Volatility of Volatility CBOE Risk Management Conference Kambiz Kazemi Portfolio Manager
About us
Picton Mahoney Asset Management (PMAM) is a Canadian portfolio management boutique. We manage over $9 billion CAD in assets for investors through three lines of investment solutions:
• Authentic hedge strategies • Sub-advisory services • Institutional long-only mandates Our Founding Principles:
• Authenticity • Transparency • Capacity
1
Assets under management
Volatility of volatility is not new in town
•
Every option book has exposure to vol of vol (i.e. gamma of gamma or 4th moment)
•
Vol of vol is the sensitivity of out-of-money options in relation to those at-the-money
•
Why we increasingly hear about it: •
Because vol of vol is directly related to “convexity”
•
Because vol of vol is directly related to “tails” (post-crisis everyone cares about “tails”)
•
Because VIX options are now being used by a wide range of market participants, and vol of vol matters in pricing and trading them 3
How to get exposure to vol of vol (pre-VIX options or other underlyings) Ratio back spreads: trade ATM options vs. multiple OTM options •
Sell 1 ATM call Buy 2 x OTM call delta hedged
•
Not as “clean” as trading vol of vol products (lower moments can take over)
125 « strike »
P&L
100
4
Great news: Vol of vol is increasingly tradable (thank you CBOE!) Open Interest of VIX options VIX Call Total OI 9000000 8000000 7000000 6000000 5000000 4000000 3000000 2000000 1000000 0
Source: Bloomberg, Picton Mahoney Research, as at Feb 27, 2015.
VIX put total OI
Great news: Vol of vol is increasingly tradable (thank you CBOE!)
Millions
Axis Title 20 18 16 14 12 10 8 6 4 2 0 2/24/2006
2/24/2007
2/24/2008
2/24/2009
2/24/2010
VixOptionVegaOutstanding
Source: Barclay’s Equity Derivatives Strategy Group, as at Feb 24, 2015.
2/24/2011
2/24/2012
2/24/2013
VixOptionVegaVolume
2/24/2014
2/24/2015
Volatility of volatility in the context of VIX options •
Implied terminal PDF of VIX based on VIX options prices
•
Realized distribution of VIX returns
•
Implied distribution of VIX returns
•
Characteristics of implied surface of volatility of VIX options •
Term structure
•
The skew
7
Vol of vol distribution: lognormal? Implied price distribution Implied price distribution for Mar 2015 on Feb 26th, 2015 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10
Source: Picton Mahoney Asset Management, Bloomberg
8
Vol of vol distribution: lognormal? 1 month constant maturity VIX daily returns
9 Source: Bloomberg
Vol of vol distribution: Lognormal? Implied volatility by strike (as of Feb 27th) 15-Mar
15-Apr
15-May
15-Jun
140.00
120.00
100.00
80.00
60.00
40.00
20.00
13
14
15
16
16
17
18
19
20
21
22
23
24
25
10 Source: Picton Mahoney Asset Management, Bloomberg
Vol of vol term structure: Backwardation Term structure of volatility of VIX and V2X on Feb 27 (ATM Options) VIX
V2X
90
85
80
75
70
65
60
55
50 March
April
Source: Picton Mahoney Asset Management, Bloomberg
May
June
July
August
Vol of vol term structure: Backwardation Rolling 3 months beta of VIX futures to VIX spot 5th mths 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Source: Picton Mahoney Asset Management, Bloomberg
4th mths
3rd mths
2nd mths
1st mths
Vol of vol term structure: Backwardation Beta of VIX futures with VIX spot (3 mths rolling since June 2012) Max
Min
Average
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1
2
Source: Picton Mahoney Asset Management, Bloomberg, as at Feb 27, 2015
3
4
5
Vol of vol in practice: Similarities to commodities and fixed income •
Each maturity represents a different underlying •
•
•
VIX futures are “forwards”: curve dynamics similar to forward rates
VIX and commodities exhibit higher uncertainty in the shorter maturities •
For commodities, the reason is supply/demand disruptions and implication of storage
•
VIX is similar: supply demand of gamma (the shorter expiry S&P option prices are – all else being equal – more sensitive to market movements, hence buying or selling gamma)
While the curves of the underlyings have many degrees of freedom, they are held by various relationships •
Fixed income: bootstrapping
•
Commodity: cost of carry 14
Vol of vol term structure: Similarities with commodity vol term structure Volatility term structure for NatGas and Crude Oil futures Henry Hub Natgas
WTI Crude
60
Volatility
55
50
45
40
35
30 1
2
3
4
5
Generic future contract
Source: Picton Mahoney Asset Management, Bloomberg
6
7
8
Vol of vol term structure: Similarities with forward rates vol term structure
Implied volatility (bps annual) of 1yr rate forward (1y in … years) USD Feb 27th 60 55 50 45 40 35 30 25 20 1Yr x 2Yr
Source: Picton Mahoney Asset Management, Bloomberg
1Yr x 5Yr
1Yr x 10Yr
1Yr x 20Yr
1Yr x 30Yr
Vol of vol in practice: Similarities to commodities and fixed income What kind of practical implications? •
If one has fundamental views on the underlying:
•
Calendar spread trades
•
Conditional curve trades
•
Roll down (carry) trades
•
Options on spread (i.e curve options in fixed income or CSO)
•
Midcurve options (ex: an option on June VIX expiring in April)
17
Vol of vol in practice: Examples of carry and hedge
Volatility (%)
Roll down (carry trade)
Buy a short dated put
Sell a long dated put
•
Put calendars
•
Starts by having a view on the VIX term structure
•
Takes into account concavity, vol of vol level to estimate positive carry
VIX future maturity
Volatility (%)
Risk-off hedge
Buy a short dated call
Sell a long call
VIX future maturity
•
Call calendars
•
Takes into account concavity, vol of vol level to estimate negative carry 18
Vol of vol in practice: Future developments? Option on spreads •
A pure way of playing the steepening/flattening
•
Trading vol of and vol and the correlation of VIX future curve
Volatility (%)
UX3 – UX1
1M future
3M future
VIX future maturity
Mid-curves •
The possibility of trading the curve conditionally
•
Price discovery of the term structure of a given maturity VIX future and gaining exposure to it 19
Vol of vol and VIX options: Some practical considerations Volatility of VIX options is high enough for usual “intuition” and “common sense” to be misleading •
Delta of a month ATM call with a 120 vol and 2 month to expiry is 60%
Delta hedging (for those who want to pick up the risk premium) •
Can we (should we) use a different model than B&S? •
•
CEV, local volatility, SABR, etc.
