in parallel

Similarly, when the market sells off the duration of the 10y30y
Rate (%) PV01 Notional (mm) Risk
falls faster, and now the investor needs to receive on around
Pay 10y10y 6.75 4.18 190.91 7.98
$ 14 mm 10y30 at 6.60% to re-hedge.
Receive 10y30y 6.60 7.47 93.06 6.95

Market rallies back to original level of yields

Rate (%) PV01 Notional (mm) Risk
Pay 10y10y 5.75 4.85 190.91 9.26
As the market rallies back to the original level, a final hedge of
Receive 10y30y 5.60 9.26 106.8 9.89 paying around $ 7 mm of 10y30y at 5.60% is required.

The market has returned to the original levels, suggesting the flattener has had zero P&L -
So what has however, during the hedging, the investor has paid at 4.60% and received at 6.60% and 5.60%
happened? resulting in profit. This is due to being long convexity, and so the forward curve demands a
premium for this privilege - hence, the 10y30y rate is lower and the forward curve is inverted.

See additional important disclosures at the end of this report.

34
Significance Ratio – Volatility Adjusted Carry
• Significance Ratio = [Rolldown & Carry] / Volatility
• A metric to find good risk / reward carry trades.
Levels on 3/15/2007
Spot 1s10s -15 bp
1y Fwd 1s10s 35 bp
Rolldown 50 bp
3m Realized Volatility 27.2
Sig Ratio 1.9

Levels on 10/15/2007
Spot 1s10s 35 bp
1y Fwd 1s10s 65 bp
Rolldown 30 bp
3m Realized Volatility 54.2
Sig Ratio 0.5

See additional important disclosures at the end of this report.

35
Morgan Stanley Forward Grid
• Black Cell if percentile for the rate is
greater than 1 standard deviation ; Grey
Cell if percentile for the rate is less than
/ equal to -1 standard deviation.

• ▲ if percentile for spread from spot is

greater than 1 standard deviation ;▼ if
percentile for spread from spot is less
than / equal to -1 standard deviation.

• Green if value is less than zero ; Red if

value is greater than zero.

See additional important disclosures at the end of this report.

36
The Details of Asset Swapping

See additional important disclosures at the end of this report.

37
Yield/Yield Asset Swap
The focus on simplicity
− On a long swap spread position, the investor simply purchases a bond and
pays fixed on a swap to the maturity of the bond, duration weighted

− The yield/yield asset swap spread is simply the difference between the yield-
to-maturity of the bond and the par swap rate to the maturity of the bond

− Example (10/16/07 trade date)

• Investor buys $100mm UST 8/17 at a yield of 4.75%

• Investor pays 5.252% on a $101.2mm of a swap from 10/18/02 to 8/15/17
• Yield/yield swap spread: 60.2 bp (5.252% - 4.650%)
• DV01 of the bond: 7.862
• DV01 of the fixed leg of the swap: 7.769
• Hedge ratio: 1.012

See additional important disclosures at the end of this report.

38
 Par/Par Asset Swap Methodology
Upfront Exchange of $$ to Bring the Bond to Par

UST 4.75% $100.86 Investor $0.86 Swap Dealer

8/15/17 (initial payment) (initial payment)

Trade
date:
4.75% (S/A Act/Act)
UST 4.75% 4.75% (S/A Act/Act)
8/15/17 (coupon payments) Investor Swap Dealer
USDLibor – 60.2 bp
(Q Act/360)

UST 4.75% $100.00 Investor

Maturity
8/15/17 (final payment)
date:

See additional important disclosures at the end of this report.

39
 MVA Asset Swap Methodology
Final exchange and change of floating notional to bring the bond to par

UST 4.75% $100.86 Investor

8/15/17 (initial payment)

Trade
date:
4.75% (S/A Act/Act)
UST 4.75% 4.75% (S/A Act/Act)
8/15/17 (coupon payments) Investor Swap Dealer
USDLibor – 60.3 bp
(Q Act/360)
Notional amount = 100.86

UST 4.75% $100.00 Investor

Maturity
8/15/17 (final payment) $0.86 Swap Dealer
date:
(final payment)

See additional important disclosures at the end of this report.

