Deutsche
DeutscheBank
Bank
Corporate
&
Corporate &Investment
InvestmentBank
Bank
#1 USD Inflation Swaps
#1 USD inflation Options
Strictly Private and Confidential
CPI – The Consumer Price Index
Consumer Price Index
Definition of CPI
The Consumer Price Indexes (CPI) program produces monthly data on changes in the prices
paid by urban consumers for a representative basket of goods and services.
7
4
Food
14
Energy
6
Housing
10
7
Apparel
Transportation
%
Medical Care
11
Recreation
3
Education and Communication
37
Other Goods & Services
Source: Bureau of Labor Statistics.
The index includes owner occupied housing using a rental equivalence approach
It is published once per month, usually around the middle of the following month
3
Energy is by far the most Volatile component of CPI
(Transportation costs are highly correlated with Energy)
Annual Volatility of CPI Sub-Indices (1994-2012)
Food and
Beverage Prices
are much less
volatile than
Energy
Energy
Food & Beverages
Housing
Apparel
Transportation
Medical Care
Recreation
Education & Communication
Other Goods & Services
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
Source: Deutsche Bank
4
CPI History
Inflation is Seasonal
Inflation is generally
higher leading into
the Summer and
lower heading into
year-end
This can be observed
by comparing
seasonal adjusted
CPI (CPI_INDX) with
non-seasonal
adjusted CPI
(CPURNSA)
Source: Bloomberg : CPI INDX <Index> CPURNSA <Index> HS
5
TIPS Issuance has Increased Significantly
TIPS Outstanding by Issue Year in $mm (as at 16 Jan 2013)
Treasury has
committed to
support the TIPS
market as it
provides a
diversifying
source of funds
Daily Trading
Volume is
approximately
$11 Billion
160,000
140,000
120,000
100,000
80,000
60,000
40,000
20,000
0
2008
2009
2010
Source: Bloomberg / Deutsche Bank Forecast
2011
2012
6
US Inflation Derivative Market has been Growing
A reflection of an
increased number of
clients participating
in the market
Daily Trading
Volume is
approximately
$1 Billion
Interdealer Volumes in $'mm
80,000
Options
70,000
TIPS ASW
60,000
Swaps
50,000
Especially strong
growth in Inflation
Options
Deutsche Bank’s
currently has 25%
market share in US
Inflation derivatives
(BGC Partners Interdealer Statistics)
40,000
30,000
20,000
10,000
-
2007
2008
Source: BGC Partners
2009
2010
2011
2012
7
Strictly Private and Confidential
Inflation-linked Products
Inflation Products : TIPS
The TIPS market is
the largest inflationlinked market in the
world. Regular
auctions are
conducted in 5y, 10y
and 30y TIPS
TIPS (“Treasury Inflation Protected Securities”) are securities issued by the US government
that offer investors inflation protection
The principal is accredited daily based on the CPI-Urban index and repaid at maturity
subject to a minimum of par, providing deflation protection i.e. embedded deflation floor
Semi-annual coupons paid on TIPS are based on the inflation-adjusted principal
TIPS coupons and principal repayment at maturity
10%
140%
9%
120%
8%
Real Coupon
Inflation
Notional
100%
7%
6%
80%
5%
60%
4%
3%
40%
2%
20%
1%
0%
0%
1
2
3
4
5
6
7
8
9
10
9
20,000
15,000
10,000
15-Apr-32
25,000
0
2013
2015 2017 2019 2021
Data Source: Bloomberg
2023
2025
15-Feb-40
2027 2029 2031 2033
2035
15-Feb-42
15-Feb-41
15-Jan-29
15-Apr-29
15-Jan-28
15-Apr-28
15-Jan-25
30,000
15-Jan-27
35,000
15-Jan-26
40,000
15-Jul-20
15-Jan-21
15-Jul-21
15-Jan-22
15-Jul-22
15-Apr-17
45,000
15-Apr-16
50,000
15-Jan-23
15-Apr-13
15-Jul-13
15-Jan-14
15-Apr-14
15-Jul-14
15-Jan-15
15-Apr-15
15-Jul-15
15-Jan-16
15-Jul-16
15-Jan-17
15-Jul-17
15-Jan-18
15-Jul-18
15-Jan-19
15-Jul-19
15-Jan-20
TIPS Issues
Total Market value is approximately $1 Trillion
TIPS Outstanding by Issue in $mm (as at 12 February 2013)
