volatility as an asset class february 2017 models, market...
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Volatility as an asset classModels, market making, supply and demand
Josh YoungerHead of U.S. Interest Rate Derivatives StrategyJ.P. Morgan Securities LLC
(212) 270-1323
February 2017
The data sources contained in this report are J.P. Morgan, unless otherwise indicated.
See page 41 for analyst certification and important disclosures.
Page
Agenda
Models, market making, and trade construction 1
The gamma sector 16
The vega sector 27
The US volatility market: supply and demand for short-dated options (gamma
sector)
Money ManagersMBS Homeowner/
Investor
MortgageServicers/REITs
Derivative Dealers
Banks/Corporates(Treasury) GSEs
Hedge FundsCross
Currency
MB
S
Calla
ble
Debt
Rate DrivenSupply/Demand
RelativeValue
Long-dated FXOption Hedging
DealerPositions
Caps/Swaptions
Swaptions/MBS Options/
CMM
Callable/Puttable
Swapping
Caps/Swaptions
Callables/Structured
Notes
Banks(Asset Side)
Caps/Swaptions
Insurance Co/Pension Funds
SwaptionsCMS Caps
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Interest rate volatility markets
“Vanilla” Options
Exotics
Options on futures
Swaptions
Correlation products
Bermudan options
Contingent optionsand other hybrids
Curve options
Midcurve swaptions
USD Vols Current Level (bp/day)
Exp/Tenor 1Y 2Y 3Y 5Y 7Y 10Y 30Y
1M 1.21 2.18 3.26 4.41 4.54 4.46 4.00
3M 1.23 2.37 3.44 4.51 4.60 4.52 4.01
6M 1.83 3.11 4.11 4.95 5.01 4.93 4.34
1Y 3.13 4.47 5.21 5.52 5.48 5.30 4.61
2Y 5.65 6.16 6.28 6.06 5.87 5.59 4.76
3Y 6.74 6.69 6.53 6.13 5.93 5.65 4.73
5Y 6.72 6.57 6.40 6.05 5.89 5.66 4.70
10Y 5.69 5.61 5.53 5.38 5.23 5.01 4.16
The Implied Volatility Surface
Gamma
Vega
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Call Deltas
increase as the underlying price increases
can be interpreted as the probability that the option will finish in the money
Put Deltas
increase as the underlying price increases
can be interpreted as
-1 times the probability that the option will finish in the money
As time passes,
the delta of ITM options increases
the delta of OTM options decreases
As volatility falls,
the delta of ITM options increases
the delta of OTM options decreases
0
0.5
1
1.5
2
2.5
3
3.5
97 98 99 100 101 102 103
100 Call Option Premium (10% vol)
Price
1 month to expiration
Delta=0.85
0.76
0.64
0.5
0.370.24
expiration
0
0.5
1
1.5
2
2.5
3
3.5
97 98 99 100 101 102 103
100 Put Option Premium (10% vol)
Price
1 month to expirationDelta=-0.85
-0.75
-0.63
-0.15
-0.36-0.24
expiration-0.49
0
0.2
0.4
0.6
0.8
1
97 98 99 100 101 102 103
100 Call Option Deltas (10% vol)
Delta1 week
4 months
ITM deltas increase
as time passes
OTM deltas decrease
as time passes
0
0.2
0.4
0.6
0.8
1
97 98 99 100 101 102 103
100 Call Option Deltas (1 month)
Delta5%vol
10% vol
ITM deltas increase
OTM deltas decrease
as vol falls
as vol falls
Reviewing the “Greeks” - Delta
Definition
Delta is the change in the price of an option for a 1-unit move in the underlying. For example, a delta of 0.6 means
that a one cent increase in the underlying price will cause a 6/10th of a cent increase in the option price.
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Vega is the change in the price of an option for a one percentage point increase in implied volatility.
ATM options have the largest vega.
As time passes,
vega decreases
As volatility falls,
vega decreases for ITM and OTM options
vega is unchanged for ATM options
volatility
00.2
0.4
0.6
0.81
1.2
1.41.6
6 8 10 12 14
100 Call Option Premium (1 month)
Premium
1%0.114
F=100
F=98
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
97 98 99 100 101 102 103
100 Call Option Vega (1 month)
Vega
10% vol
days to expiration
0
0.05
0.1
0.15
0.2
0.25
120 90 60 30 0
ATM Call Option Vega (10% vol)
Vega
0.226
0.114
0
0.02
0.04
0.06
0.08
0.1
0.12
97 98 99 100 101 102 103
100 Call Option Vega (1 month)
Vega
10 % vol
5% vol
Reviewing the “Greeks” - Vega
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Gamma is the change in delta for one unit move in the underlying.
ATM options have the largest gamma.
As time passes,
the gamma of an ATM option increases
the gamma of deep ITM and OTM options decreases
As volatility falls,
the gamma of an ATM option increases
the gamma of deep ITM and OTM options decreases
0
0.5
1
1.5
2
2.5
3
3.5
97 98 99 100 101 102 103
100 Call Option Premium (10% vol)
Price
1week to expiration
Delta=0.98
0.92
0.77
0.50.24
0.07
expiration
0
0.05
0.1
0.15
0.2
0.25
0.3
97 98 99 100 101 102 103
0.27
0.060.06
100 Call Option Gammas (1 week)
Gamma10% vol
0
0.05
0.1
0.15
0.2
0.25
0.3
97 98 99 100 101 102 103
100 Call Option Gammas (10% vol)
Gamma
1 week
1 month
0
0.05
0.1
0.15
0.2
0.25
0.3
97 98 99 100 101 102 103
100 Call Option Gammas (1 month)
Gamma
5% vol
10% vol
Reviewing the “Greeks” - Gamma
Gamma is the change in an option’s delta for a one-unit change in the price of the underlying. The numbers above show
the change in delta for a one point increase in the underlying futures price. For example, a gamma of 0.14 on a
one-month at-the-money option means that delta would increase from 0.50 to 0.64 for a one-point increase in the
underlying.