40
Other Methods to Note
− Main issue: How to cope with a bond that does not
trade at par
• Premium/discount can be amortized over time
according in different ways
− Linear
− Constant bond yield (yield accrete)
− Theoretical LIBOR OAS
• Shifting LIBOR forwards to discount the bond’s
cashflows back to the price of the bond
• Theoretical notion, not able to trade

See additional important disclosures at the end of this report.

41
Summary Matrix
•Par/Par •MVA •Yield/Yield

•True match of cash

•Brings all bonds
flows - notional on •Ease of execution
back to par
LIBOR leg is equal
•Bestfor comparing to repo notional •Market standard
•Pros bonds with volatility •Easy to monitor and
•Compare directly to
exposure value
repo/LIBOR spread
•Relatively
constant
•No collateral/credit
spread duration
issues on day one

•Convexity risk -
•LIBOR financing
•Large upfront trade is duration
assumption on the
payment creates weighted, not
final payment
credit/collateral convexity weighted.
issues •Trade effectively
•Impliedcurve risk
embeds a LIBOR
•Cons •Financing for bonds with off-
based loan
assumption for the market coupons
upfront payment •Spread duration not
•Carry estimation for
constant (too many
•Execution bonds not trading
changing parts)
close to par
•Execution

See additional important disclosures at the end of this report.

42
Other Topics

See additional important disclosures at the end of this report.

43
Swap Market Correlations to Be Aware of...
Most swap curve trades and many butterfly trades have a high degree of market directionality which
should always be kept in mind when considering such trades. The correlations are useful guides in
relative value analysis - it should always be remembered, however, that they can break down and
reasons for such breakdowns are usually of interest.
The following graphs highlight a few such correlations...
USD 2s10s vs 1y1y Rate USD 50/50 2s10s30 Fly vs 2s10s Curve

In general, the yield curve steepens in rallies and flattens in sell-offs as central bank movement leads the way.
In general the 2s10s curve is more volatile than the 10s30s curve, so the belly of the 2s10s30s fly tends to cheapen
when the 2s10s curve steepens

See additional important disclosures at the end of this report.

44
Butterfly Trades - Risk Weighting Methodologies
Trading one curve against another
Risk weightings can be developed in several ways.
Simple Butterfly (50/50 Risk Weighted)
Butterfly Level quoted as 1 x 5y rate – 0.5 x 2y rate – 0.5 x 10y rate
Risk distributed equally on each wing.

Volatility-adjusted Butterfly
Risk assigned according to volatility of the curves involved in the butterfly.
Accounts for relative volatilities but not correlations.

Regression Weighted Butterfly

Regress one curve in the butterfly against the other and determine the hedge ratio based on the beta of the regression.
Regressions are not symmetrical. The hedge ratio is dependent on which curve is chosen as the independent variable.

PCA Weighted Butterfly

Principal component analysis – Decomposes the covariance matrix between points on the yield curve into orthogonal
eigenvectors
Weight trades to minimize exposure to the 2 eigenvectors that explain 99% of curve movements.
Accounts for correlations and relative volatilities, and results are symmetrical.

See additional important disclosures at the end of this report.

45
PCA or Regression

• Hedging 10-year rate with 5-year rate

• Regression 10Y changes on 5Y changes results in different hedge ratios than
regressing 5Y changes on 10Y changes – conditional analysis
• PCA does not have this problem – unconditional analysis

• Rich-Cheap detection
• Regression is time consuming as you would need regressions of 1s/5s, 2s/10s,
2s/5s/10s, 1s/3s/7s, 1s/4s/8s, 5s/7s/10s etc. to accomplish what PCA does

• PCA isolates direction, slope and curvature movements whereas this is

difficult to do with regression
• Hence, PCA can isolate a trade’s exposure to curvature net of direction and slope

See additional important disclosures at the end of this report.

46
Morgan Stanley PCA Report

• The PCA weights are determined using data since January 01, 1993
• The lifetime of the butterfly is determined from data since Jan 01 1993

• Rolldown and Carry assume as 6M investment horizon

• An investor who is long a butterfly is positioned for the level to fall. Roll and
Carry are computed to agree with this. That is, a negative value for carry or
rolldown works in favor of a long butterfly.

See additional important disclosures at the end of this report.

47
Morgan Stanley Quotient –
Historical Data & Basic Analytics

See additional important disclosures at the end of this report.