If we use B&S to price, what approach should we have: “sticky delta” or “sticky strike”? •
Let’s look at the real option prices and see how they have behaved to get a clue
20
The vol / vvol relationship: Sticky delta? (Jan-08 to Feb-15) VIX 1Month constant maturity vs. VIX ATM 1Month Implied Vol Series1
Linear (Series1)
250 y = 0.7426x + 75.283 R² = 0.0886 200
150
100
50
0 0
10
Source: Picton Mahoney Asset Management, Bloomberg
20
30
40
50
60
70
The vol / vvol relationship: Sticky strike (Jan-14 to Feb-15) VIX future vs. vol of 50 delta VIX option 1st month VIX
2nd month VIX
Linear (1st month VIX)
Linear (2nd month VIX)
230 y = 10.777x - 76.378 R² = 0.6068
210 190 170 150 130 110 90
y = 5.132x - 7.8289 R² = 0.4056
70 50 10
12
Source: Picton Mahoney Asset Management, Bloomberg
14
16
18
20
22
24
Volatility products and the vol of vol
We have witnessed tremendous evolution (increase) in VIX ETNs •
1 Month constant maturity ETN launched in 2010
•
Increase in levered ETNs AUM (and vega) since 2012
•
Addition of dynamic ETNs
•
And many OTC products offered by dealers (systematic and dynamic/rule based)
Has this proliferation of volatility products had any effect on the behavior of volatility? •
We have observed increased vol of vol in recent past
23
Vol of vol changing landscape: Volatility ETNs ETN (unlevered + levered) vega VXX
XIV
SVXY
TVIX
UVXY
350000
300000
250000
200000
150000
100000
50000
0
24 Source: Picton Mahoney Asset Management, Bloomberg
Vol of vol changing landscape: Volatility ETNs a driver? VIX ETN Vega * vs. Subsequent 1 Month Realized Volatility of 1st Month VIX future (Oct 11 to Feb 15) Series1
Linear (Series1)
160% 140% 120% 100% 80% 60% 40% y = -1E-07x + 0.8449 R² = 0.0006 20% 0% -
50,000
100,000
150,000
200,000
250,000
300,000
350,000
* Includes the following Exchange traded notes: VXX, XIV, TVIX, SVXY, UVXY 25 Source: Picton Mahoney Asset Management, Bloomberg
Vol of vol changing landscape: Levered ETNs seem plausible cause of increased VIX future volatility VIX ETN Vega * vs. Subsequent 1 Month Realized Volatility of 1st Month VIX future (Apr 14 to Feb 15) Series1
Linear (Series1)
160%
140%
120%
100%
80% y = 4E-06x - 0.1814 R² = 0.138
60%
Increase in vega outstanding especially of levered volatility ETN seems to have a causal effect on the level of vol of vol
40%
20%
0% -
50,000
100,000
150,000
200,000
250,000
300,000
350,000 26
Source: Picton Mahoney Asset Management, Bloomberg
Volatility of volatility: Final thoughts •
A direct way to hedge or get exposure to “convexity”
•
The advent of volatility products has made vol of vol accessible to many participants and is efficiently tradable
•
The liquidity in the VIX complex has made many previously theoretical strategies a possibility
•
Trading instruments with vol of vol exposure requires some preparation: understand pricing and sensitives
•
More products will (hopefully) emerge and complete the market •
Mid-curves, spread options, etc.
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This report is published by Picton Mahoney Asset Management (PMAM) on March 2, 2015. It is provided as a general source of information and should not be considered personal investment advice or an offer or solicitation to buy or sell securities. The information contained in this report has been obtained from sources believed reliable however the accuracy and/or completeness of the information is not guaranteed by PMAM, nor does PMAM assume any responsibility or liability whatsoever. All opinions expressed are subject to change without notification. PMAM and/or its funds may currently hold long and/or short positions in the securities of the companies mentioned in this report. This report is confidential and not for redistribution. Any review, re-transmission, dissemination or other use of this information by persons or entities other than the intended recipient is prohibited.