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If you delta-hedge
You don’t care about market direction
You monetize all the moves that occur between delta-hedging events
You do care about realized volatility
Profit/Loss profile
P/L
Futures price
Implied volatility up 0.10%
Implied volatility down 0.10%
Implied volatility is always a determinant of option pricing, but realized volatility
only matters if you monetize it
If you don’t delta-hedge
Your P/L is determined by the total move that occurs between the day you purchase the option and expiry
You care about market direction, unless you buy a straddle
You care about the terminal outcome, not how volatile the path was to get there
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Pure volatility positions – delta hedging frequency can make a big difference
When yields are more mean-reverting, realized volatility measured on a longer timescale is below that measured based on daily changes…
1-month standard deviation of daily versus two-week changes in 2-year swap yields, converted to daily bp/day
* Options are struck ATMF and rolled on the first of the month, and delta-hedged daily or every two weeks, assuming no transaction costs.
…and delta-hedging at different frequencies allows you to monetize different volatilities
Cumulative returns* over the two years on short delta-hedged 3Mx2Y ATMF straddles using daily versus two-week delta rebalancing and an unhedged position; bp of notional
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Sep 13 Mar 14 Sep 14 Mar 15
1d changes2w changes
-40
-30
-20
-10
0
10
20
30
40
50
Sep 13 Mar 14 Sep 14 Mar 15
Daily delta rebalancingBi-weekly delta rebalancingNo delta hedging
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Options markets don’t know any more about the future than anyone else!
Buying straddles and actively hedging the delta generates returns that track implied vs realized vol…
1-month rolling returns* on long delta-hedged 3Mx10Y ATMF straddles; bp of notional
* Options are struck ATMF and rolled on the first of the month, and delta-hedged daily assuming no transaction costs.** Delivered vol is measured as the 1-month standard deviation of daily changes in 10-year swap yields.
ex-ante implied minus ex-post realized vol**; bp/day
…but the trailing realized/implied spread is not usually a good predictor of subsequent returns
1-month rolling returns* on long delta-hedged 3Mx10Y ATMF straddles; bp of notional
ex-ante implied minus realized vol**; bp/day
-150
-100
-50
0
50
100
150
200
-4 -3 -2 -1 0 1 2 3 4
Y = -34.37 X1 + 8.03R² = 79%period = Mar 16,10 - Mar 16,15
-150
-100
-50
0
50
100
150
200
-3 -2 -1 0 1 2 3
Y = -1.35 X1 - 10.38R² = 0%period = Mar 16,10 - Mar 16,15
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But they do a pretty good job in estimating sensitivities on short time frames…
Option pricing models are not, for the most part, good at predicting the future…
Rolling 1-year R-squared of 3-month delivered volatility in 10-year swap yields versus ex-ante 3Mx10Y ATMF implied volatility; %
0
10
20
30
40
50
60
70
80
2003 2007 2011 2015
…but they are much better at providing point in time estimate of short-term sensitivities
Weekly P/L on a long 3Mx10Y payer versus an estimate taken from the ex-ante Greeks* over the past 15 years; bp of notional
* P/L ≈ Delta x chg(F) + 0.5 x Gamma x chg(F)2 – Theta x Ndays
y = 0.9481x + 0.3493R² = 98%
-400
-200
0
200
400
-400 -200 0 200 400 600
Estimated P/L from ex-ante Greeks*; bp of notional
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Keeping it all in context. Why spend all this time on models?
What are models really good for at the end of
the day?
Models sound like forecasts, but context is
important…
Options traders don’t know any more about the
future than anyone else
Similar to forward rates from the swaps market
Implied volatility is a measure of breakeven and
risk premium, rather than a prediction for the
future….
…and models are primarily useful for point in
time sensitivities for hedging and risk
management
Who
What
I don’tgive a darn
I don’t know
Why
Tomorrow
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Keeping it all in context. Why spend all this time on models?
What are models really good for at the end of
the day?
Models sound like forecasts, but context is
important…
Options traders don’t know any more about the
future than anyone else
Similar to forward rates from the swaps market
Implied volatility is a measure of breakeven and
risk premium, rather than a prediction for the
future….
…and models are primarily useful for point in
time sensitivities for hedging and risk
management
Who
What
I don’tgive a darn
I don’t know
Why
Tomorrow
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Interest rate options: risk management
TradingModels
Trading Positions
Risk Measures
Delta
Gamma
Vega
Theta
dVega/dRate
dVega/dVol
dDelta/dVol
dDelta/dTime
Vega by Strike
Smile
Backbone
Implied Swaption Volatility (bps / yr)
Exp 1Y 2Y 5Y 10Y 20Y 30Y
1M 33.7 34.6 64.2 86.7 92.5 94.5
3M 34.5 37.0 66.8 91.7 95.3 96.6
6M 33.9 41.0 69.7 93.4 96.2 97.2
1Y 41.6 46.6 75.6 96.2 97.9 97.9
2Y 62.8 70.0 86.6 98.6 97.7 96.6
3Y 82.5 86.8 95.2 99.0 96.9 94.7
4Y 94.2 95.6 99.4 99.9 94.9 92.3
5Y 99.3 99.7 99.5 99.9 93.3 90.2
7Y 99.3 99.1 99.0 96.4 89.0 85.8
10Y 97.4 96.1 94.1 91.4 82.9 79.5
Swap Curve
3 M 0.48
6 M 0.46
9 M 0.46
1 Yr 0.48
1.5Yr 0.52
2 Yr 0.56
3 Yr 0.70
4 Yr 0.91
5 Yr 1.16
7 Yr 1.63
10 Yr 2.12
12 Yr 2.33
15 Yr 2.54