48
Follow Up
Please do not hesitate to contact us if you have any further questions:

Jason Stipanov
US Interest Rate Strategy
Jason.Stipanov@morganstanley.com
(212)-761-2983

See additional important disclosures at the end of this report.

49
Disclosures
The information and opinions in this report were prepared by Morgan Stanley & Co. Incorporated and/or one or more of its affiliates (collectively,
“Morgan Stanley”) and the research analyst(s) named on page one of this report.
As of September 28, 2007, Morgan Stanley held a net long or short position of US$1 million or more of the debt securities of the following issuers
covered in this report (including where guarantor of the securities): FANNIE MAE.
As of September 28, 2007, Morgan Stanley beneficially owned 1% or more of a class of common equity securities/instruments of the following
companies covered in this report: FANNIE MAE.
Within the last 12 months, Morgan Stanley managed or co-managed a public offering (or 144A offering) of securities of FANNIE MAE.
Morgan Stanley policy prohibits research analysts from investing in securities/instruments in their MSCI sub industry. Analysts may nevertheless own
such securities/instruments to the extent acquired under a prior policy or in a merger, fund distribution or other involuntary acquisition.
Morgan Stanley is involved in many businesses that may relate to companies or instruments mentioned in this report. These businesses include
market making, providing liquidity and specialized trading, risk arbitrage and other proprietary trading, fund management, investment services and
investment banking. Morgan Stanley trades as principal in the securities/instruments (or related derivatives) that are the subject of this report. Morgan
Stanley may have a position in the debt of the Company or instruments discussed in this report.

See additional important disclosures at the end of this report.

50
Other Important Disclosures
The securities/instruments discussed in this report may not be suitable for all investors. This report has been prepared and issued by Morgan Stanley
primarily for distribution to market professionals and institutional investor clients. Recipients who are not market professionals or institutional investor
clients of Morgan Stanley should seek independent financial advice prior to making any investment decision based on this report or for any necessary
explanation of its contents. This report does not provide individually tailored investment advice. It has been prepared without regard to the individual
financial circumstances and objectives of persons who receive it. Morgan Stanley recommends that investors independently evaluate particular
investments and strategies, and encourages investors to seek the advice of a financial advisor. The appropriateness of a particular investment or
strategy will depend on an investor’s individual circumstances and objectives. You should consider this report as only a single factor in making an
investment decision.
Morgan Stanley fixed income research analysts, including those principally responsible for the preparation of this research report, receive
compensation based upon various factors, including quality, accuracy and value of research, firm profitability or revenues (which include fixed income
trading and capital markets profitability or revenues), client feedback and competitive factors. Analysts’ compensation is not linked to investment
banking or capital markets transactions performed by Morgan Stanley or the profitability or revenues of particular trading desks.
This report is not an offer to buy or sell any security/instrument or to participate in any trading strategy. In addition to any holdings disclosed in the
section entitled “Important Disclosures on Subject Companies,” Morgan Stanley and/or its employees not involved in the preparation of this report may
have investments in securities/instruments or derivatives of securities/instruments of companies mentioned in this report, and may trade them in ways
different from those discussed in this report. Derivatives may be issued by Morgan Stanley or associated persons.
Morgan Stanley makes every effort to use reliable, comprehensive information, but we make no representation that it is accurate or complete. We have
no obligation to tell you when opinions or information in this report change.
With the exception of information regarding Morgan Stanley, reports prepared by Morgan Stanley research personnel are based on public information.
Facts and views presented in this report have not been reviewed by, and may not reflect information known to, professionals in other Morgan Stanley
business areas, including investment banking personnel.
The value of and income from investments may vary because of changes in interest rates, foreign exchange rates, default rates, prepayment rates,
securities/instruments prices, market indexes, operational or financial conditions of companies or other factors. There may be time limitations on the
exercise of options or other rights in securities/instruments transactions. Past performance is not necessarily a guide to future performance. Estimates
of future performance are based on assumptions that may not be realized.
This report may include research based on technical analysis. Technical analysis is generally based on the study of trading volumes and price
movements in an attempt to identify and project price trends. Technical analysis does not consider the fundamentals of the underlying issuer or
instrument and may offer an investment opinion that conflicts with other research generated by Morgan Stanley. Investors may consider technical
research as one input in formulating an investment opinion. Additional inputs should include, but are not limited to, a review of the fundamentals of the
underlying issuer/security/instrument.