5,000
2037 2039 2041
10
TIPS, Real Rates and Inflation
TIPS provide a real
rate of return. To
express a view in
inflation, one can
trade the spread
between TIPS and
nominal treasuries
TIPS provide exposure to real interest rates rather than inflation
Coupons and Redemption amount grow at the inflation rate. However, these are discounted at
the nominal rate to determine the Present Value. Accordingly, the market values of TIPS are a
function of both future inflation expectations and nominal rates
Breakeven trades can isolate the exposure to expected inflation
TIPS Breakeven = Long TIPS bond + Short Treasury of similar maturity
11
Inflation Swaps
Inflation swaps are
the most liquid
inflation derivatives,
providing a clean
way to trade in
inflation
Inflation swaps offer a mechanism to trade inflation over a given time horizon
At maturity, one party pays the cumulative percentage increase in the reference inflation index
over the life of the swap in exchange for an annually compounded fixed rate
ISDA documentation typically employed
Fixed
(1
Happy Client
fixed) N
CPI ( N )
CPI ( 0 )
1
1
Floating
12
Inflation Products: Inflation Swap Example
Client asked DB to quote a price to buy a 5-year inflation swap
Agrees on a fixed rate of 2% (“Swap Breakeven Rate”)
Client will “break even” if inflation turns out to be 2% per annum over the 5-years; Accordingly,
will lose money if inflation is less than 2% and make money if inflation exceeds 2%
If actual inflation over the 5 years turns out to be 3% per annum, the client be paid the
difference between 3% compounded for 5-years and 2% compounded for five years
Happy Client
Fixed
(1
Happy Client
2% ) 5
CPI ( 5 )
CPI ( 0 )
1
1
Floating
13
Product : Inflation Swaps
Curve
Zero Coupon Inflation Swap Levels
3.50%
Typically traded in
discrete years from
1-year to 30-years
3.00%
Often traded on a
forward basis
e.g. 5y5y or 1y9y
Trading in Core
Inflation recently
initiated by
Deutsche Bank
Core
2.50%
Level
The zero-coupon
structure makes it
possible to match
an exact cash flow
profile by combining
swaps of different
maturities
Headline
2.00%
1.50%
1.00%
1Y
2Y
3Y
4Y
5Y
6Y
7Y
8Y
9Y
10Y 12Y 15Y 20Y 25Y 30Y
Maturity
14
Range Trade 5y5y Inflation Forward
More convenient to implement this in inflation derivatives than TIPS
As historically forward-starting inflation, e.g. 5y5y, has always been
within a tight band
Forward-starting tends to be the easiest way to implement this and has
other attractive features e.g. no seasonality, relatively flat carry
Historical 5Y5Y Inflation Swap Levels
400 bps
350 bps
300 bps
250 bps
200 bps
150 bps
Source: Bloomberg LP
Past Performance is no Guarantee of Future Results
Aug-12
Aug-11
Aug-10
Aug-09
Aug-08
Aug-07
Aug-06
Aug-05
Aug-04
100 bps
15
Implied Inflation
TIPS vs. Inflation Swaps
Expected Inflation
implied by Inflation
Swaps is higher than
that implied by TIPS
Breakevens
For the most part,
reflects a
supply/demand
imbalance
No natural sellers of
Inflation swaps
TIPS vs. Swap Breakevens
3.25%
Swap BEI
2.75%
2.50%
Large seller of TIPS:
The US Government
2.25%
Why is this not
arbitraged away?
2.00%
1. Limits on balance
sheet capacity
1.75%
2. Mark-to-market risk
TIPS BEI
3.00%
1.50%
2
5
10
Years
Data Source: Bloomberg LP
20
30
TIPS Asset Swap
The National Bureau of Economic Research (NBER)*
“Why Does the Treasury Issue Tips? The Tips–Treasury Bond Puzzle”
Matthias Fleckenstein, Francis A. Longstaff, and Hanno Lustig
NBER Working Paper No. 16358
September 2010
http://www.nber.org/papers/w16358.pdf
“To the best of our knowledge, the relative mispricing of TIPS and Treasury bonds
represents the largest arbitrage ever documented in the financial economics literature.