20 Yr 2.71
25 Yr 2.79
30 Yr 2.83
40 Yr 2.84
Market Data
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Risk management: dVega/dRate
ATM options have the largest vega:
Vega of a Call Option struck at 100:
Underlying Price Vega
98 0.08
100 0.11
102 0.08
dVega/dRate exposure creates Rate Driven Supply/Demand:
Change in Vega for a +25 bp move in Rates
Exp\Und 2Y 5Y 10Y 30Y Total
<=6M (13) 3 (38) (10) (58)
1Y 15 28 34 (25) 52
2Y 58 41 54 (19) 134
3Y 60 32 (30) 15 76
5Y 32 38 (1) 54 123
10Y 24 6 (9) 133 155
20Y 0 (7) 170 10 174
Total 176 142 180 158 655
Change in Vega for a -25 bp move in Rates
Exp\Und Caps-2Y 5Y 10Y 30Y Total
<=6M (82) (28) (7) 21 (96)
1Y (90) (27) (36) 6 (147)
2Y (38) (29) (44) 10 (101)
3Y (38) (18) 31 (19) (44)
5Y (21) (24) 14 (70) (101)
10Y (16) 7 20 (133) (122)
20Y 4 8 (168) (10) (166)
Total (280) (112) (190) (196) (777)
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Fundamental drivers of volatility: market depth
Periods of heighted volatility are characterized by poor liquidity, and in particular low market depth…
3-month moving average of market depth* (LHS; $mn) and realized volatility (RHS; bp/day) in 10-year Treasuries
* Market depth is the average of the top 3 bid/ask sizes in 10-year Treasuries, averaged between 8:30am and 10:30am daily.Source: J.P. Morgan, BrokerTec
…but the trailing realized/implied spread is not usually a good predictor of subsequent returns
3Mx10Y ATMF implied volatility; bp/day
log(market depth*)
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50
100
150
200
250
300
350 3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
2013 2015 2017
Market depthRealized volatility
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0
Y = -1.46 X1 + 12.57R² = 45%period = Jan 23,12 - Jan 23,17
14
Fundamental drivers of volatility: the “log-normal” shuffle
…but this only applies if we think rates cannot drop below the zero bound, which though once orthodoxy is an increasingly leaky floor
Probability of negative rates inferred from zero-strike receivers in 1Yx5Y USD and EUR swpations; %
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When rates are very low, the level of implied volatility becomes highly correlated with the level of rates…
ATMF implied volatility; bp/day
ATMF rate; %
1
2
3
4
5
6
0.00 1.00 2.00 3.00 4.00
As of March 2013
0
1
2
3
4
5
6
7
8
0
10
20
30
40
50
60
70
2013 2015 2017
USDEUR
15
Page
Agenda
The gamma sector 16
Models, market making, and trade construction 1
The vega sector 27
The US volatility market: supply and demand
Money ManagersMBS Homeowner/
Investor
MortgageServicers/REITs
Derivative Dealers
Banks/Corporates(Treasury) GSEs
Hedge FundsCrossCurrency
MBS
Calla
ble
D
ebt
Rate DrivenSupply/Demand
RelativeValue
Long-dated FXOption Hedging
DealerPositions
Caps/Swaptions
Swaptions/MBS Options/CMM
Callable/PuttableSwapping
Caps/Swaptions
Callables/StructuredNotes
Banks(Asset Side)
Caps/Swaptions
Insurance Co/Pension Funds
SwaptionsCMS Caps
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The growth of the market in U.S. interest rate options is closely tied to the mortgage market, and in particularly the rise and fall of the GSEs…
…but more recently the decline in GSE holdings has left other, smaller dynamic hedgers as the primary driver of volatility markets
Gamma demand: the growth of interest rate volatility markets was closely
tied to the mortgage market—though this is less true recently
Gross market value of USD IR options (RHS), GSE retained agency MBS holdings (RHS), and total current balance of agency MBS (LHS); both axes in $bn
Total balance of dynamically hedged mortgages held by REITs, GSEs, and bank servicers*; $bn
Source: J.P. Morgan, BIS, FHMC, FNMA Note: Bank servicer adjusts for holdings by non-bank servicers, who do not hedge, and is dollar-convexity weighted versus the overall agency MBS indexSource: J.P. Morgan, ISDA
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AM
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$0
$500
$1,000
$1,500
$2,000
06 07 08 09 10 11 12 13 14 15 16
REITs GSEs Bank servicers
$0
$200
$400
$600
$800
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
$5,000
00 02 04 06 08 10 12 14 16
Agency MBS current balance (LHS)
Total gross notional of USD IR options (RHS)
GSE retained agency MBS holdings (RHS)
17
Federal Reserve System
27%
Commercial Banks24%
Foreign Investors14%
Mutual & Money Market Funds
11%
Fannie Mae/Freddie
Mac5%
REITs4%
Public/Private Pension Funds
3%
Life Insurance Companies
3% Other9%
4Q13 4Q14 4Q15 4Q15
All MBS All MBS All MBS Agency Non-Agency
Federal Reserve System 1,490 1,747 1,748 1,748 -
Commercial Banks 1,369 1,406 1,519 1,438 81
Foreign Investors 835 883 912 741 171
Mutual & Money Market Funds 778 701 705 645 60
Fannie Mae/Freddie Mac 456 350 293 236 57
REITs 265 283 233 216 18
Public/Private Pension Funds 290 236 224 175 49
Life Insurance Companies 239 191 205 145 60
FHLBanks 140 138 135 120 15
Savings Institutions 143 124 124 121 3
Credit Unions 104 100 97 95 2
Primary Dealers 72 83 76 63 12
Property/Casualty Insurers 52 42 43 21 22
State/Local Government 24 11 - - -
Total Outstanding 6,392 6,346 6,412 5,806 606
Source: Mortgage Market Statistical Annual 2016 Yearbook
MBS Investor Breakdown – 2015 YE
Major MBS investors
MBS Investors ($ billion)
Total = $6.4 trillion
18
A closer look at prepayments: The major components
Rate refinancing
Largest component of prepayments
Borrowers take advantage of lower interest rates to refinance