See additional important disclosures at the end of this report.

51
Other Important Disclosures (Cont.)
To our readers in Taiwan: Information on securities/instruments that trade in Taiwan is distributed by Morgan Stanley Taiwan Limited ("MSTL"). Such
information is for your reference only. The reader should independently evaluate the investment risks and is solely responsible for their investment
decisions. This publication may not be distributed to the public media or quoted or used by the public media without the express written consent of
Morgan Stanley. Information on securities/instruments that do not trade in Taiwan is for informational purposes only and is not to be construed as a
recommendation or a solicitation to trade in such securities/instruments. MSTL may not execute transactions for clients in these securities/instruments.
To our readers in Hong Kong: Information is distributed in Hong Kong by and on behalf of, and is attributable to, Morgan Stanley Asia Limited as part of
its regulated activities in Hong Kong. If you have queries concerning this publication, please contact our Hong Kong sales representatives.
Certain information in this report was sourced by employees of the Shanghai Representative Office of Morgan Stanley Asia Limited for the use of
Morgan Stanley Asia Limited.
THIS PUBLICATION IS DISSEMINATED IN JAPAN BY MORGAN STANLEY JAPAN SECURITIES CO., LTD.; IN HONG KONG BY MORGAN
STANLEY ASIA LIMITED; IN SINGAPORE BY MORGAN STANLEY ASIA (SINGAPORE) PTE., REGULATED BY THE MONETARY AUTHORITY OF
SINGAPORE, WHICH ACCEPTS RESPONSIBILITY FOR ITS CONTENTS; IN AUSTRALIA BY MORGAN STANLEY AUSTRALIA LIMITED A.B.N. 67
003 734 576, A LICENSED DEALER, WHICH ACCEPTS RESPONSIBILITY FOR ITS CONTENTS; IN CANADA BY MORGAN STANLEY CANADA
LIMITED, WHICH HAS APPROVED OF, AND HAS AGREED TO TAKE RESPONSIBILITY FOR, THE CONTENTS OF THIS PUBLICATION IN
CANADA; IN GERMANY BY MORGAN STANLEY BANK AG, FRANKFURT AM MAIN, REGULATED BY BUNDESANSTALT FUER
FINANZDIENSTLEISTUNGSAUFSICHT (BAFIN); IN SPAIN BY MORGAN STANLEY, S.V., S.A., A MORGAN STANLEY GROUP COMPANY, WHICH
IS SUPERVISED BY THE SPANISH SECURITIES MARKETS COMMISSION (CNMV) AND STATES THAT THIS DOCUMENT HAS BEEN WRITTEN
AND DISTRIBUTED IN ACCORDANCE WITH THE RULES OF CONDUCT APPLICABLE TO FINANCIAL RESEARCH AS ESTABLISHED UNDER
SPANISH REGULATIONS; IN THE UNITED KINGDOM BY MORGAN STANLEY & CO. INTERNATIONAL PLC, AUTHORISED AND REGULATED
BY THE FINANCIAL SERVICES AUTHORITY; AND IN THE UNITED STATES BY MORGAN STANLEY & CO. INCORPORATED, WHICH ACCEPTS
RESPONSIBILITY FOR ITS CONTENTS. IN AUSTRALIA, THIS REPORT, AND ANY ACCESS TO IT, IS INTENDED ONLY FOR “WHOLESALE
CLIENTS” WITHIN THE MEANING OF THE AUSTRALIAN CORPORATIONS ACT. NOT FOR DISTRIBUTION TO PRIVATE CUSTOMERS AS
DEFINED BY THE UK FINANCIAL SERVICES AUTHORITY.
The trademarks and service marks contained herein are the property of their respective owners. Third-party data providers make no warranties or
representations of any kind relating to the accuracy, completeness, or timeliness of the data they provide and shall not have liability for any damages of
any kind relating to such data.
This report may not be sold or redistributed without the written consent of Morgan Stanley.
Morgan Stanley research is disseminated and available primarily electronically, and, in some cases, in printed form.
Additional information is available upon request. © 2007 Morgan Stanley 10-18-07 po

See additional important disclosures at the end of this report.

52