The TIPS–Treasury arbitrage poses a major puzzle to classical asset pricing theory.”
* The NBER is the nation's leading nonprofit economic research organization. Eighteen of the 33 American Nobel Prize
Winners in Economics and six of the past Chairmen of the President's Council of Economic Advisers have been
researchers at the NBER. The more than 1,000 professors of economics and business now teaching at colleges and
universities in North America who are NBER researchers are the leading scholars in their fields,
http://www.nber.org/info.html
17
Product : TIPS on Asset Swap
The link between TIPS and Inflation Swaps – no net exposure to inflation
Obtain duration/yield pickup via a top-credit quality assets (US Sovereign)
Competing product to Nominal Treasuries, Agencies, …
E.g. Post as collateral, replace treasury holdings, or hedge duration (with Repo) inexpensively
Fixed TIPS Assets Swap Levels
4.00%
Fixed TIPS ASW
3.50%
Treasury
3.00%
2.00%
1.50%
1.00%
0.50%
Source: Deutsche Bank Closing Levels
Maturity
2041
2039
2037
2035
2033
2031
2029
2027
2025
2023
2021
2019
2017
2015
0.00%
2013
Level
2.50%
Product : TIPS on Asset Swap
Floating TIPS Asset Swap
Earn an carry over repo rates / fed funds
TIPS are easy to repo as they are US Government Treasuries
Floating TIPS Asset Swap Spreads
1.00%
3mL+Spread
FF+Spread
0.80%
0.60%
0.40%
0.20%
0.00%
Maturity
Source: Deutsche Bank Closing Levels
2041
2039
2037
2035
2033
2031
2029
2027
2025
2023
2021
2019
2017
2015
-0.20%
2013
Pickup
Feb ’42 offers a much
higher spread than
Feb ’41s as it has a
much lower coupon
(0.75% vs 2.125%)
Product : TIPS on Asset Swap
Mechanics
Investor buys a TIPS
Investor agrees to pay away all the cash-flows (P+I) from the bond
Investor receives in return Libor + X% until maturity
Investor receives Par (100) at maturity
TIPS
Inflated Notional
Inflated Notional
CPI
CPI
Investor
Libor + X
Notional
Product : TIPS on Asset Swap
Example: How to make almost risk-less money
Buy $100m Notional of TIPS maturing in January 2014 i.e. $130mm Dirty Price
Fund the $130mm on overnight repo (current rate 0.06%, say)
Swap out all the TIPS cash-flows in exchange for 3mL-0.07% coupons + $130mm on
Maturity Date (current 3m Libor rate is 0.29%)
Accordingly, asset swap will pay back the full $130mm on maturity date
3m Libor is almost always higher than repo rates
(as it should be given it is an uncollateralized rate)
Accordingly, assuming no change in the spread between Libor and Repo rates,
earn carry of 0.29%-0.07% - 0.06% = 0.16% per annum on $130mm
Strictly Private and Confidential
Inflation Products – ETPs, TRS and Notes
Exchange Based Products
DB is an active market maker in Fixed Income ETPs
A large number of ETFs track inflation-linked sovereign bonds
e.g.TIP, WIP, STPZ, IPE, LTPZ, STIP, TIPZ, TDTF, TDTT, ITIP, GTIP, VTIP, etc.