A steep curve can cause borrowers to refinance into shorter mortgages (ARMs)
Turnover
Prepayment occurs when borrower moves from one home to another
As loans age (or “season”) they show higher turnover speeds
Seasonality is an important driver of turnover, as most families move during the summer (when
kids are out of school)
Cash-out refinancing
Borrowers with accumulated equity can refinance and take out a larger mortgage
Cash can be used for home improvement, paying off bills, or other debt consolidation
This effect is driven primarily by home price appreciation (HPA)
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Mortgages are long duration, short convexity and short volatility…
0
10
20
30
40
50
60
70
-250 -200 -150 -100 -50 0 50 100 150 200 250
Refi Incentive (bp)
CP
R (
%)
Turnover
Burnout: Refi response
slows once deep in-the-
money
Refi: How quickly
speeds increase as
incentive increases
Elbow: The amount of incentive to
get borrowers to begin refinancing
(to overcome fixed costs)
Different areas of the S-curve reflect different patterns in borrower behavior FN 4.5 prices ($) vs. shift in rates (bps)
80
85
90
95
100
105
110
115
120
-200 -150 -100 -50 0 +50 +100 +150 +200 +250 +300
FN 4.5 Prices Zero Convexity Bond
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Mortgages are long-duration and short convexity due to the prepayment option…
…and can be decomposed into duration, convexity and basis risks, and TBAs
can be replicated with a package of swaps and options
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
Components Primary mtge rate
Mtge Basis (0.28%)
Option cost(0.28%)
Risk-freerates (Tsy)
(2.41)
Prim/Secspread(0.91%)
…and can be (mostly) replicated via a combination of swaps and options with infrequent rebalancing
Cumulative total returns from J.P. Morgan Agency MBS index versus a replicating portfolio of swaps and swaps+options; bp of notional
Note: Swaps include 2-, 5-. 10-, and 30-year tenors, and options are 3Mx10Y, both with monthly rebalance and re-strike.Source: J.P. Morgan
-100
0
100
200
300
400
500
600
700
800
2015 2016 2017
TBAsSwaps (1m rebal)swaps+options (1m rebal/restrike)
21
Gamma supply: taking the other side of the mortgage bid
When money managers have a net underweight in mortgages they have capacity to add negative convexity positions in other assets such as rates options
MBS allocation with respect to the index among the 12 largest actively managed fixed income mutual funds; %
* Includes the 12 largest funds.Source: J.P. Morgan, Morningstar
-15%
-10%
-5%
0%
5%
10%
Feb 11 Feb 12 Jan 13 Jan 14 Jan 15 Jan 16
The resiliency of programmatic short gamma strategies can structurally depress volatility
Intercept of a rolling 2-year regression of 3Mx10Y swaption implied volatility against 5-day moving average of 10-year Treasury market depth*; bp/day
* Market depth is the average size of the top 3 bids/offers in on-the-run Treasuries, averaged daily between 8:30am and 10:30am. Source: J.P. Morgan, Morningstar, BrokerTec
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10
11
12
13
14
15
16
17
2013 2015 2017
22
Taking the other side of this imbalance of flows via programmatic short
gamma strategies
By some measures, systematically short volatility strategies in interest rates rival those in equity and credit options markets
5-year median divided by inter-quartile range of monthly total returns from systematic short gamma strategies in interest rate*, FX†, equity** and credit‡ markets by currency; unitless
* Assumes daily sales of 1Mx10Y ATMF straddles with daily delta rebalancing, held to maturity.† Also assumes daily sales of 1-month opitons with daily delta rebalancing, held to maturity.** Taken from J.P. Morgan NexusSM investable short volatility risk premia products for S&P500, E-Stoxx 50, FTSE 100 and Nikkei indices. Assumes daily delta rebalancing.† Taken from J.P. Morgan investible credit indices for CDX.IG (USD) and iTraxx Main (EUR). Assumes daily delta rebalancing.Source: J.P. Morgan, Bloomberg
The divergence in risk-adjusted returns from selling unhedged strangles versus delta-neutral straddles suggests a shift in the balance of flows
Rolling 5-year median divided by inter-quartile range of returns (a non-parametric "Sharpe" ratio*) for unhedged strangle versus delta-neutral straddle†, both for 1Mx10Y held to expiry; unitless
* We use a non-parametric formulation to compensate for the highly non-normal returns generated by systematic options trading strategies, which we discuss in more detail later in this publication.Note: P/L assumes daily trades, held to expiry. Strangles are struck 25-delta, and straddles are ATMF. Straddle returns also assume daily delta rebalancing with zero transaction costs.Source: J.P. Morgan
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Currency Rates FX Equities CreditUSD 0.39 na 0.33 0.39EUR 0.44 -0.11 0.05 0.23JPY 0.39 -0.10 0.23 naGBP 0.27 -0.10 0.32 na
Macro Product Risky Assets
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
05 06 07 08 09 10 11 12 13 14 15 16
Unhedged strangle
Delta-neutral straddle
23
Sharpe ratios can let you down…when P/L is highly non-linear
benchmarking returns is easier said than done
Returns from systematic options-based trading strategies are highly non-normal, with limited upside and fat tails from non-linear downside…
Distribution of total returns for two systematic short gamma strategies* over the past five years; %
Total returns; bp of notional