New ETFs: Breakeven: INFL, DEFL, UINF, SINF, RINF, FINF and Active: ILB
First Inflation ETNs were recently listed
INFL
Powershares DB US Inflation ETN
DEFL
Powershares DB US Deflation ETN
Combines Long TIPS with Inverse Treasury position
Daily liquidity provision at NAV
Live market making
Designed such that 1bp change in inflation expectations equates to
a 10c change in ETN price
Different Credit and Tax Treatment compared to ETFs
CME considering launching Futures on CPI and TIPS
23
Total Return Swaps and Inflation-linked Notes
Total Return Swaps
–
Allows clients to go long or short cash instruments in an unfunded form
–
E.g. 1: Return of the 10+ year TIPS index vs Libor +/- Spread
–
E.g. 2: Return of Overall TIPS Breakeven Index vs Libor +/- Spread
Inflation-linked Notes
–
Creation of a customized note issued by DB or a Third Party
–
E.g. 1: Provide coupons of Annual Inflation + 1.50%
–
E.g. 2: Provide coupons of 1.5 Leverage x Annual Inflation
Strictly Private and Confidential
Inflation Products – Options
Understanding Inflation Options
Two key concepts
1) Inflation Options are either
CAPS
i.e. Calls
or
FLOORS
i.e. Puts (strikes can be negative)
2) Inflation Options are either
YEAR-on-YEAR (YoY)
References Annual Inflation
or
ZERO COUPON (ZC)
References CPI (cumulative inflation)
26
Year on Year Inflation Options
Regular payments based on annual Levels of Inflation
Payout based on difference between YoY Inflation and Strike each year
YOY Inflation by Calendar Year
Often these
options are
embedded in
inflation-linked
notes
4.5%
E.g. $100mm 3%strike five-year
cap starting in
2004 would have
paid out $0.4mm
at the end of 2005
and $1.1mm at the
end of 2007 with
no other
payments
2.5%
4.0%
3.5%
4.1
3.4
2.7
3.0%
2
2.0%
1.5%
1.0%
0.5%
0.1
2009
2008
2007
2006
0.0%
2005
Year-on-year
options generally
have annual pay
dates, but more
frequent payouts
are possible
27
Zero Coupon Options
Payment on maturity based on cumulative inflation and compounded strike
There is
particularly good
liquidity in 0%
options since
they are similar to
the redemption
options
embedded in TIPS
-0.89%
Single payment at maturity based on cumulative inflation from inception
CPI Index Value
225
219.964
218.011
220
215
210
205
Jul-10
Apr-10
Jan-10
Oct-09
Jul-09
Apr-09
Jan-09
Oct-08
Jul-08
Apr-08
Jan-08
Oct-07
Jul-07
Apr-07
200
Jan-07
E.g. $100mm 0%strike two-year
floor with a
starting reference
of July 2008 will
pay out $0.89mm
(-0.445% per
annum deflation)
in October 2010
(3-month lag)
28
Understanding Inflation Options: Inflation Volatility
Market vs Economist Expectations
Negative skew in
the options market.
Economic theory
suggests prices are
sticky downwards i.e.
market implied
probability of
deflation is too high
Implied Volatility
is too high
relative to
economist
expectations
‘Fat tailed’
distribution
means wings
have too much
value
29
Building a CPI Curve
30
Building the CPI Curve
Process
Given market quotes for the zero coupon inflation-swap rates or TIPS breakevens it is possible
to build a forward CPI curve
Constructing a complete forward curve involves
(a) extracting future fixings from quoted ZCIS rates
(b) interpolating the available points to obtain the inflation trend
(c) adding the CPI seasonality
1. For the quoted tenors the future fixings can be obtained using:
Implied Ref CPI t+tenor = Ref CPI t x (1+ ZCIS rate) tenor
2. Interpolation between quoted ZCIS rates can be
linear, cubic, which may lead to a smoother
forward curve, or other depending on the data
240
220
Projected CPI Trend
200
180
160
3. To obtain the monthly CPI projections seasonality
needs to be taken into account (next slide)
140
120
100
0
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30
Source: DB Global Markets Research
31
Building the CPI Curve
Example
Co n st ru ct io n o f t h e f o rw ard CPI cu rve
C P I P r o je c t ed M o n t h ly
se a so In d e x
v a lu e
n a lit y
f rom
Z C IS
Sep-09
109.8420
Re m o vin g t h e
se a so n a l co m p o n e n t
109.7541