* Trades are initiated daily in 1Mx10Y ATMF swaption straddles and held to expiry. Delta hedges are rebalanced daliy and we ignore transaction costs.Source: J.P. Morgan
…and we recommend focusing on non-parametric risk measures, though each has its own advantages and disadvantages
Various risk measures for 5-year total returns from several systematic short gamma strategies in 1Mx10Y swaptions†; unitless
Risk measure*
* Sharpe ratio (1) is average divded by standard deviation of returns, and Sortino ratio (2) is averaged returns divded by standard deviation of losses. Median versus inter-quartile range (3) and median returns versus median losses (4) are non-parametricSharp and Sterling ratios, and returns versus 5th percentile (5) as expected returns versus downside risk.† Assumes daily trades (1Mx10Y straddles), held to expiry with delta rebalancing either daily or based on a threshold rule as indicated.Source: J.P. Morgan
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0%
5%
10%
15%
20%
25%
30%
-500 -400 -300 -200 -100 0 100 200 300
Daily delta hedging
No delta hedging
0.0
0.2
0.4
0.6
0.8
(1) (2) (3) (4) (5)
Daily hedging10% delta threshold25% delta threshold50% delta thresholdUnhedged
24
Delta risk management and strike selection are crucial considerations,
particularly when we take transaction costs into account
Occasional delta rebalancing can improve risk-adjusted returns, but the benefits of very frequent hedging are more than offset by transaction costs
5-year risk-adjusted* returns for various systematic short gamma strategies† and delta management rules, both including and excluding indicative transaction costs; unitless
* The straight average of non-parametric Sharpe, Sterling and drawdown ratios. Details in Exhibit 6.† Straddles struck ATMF at intiiation, and strangles are 25% fractional delta on the payer and receiver leg. We manage each leg independantly for the strangle strategy, and as a package for straddles. Transaction costs assume 0.2 bp of yield for each rebalancing.Source: J.P. Morgan
Strangles tend to maintain their gamma under rate shocks better than straddles
Gamma for 1Mx10Y ATMF straddles and a gamma-neutral amount of 25-delta strangles under rate shocks, initial and aged by two weeks, and set to 100% as of trade initiation; %
Rate shocks; bp
Source: J.P. Morgan
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0.00
0.20
0.40
0.60
0.80
Daily 10%thresh
25%thresh
50%thresh
None Daily 50%thresh
None
w/o transaction costs
w/ transaction costs
Straddle Strangle
0%
20%
40%
60%
80%
100%
120%
140%
160%
-50 -40 -30 -20 -10 0 10 20 30 40 50
Straddle (initial)Straddle (aged)Strangle (initial)Strangle (aged)
25
Can we improve returns with dynamic strike management or ex-ante
trading signals?
Gamma risk-targeting via re-striking straddles does not improve risk-adjusted returns
5-year risk-adjusted* returns for ATMF short straddles with different gamma management rules† and daily delta rebalancing; unitless
* The straight average of non-parametric Sharpe, Sterling and returns versus downside ratios. Details in Exhibit 6.† We assume the straddles are re-struck to the current ATMF if the total gamma falls below a given threshold over the holding period, with the notional also scaled to match the initate gamma of the position.Source: J.P. Morgan
A variety of ex-ante trading signals result in higher risk-adjusted returns
5-year risk-adjusted* returns (net of transaction costs) for 25-delta 1Mx10Y strangles with a 50% delta rebalancing threshold using several† ex-ante trading signals, % of days with "on" signal as indicated; unitless
ex-ante trading signal*
* As before, we use the average of non-parametric Sharpe, Sterling, and drawdown ratios. Details in Exhibit 6. We assume 0.2 bp bid to mid for delta rebalancing.† We consider a range of possible signals, each of which is used as an “on/off” trigger, meaning we only sell strangles when a single factor exceeds a particular threshold. The ex-ante trading signals are as follows: (1) for volatility returns clustering, we only sell if a comparable trade initiated one month prior (i.e., most recent that has since expired) was profitable; (2) for expiry curve, we require the ex-ante 1Mx10Y minus 3Mx10Y ATMF implied volatility spread be greater than zero; (3) for vol level, we require the ex-ante 1-year trailing Z-score be greater than 0.5; and (4) for vol carry, we require ex-ante 1Mx10Y ATMF implied divded by 1-month trailing realized volatillity be greater than 1.2x.Note: We also indicate the frequency with which one trades using each rule.Source: J.P. Morgan
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0.00
0.20
0.40
0.60
None 10%thresh
25%thresh
50%thresh
100%
65%
27%28%
28%
0.55
0.65
0.75
0.85
No ex-antetrigger
Clust inreturns
Flatter expirycurve
High vollevels
High volcarry
26
Page
Agenda
The vega sector 27
The gamma sector 16
Models, market making, and trade construction 1
The US volatility market: supply and demand
Money ManagersMBS Homeowner/
Investor
MortgageServicers/REITs
Derivative Dealers
Banks/Corporates(Treasury) GSEs
Hedge FundsCross
Currency
MBS
Calla
ble
D
ebt
Rate DrivenSupply/Demand
RelativeValue
Long-dated FXOption Hedging
DealerPositions
Caps/Swaptions
Swaptions/MBS Options/
CMM
Callable/Puttable
Swapping
Caps/Swaptions
Callables/Structured
Notes
Banks(Asset Side)
Caps/Swaptions
Insurance Co/Pension Funds
SwaptionsCMS Caps
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27
Who buys callable bonds?