= 109.754 x exp(0.08% ) =
109.8420
Oct-09
0.02%
109.9722
= 109.972 x exp(0.02% ) =
109.9942
Nov-09
-0.19%
110.1902
= 110.190 x exp(-0.19% ) =
109.9810
Dec-09
0.17%
110.4083
= 110.408 x exp(0.17% ) =
110.5963
Jan-10
-0.46%
110.6263
= 110.626 x exp(-0.46% ) =
110.1175
Feb-10
0.14%
110.8444
= 110.844 x exp(0.14% ) =
111.0002
M ar-10
0.35%
111.0624
= 111.062 x exp(0.35% ) =
111.4523
Apr-10
0.23%
111.2805
= 111.280 x exp(0.23% ) =
111.5363
M ay-10
0.05%
111.4985
= 111.499 x exp(0.05% ) =
111.5541
Jun-10
-0.08%
111.7166
= 111.717 x exp(-0.08% ) =
111.6275
Jul-10
-0.29%
111.9346
= 111.935 x exp(-0.29% ) =
111.6108
112.1527
= 112.153 x exp(-0.02% ) =
112.1302
112.3707
= 112.371 x exp(0.08% ) =
112.4607
Aug-10
Sep-10
0.08%
= 109.8420/exp(0.08% )=
T r e n d C P I In c o rp o r a t in g se a so n a l Fu ll C P I
co m p o n e n t
curv e
b y lin e a r
in t er p o la t io n
-0.02%
112.4607
0.08%
= 112.4607/ exp (0.08% ) =
120
118
116
109.7541
112.3707
14
12
CPI curve
%
f orward rat es
trend
with seasonality
10
projected trend
8
6
114
4
112
2
0
110
-2
108
106
2009
-4
2010
2011
2012
-6
Oct-09
Oct-11
Oct -13
Oct -15
32
CPI Volatility Models
33
Jarrow and Yildirim (2003)*
Foreign Currency Analogy
The “Real” is a “foreign currency” pegged to the value of a basket of goods and services
Real Rates are the interest rates in the “foreign currency”
CPI Index is the exchange rate between USD and the “Real” Currency
Three-Factor HJM Model (Nominal Rates, Real Rates and Inflation Index)
Nominal Forward Rates:
Real Forward Rates:
Inflation Index:
In Practice
Adjusted to incorporate Stochastic Volatility
Calibrate volatility assumptions as well as correlations between factors
Used to value Exotic (Path-dependent) Payoff Structures
* Pricing TIPS and Related Derivatives…: http://forum.johnson.cornell.edu/faculty/jarrow/084 Tips JFQA 2003.pdf
34
Black-Scholes Type Models
Option Pricing Models
Black’s Model:
Treat Inflation Index as Log-normally Distributed
Bachelier Model:
Treat Inflation Rate as Normally Distributed
Shifted Log-normal Model: Inflation Rate cannot go below -100%
In Practice
Intraday calculations for vanilla Inflation Options
e.g. TIPS Redemption Floors
Different volatilities by Term and Strike based on calibrations to market trading levels
35
SABR Model *
Incorporates Stochastic Volatility.
SABR: Stochastic Alpha Beta Rho
Allows better fitting of Volatility Skews/Smiles
Process:
Alpha is the (log-normal) volatility of volatility - influences the Volatility Smile
Beta is the sensitivity of the change in forward to the level of the forward – influences the
Volatility Skew (e.g. normal vs. log-normal)
Rho is the correlation between the two processes i.e. the correlation between change in
Forward Level and change in Volatility – also influences the Volatility Skew
Generally, Beta is fixed based on historical experience, and Rho is calibrated
In Practice
Pricing of all vanilla inflation options, including daily mark-to-market of vanilla option books
Much quicker and more stable than JY Monte Carlo Model, but cannot value exotics
* Managing Smile Risk, P. Hagan et al., 2002: http://www.math.columbia.edu/~lrb/sabrAll.pdf
36
Inflation Market
Summary
Products
• TIPS
Treasuries whose principal adjusts in-line with CPI
• TIPS Asset-Swap
Obtain a yield pickup over treasuries / repo rates
• Inflation Swaps
Hedge or take a view on inflation
• ETFs / ETNs
Trade in a similar way to Equities
• Total Return Swaps
Unfunded exposure to TIPS or TIPS Breakevens
• Inflation-linked Notes
Customized inflation-linked cash flows
• Inflation Options
Capped or floored exposure to inflation
Models
• Jarrow -Yildirim
Exotic inflation options
• BS-Type
Intraday calculations
• SABR
Vanilla inflation option
Structural Imbalances in the Inflation Market
• Inflation Swaps imply higher CPI levels than TIPS
• Very front-end of the inflation curve tends to be cheap
• Implied volatility significantly exceeds realized volatility
37
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38