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Taiwanese and Korean life insurance companies have very large portfolios relative to local GDP, and should continue to grow at a fairly rapid clip…
* Based on J.P. Morgan estimates for life insurance companies in each country with equity coverage, which together constitute the vast majority of total assets. In Taiwanthis includes Cathay, China Life, Shin Kong & Fubon; in Korea it includes Samsung,Hanwha, Tong Yang, & Dongbu. Forecasts as of 3Q 2016 filings. For details, seecoverage on J.P. Morgan markets under Jemmy S. Huang (Taiwan) and M.W. Kim(Korea).Note: FX rates based on yearly averages, including J.P. Morgan forecasts through mid2017.Source: J.P. Morgan, Company filings, Korea Life Insurance Association, TaiwanInsurance Institute
Taiwanese and Korean life insurance invested assets, historical andforecasts*; $bn of USD-equivalents
0
200
400
600
800
1000
1200
1400
1600
18F17F16F1514131211
Taiwan Korea
…and owing to competition and legacy policies have a very daunting ALM mismatch to manage
10-year local currency swap yields, estimated liability cost* for Taiwanese and Korean life insurance companies, and indicative IRR for USD-denominated zero coupon 30nc1 callable yields adjusted for FX hedging costs†; %
* Based on J.P. Morgan estimates. For Taiwan, we take the average of Cathay,Fubon, Shinkong and China Life (4Q16 numbers are current forecasts). For Korea, wetake the average of Samsun and Hanhwa (2016 numbers are latest as of 3Q16 filings). † Indicative hedging costs are calculated from 1-year forward versus spot USD/TWD orUSD/KRW in the onshore markets.Note: We assume funding spreads equal to the average 5-year CDS of Libor panelbanks.Source: J.P. Morgan, Company filings
0%
2%
4%
6%
8%
10%
12%
11 13 14 15 16
30nc1 w/ KRW/USD 30nc1 w/ TWD/USD
KRW liab TWD liab
KRW 10Y yields TWD 10Y yields
28
Demand from Taiwanese and increasingly Korean lifers should continue
to drive callable supply; China and Japan in particular should remain on
the sidelines
Summary of Asian life insurance industry size and penetration, current foreign asset exposure, regulatory constraints, and local currency bond market statistics
Summary of various bond markets, life insurance assets, regulatory constraints, and propensity to buy USD callables across Asia
* Defined as gross premium intake relative to GDP, as of year-end 2015 from the most recent SIGMA report from Swiss Re.† Obtained from a review of the various insurance regulations for each country, most of which are available online. ** Assets (total and foreign) based on company filings and J.P. Morgan estimates, and includes Ping An, China Life, New China Life, CPIC, & PICC Group. For details, see Asia Insurance Sector, MW Kim & JS Huang (6/26/16).‡ The larger figure includes all foreign currency assets, the latter (in parenthesis) excludes Formosa bonds, which are considered onshore for regulatory purposes (for details, see New regulations in Taiwan are bearish for long-dated vega, J. Younger et al., 8/20/14). Total Formosa bond outstanding balance from Bloomberg data.*** Based on J.P. Morgan estimates, assuming a constant asset/liability ratio (based on estimates as of year-end 2012, taken from IMF Country report No. 14/206, PRC--Hong Kong SAR Financial Sector Assessment Program, Insurance Core Principles published July 2014) and 2014 year-end liability data provided by the Hong Kong Office of the Commissioner of Insurance (OCI).Note: Assets as a % of GDP use most recent data versus 2015 GDP estimates (in USD equivalents) from Swiss Re. In the case of Hong Kong and Thailand, for which only year-end 2014 asset data is available, we use 2014 GDP as well (also from Swiss Re). Local currency bond data for sovereigns from J.P. Morgan EMBI (with the exception of Taiwan, sourced from Bloomberg), and credit from Bloomberg including outstanding issues with >1-year remaining maturity and IG based on Bloomberg Composite Credit Rating (both as of September 2016). Singapore in particular does not disclose foreign asset holdings on life insurance balance sheets.Source: J.P. Morgan, Company filings, Bloomberg, Swiss Re, Life Insurance Association of Japan, Korea Life Insurance Association, Taiwan Insurance Institute, Thai Life Insurance Association, Hong Kong Office of the Commissioner of Insurance (OCI), IMF, Monetary Authority of Singapore, Bank Negara Malaysia, Bank of Indonesia
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YE 2015 Asset as Likelihood of greater
Country Penetration* % of GDP Sovereign IG Credit Other Credit As of Total Foreign Current Reg cap† demand for callables?
Japan 8.3% 83% $4,701 $120 $622 Aug-16 $3,454 $750 22% None Low
China** 1.9% 14% $52 $8 $2,194 Dec-15 $1,479 $50 3% 15% Very low
Korea 7.3% 52% $407 $0 $271 Aug-16 $693 $58 8% 30% Very high
Taiwan‡ 15.7% 136% $177 $0 $59 Sep-16 $690 $382 ($296) 55% (43%) 45% Very high
Hong Kong*** 13.3% 64% $5 $13 $43 Dec-14 $212 $168 79% None Low
Singapore 5.6% 44% $64 $16 $48 Sep-16 $128 Not Avail. Not Avail. None Low
Thailand 3.7% 17% $49 $0 $44 Dec-14 $69 $4 6% 20% High
Malaysia 3.4% 20% $65 $0 $103 Sep-16 $57 $2 4% 10% Very low
Indonesia 1.3% 3% $77 $1 $19 Aug-16 $29 $3 10% None Very low
Foreign asset as % of totalLocal ccy bonds ($bn) Assets ($bn USD)
29
The long-dated vega ‘food chain’
DealerCallable bond
issuer
Hedge funds
Investor
Insurancecompanies
Pa
y fixed
Receive fixed
Pay floating
Be
rmu
da
n re
ceive
r sw
ap
tion
MoneyManagers
Other dealers
Callable swap
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30
Callable bonds have exposure to the slope of the yield curve, forward
volatility and correlation
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The decision to exercise the call
option is driven by:
The moneyness of that call date
Volatility in that exercise tenor
over the call frequency
The forward volatility and
correlations among subsequent
call dates
Callable bonds can be decomposed
into a strip of single call dates, which
means they have exposure to the
slope of the forward yield curve,
forward volatility, and various
correlations
They have an embedded Bermudan
receiver swaption
Lockout Call freq
Maturity
t=0 t=1Y t=6Y
─ ─ ─►
1Y (first exercise)
─ ─ ─► 5Y swap 1Yx5Y
2Y
─ ─ ─ ─ ─ ─ ─► 4Y swap 2Yx4Y
3Y
─ ─ 3Y expiry ─ ─ ─ ─ ─► 3Y swap 3Yx3Y
4Y
─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─► 2Y swap 4Yx2Y
5Y
─ ─ ─ ─ ─ ─ 5Y expiry (last exercise) ─ ─ ─► 5Yx1Y
1Yx5Y Bermudan swaption
1Y swap
31
Bermudan structures hedged with Europeans can also have somewhat
more volatile risk characteristics…
At fixed strike, the optimal exercise point for Bermudan receivers moves with rates, causing them to trade more like shorter expiries in a rally and longer in a sell-off…
Premium for a Bermudan receiver and two European receivers, all struck at 4%, under rate shocks; bp of notional
Source: J.P. Morgan
…which can also result in net risk delivery for Bermudan positions hedged with Europeans
Dollar vega of the same structures as before; bp of notional per 0.1 bp/day
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1000
2000
3000
4000
5000
-50 0 50 100 150 200
1Yx29Y Bermudan
1Yx29Y European
5Yx25Y European
0
5
10
15
20
25
-50 0 50 100 150 200
1Yx29Y Bermudan
1Yx29Y European
5Yx25Y European
32
…which can result in tradeable vega dynamics around significant moves
in rates that also affect supply
Dealers who are unable to place all their Bermudan risk with clients—i.e., all of them—typically hedge with Europeans and manage the vega dynamics…
Estimated vega delivery resulting from dealer hedging flows owing to dVega/dRate* effects under various rate shocks; $mn per abp
* We consider all outstanding Formosa bonds and all zero-coupon and fixed-rate bonds issued since 2011 with original expiry greater than 15 years. We model each outstanding callable bond as a Bermudan receiver swaption, struck ATMF as of the announcement date. We further assume that 100% of the vega risk of the whole portfolio is hedged with 10Yx10Y European swaptions, and that the notionals are held fixed thereafter.Note: Current levels are as of 11/17/16 closes.Source: J.P. Morgan, Bloomberg
…which also affects the potential for outstanding deals to be redeemed/reinvested—which in effect is a re-strike of the embedded Bermudan risk with net vega delivery
Probability-weighted redemptions of USD-denominated callables, current as well as under rate shocks; $bn
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-100
-50
0
50
100
-75 -50 -25 0 25 50 75
1/4/2016 Current
0
5
10
15
1Q17 2Q17 3Q17 4Q17
50 25 Current -25 -50
Note: We assume each callable is struck at the par callable swap rate as of the announcement date.Source: J.P. Morgan, Bloomberg
33
Putting it all together: net vega supply from issuance of callable bonds, net
of redemptions and dVega/dRate hedging flows
Volatility supply from callable issuance has accelerated in 2016, and particularly in 4Q16 amidst new entrants to the callable market and dVega/dRate
* We consider all outstanding Formosa bonds as well as zero-coupon callable bonds with original maturity greater than 15 years issued since the beginning of 2014. ** We model each outstanding callable bond as a Bermudan receiver swaption, struck ATMF as of the announcement date. Note: Levels current as of 11/18/16.Source: Bloomberg, J.P. Morgan
Cumulative vega supply* resulting from new callable issuance (blue bars; light blue bars represent those bought by Taiwanese lifers and dark blue bars represent those bought by Korean lifers), cumulative dVega/dRate** of the existing universe of Bermudan callables (grey bar), and the net of the two (black line); $mn per abp
-100
-50
0
50
100
150
200
250
2Q15 3Q15 4Q15 1Q16 2Q16 3Q16 4Q16
Vega supply from new issuance (Korea)
Vega supply from new issuance (Taiwan)
dVega/dRate
Vega supply net of dVega/dRate
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Vega dynamics are tradeable, given the propensity for long-dated vols to trade counter-directionally with moves in the level rates
1-year trailing beta of monthly changes in 10Yx10Y ATMF implied volatility with the same in 30-year rates; bp/day per %
Source: J.P. Morgan
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
2013 2015 2017
34
Taking the other side: vol slide trades in spot and forward space
The bottom right of the implied volatility surface in USD swaptions has been inverted for most of the modern era, particularly in forward volatility points
5-year average of spot and forward 1-year vol slide in vanilla swaptionsby forward point and exp/tail; bp/day
* Includes the 12 largest funds.Source: J.P. Morgan
Forward volatility can be decomposed via sum of variance into two vanilla vols and an implied correlation
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-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Spot 1Y 2Y 4Y 9Y 19Y
5Yx10Y 5Yx20Y
35
FVAs in interest rate markets aren’t terrible liquid, but the replication
does a decent job provided we use the right weights…
Weights inferred from a sum of variance approximation rather than equal notional significantly improve the performance of synthetic strategies
Unlike pure FVAs, replicating portfolios have initial delta and gamma exposures
* Notionals are sized to a partial vega-neutral amount using a normal sum of variance approximation (see Appendix A for details).
Note: We consider daily trades with a three month holding period, hedging the initial net delta with forward swaps, and compare the results to the P/L of a pure FVA.
Source: J.P. Morgan
R-squared from regressing 3-month returns from pure forward vol positions against returns from replicating portfolios (consisting of a midcurve and a swaption) over the past 4 years; partial vega-weighted notional* versus equi-notional packages; %
Initial risk exposures of various structures; units as indicated
* Notional amount (in $bn) is calculated to set initial vega risk to $1mn per abp.† Delta is measured in $k per bp.‡ Net gamma exposure is measured in $mn 10s per bp.†† Ex-ante 1-day theta in abp, scaled to 3 months assuming 63 business days.‡‡ dVega/dRate (in $k per abp) for 25bp sell-off in rates. Current as of 3/1/16.Source: J.P. Morgan
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0%
20%
40%
60%
80%
100%
5Yx5Yx25Y 2Yx5Yx25Y 1Yx5Yx25Y 6Mx5Yx25Y
Vega-weighted Equinotional
Fwd Expiry Tenor Not'l* Delta†
Gamma‡
Theta††
dV/dR‡‡
Delta†
Gamma‡
Theta††
dV/dR‡‡
5Y 5Y 25Y 0.3 460 1.6 0.4 -14 131 1.0 0.4 -49
2Y 5Y 25Y 0.3 238 1.5 0.7 -30 118 1.1 0.7 -45
1Y 5Y 25Y 0.3 163 1.4 0.8 -32 121 1.0 0.8 -44
6M 5Y 25Y 0.3 132 1.4 0.7 -33 115 1.0 0.7 -43
Spot 5Y 25Y 0.3 107 4.2 -1.9 -41
5Y 10Y 10Y 0.6 264 1.3 0.2 -33 136 0.8 0.2 -31
2Y 10Y 10Y 0.5 167 1.3 0.3 -35 117 0.9 0.3 -36
1Y 10Y 10Y 0.5 131 1.2 0.4 -35 113 0.9 0.4 -37
6M 10Y 10Y 0.5 115 1.1 0.2 -34 109 1.0 0.2 -37
Spot 10Y 10Y 0.5 104 2.6 -1.0 -37
5Y 5Y 5Y 1.5 314 1.4 0.2 -3 86 0.9 0.3 6
2Y 5Y 5Y 1.3 143 1.3 0.3 -11 83 0.8 0.3 -16
1Y 5Y 5Y 1.3 91 1.1 0.3 -12 80 0.7 0.3 -18
6M 5Y 5Y 1.3 71 1.1 0.2 -12 76 0.7 0.2 -19
Spot 5Y 5Y 1.2 62 3.5 -2.2 -19
5Y 1Y 1Y 16.8 700 1.7 -0.2 126 52 1.2 -0.1 119
2Y 1Y 1Y 13.7 178 0.8 -0.7 75 63 0.1 -0.7 15
1Y 1Y 1Y 13.2 96 1.1 0.2 61 60 0.6 0.2 2
6M 1Y 1Y 12.8 79 1.7 1.0 53 46 3.0 0.9 -2
Spot 1Y 1Y 12.7 42 18.6 -8.2 -4
Midcurve+Swaption 3 Swaptions
36
…and accessing implied correlation directly via midcurves significantly
improves replication efficiency, especially for longer-dated structures
Midcurve-based FVA replications produce the best results overall, especially for longer expiries
Note: Replications are sized to a partial vega-neutral amount of either a swaption and midcurve or three swaptions using weights inferred from a normal sum of variance approximation (see Appendix A for details). We also include an initial, static delta hedge in both replications. Hit rate is defined as the number of trades in which the replication strategy outperformed the FVA divided by the total number of trades.Source: J.P. Morgan
Average ex-ante net gamma and carry, and statistics from regressing 3-month returns (daily trades) from pure forward vol positions against returns from different strategies over the past 4 years; units as indicated
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Fwd Expiry Tail
Pure FVA
carry (abp)
Initial Gamma
($mn 10s per bp)
Initial Carry
(abp) Beta
R-sq
(%)
SE
(abp)
Excess
return (abp)
Hit rate
(%)
Initial Gamma
($mn 10s per bp)
Initial Carry
(abp) Beta
R-sq
(%)
SE
(abp)
Excess
return (abp)
Hit rate
(%)
5Y 5Y 25Y 0.93 1.52 1.07 0.88 94% 0.96 0.43 64% 1.01 1.45 0.77 80% 1.82 0.64 62%
2Y 5Y 25Y 1.20 1.46 1.32 0.78 83% 1.14 0.24 61% 1.02 1.73 0.64 70% 1.53 0.35 61%
1Y 5Y 25Y 1.62 1.44 1.94 0.72 79% 1.12 0.14 62% 1.05 2.18 0.62 69% 1.34 0.11 61%
6M 5Y 25Y 1.78 1.13 2.04 0.68 79% 1.07 0.09 54% 0.79 2.20 0.65 73% 1.19 0.21 49%
5Y 10Y 10Y 0.41 1.13 0.88 0.77 80% 1.19 0.76 63% 0.77 1.00 0.68 60% 1.73 1.14 71%
2Y 10Y 10Y 0.96 1.16 1.33 0.76 80% 1.14 0.49 64% 0.82 1.49 0.65 70% 1.40 0.37 61%
1Y 10Y 10Y 1.10 1.15 1.54 0.71 77% 1.14 0.49 63% 0.80 1.65 0.64 70% 1.27 0.44 60%
6M 10Y 10Y 1.06 1.11 1.70 0.69 73% 1.17 0.55 62% 0.82 1.79 0.64 69% 1.25 0.53 58%
5Y 5Y 5Y 1.13 1.08 1.46 0.88 91% 1.53 0.22 61% 0.58 1.78 0.83 78% 2.45 -0.16 56%
2Y 5Y 5Y 1.11 1.10 1.43 0.80 87% 1.68 -0.05 58% 0.63 1.87 0.81 82% 1.96 0.18 55%
1Y 5Y 5Y 1.49 1.08 2.08 0.74 89% 1.33 -0.17 53% 0.81 2.35 0.72 86% 1.49 -0.06 51%
6M 5Y 5Y 1.56 1.04 2.52 0.75 91% 1.26 0.03 59% 0.86 2.69 0.72 88% 1.41 0.14 54%
2Y 1Y 1Y -0.23 2.42 1.30 0.84 90% 3.49 0.78 43% -0.71 -0.02 0.68 56% 7.50 -1.43 33%
1Y 1Y 1Y -3.30 3.54 -1.96 0.76 80% 4.30 -0.11 33% 0.34 -1.97 0.59 56% 6.53 -0.33 37%
6M 1Y 1Y -3.44 6.87 -1.26 0.90 94% 2.09 -0.03 50% 3.06 -1.25 0.78 86% 3.20 -0.22 50%
Midcurve+Swaption 3 Swaptions
37
Disclosures
Disclosures
Analyst Certification: The research analyst(s) denoted by an “AC” on the cover of this report certifies (or, where multiple research analysts are primarily responsible for this report, the research analyst denoted by an “AC” on the cover or within the document individually certifies, with respect to each security or issuer that the research analyst covers in this research) that: (1) all of the views expressed in this report accurately reflect his or her personal views about any and all of the subject securities or issuers; and (2) no part of any of the research analyst's compensation was, is, or will be directly or indirectly related to the specific recommendations or views expressed by the research analyst(s) in this report. For all Korea-based research analysts listed on the front cover, they also certify, as per KOFIA requirements, that their analysis was made in good faith and that the views reflect their own opinion, without undue influence or intervention.
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"Other Disclosures" last revised January 07, 2017.
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