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Transcript of Vol Risk Premia in Equities - nomura.com · T log( E T [exp( ³ r s ds)]) ~ V T ~ (1 2) 1 2 y T y...
Connecting Markets East & West
© Nomura International plc
“Selling Vol” or Earning a Risk Premium?
May 2015
Vol Risk Premia in Equities
Dr Nick Firoozye
Derivative Research
+44-207-102-1660
See Disclosure Appendix A1 for analyst certifications and important disclaimers.
1
Table of Contents
Everyone is short vol
Smart money sells vol
Vol as insurance: when should you sell vol and which vol should you sell?
Vol risk premia are pervasive
Closing thoughts
3
Almost all asset classes are short vol
Credit is short vol
Equities are also short vol
In low rates, govies are short vol
MBS is short vol
General Rule :
if you’re making a return, you probably sold someone some sort of option
You’re short even if you don’t know it!
Investors are already selling volatility via credit
Source: Merton 1974, On the pricing of corporate debt: The risk structure of interest rates, Journal of Finance, Bloomberg, Nomura. HY Credit is CDX HY on-the-run index. US equity volatility risk premium is short variance swaps on S&P 500.
In theory long credit is short a put on the assets of a firm (Merton 1974)
The “Merton model” of credit risk The empirical evidence supports the theory in the US
4
90
95
100
105
110
115
120
125
Cu
mu
lati
ve e
xce
ss re
turn
s
US HY Credit
US Equity Volatility Risk Premium
Going short volatility has a very similar performance to going long equities.
Empirically, equities are short vol
Source: Bloomberg 5
Same Risk, Different Premia
96
98
100
102
104
106
108
Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15
Short VIX vs Long S&P 500
S&P 500 Short VIX
In low rates environments, govies are short vol
Source: Nomura Research, Bloomberg 1: Shadow rate is defined as the short rate without cash-and-carry constraints
6
USD front-ends showed a strong comovement in low rates Comovement is even stronger in low yield market like Japan
0
50
100
150
200
250
300
0
1
2
3
4
5
6
7
2001 2003 2005 2007 2009 2011 2013
Ba
sis
Po
int V
ola
tility
Sw
ap
ra
te (%
)
Low rates periods USD 1m2y Swap (lhs) USD 1m2y Vol (rhs)
0
40
80
120
160
0
0.4
0.8
1.2
1.6
2
2001 2003 2005 2007 2009 2011 2013
Ba
sis
Po
int V
ola
tility
Sw
ap
ra
te (%
)
JPY 1m5y Swap (lhs) JPY 1m5y Vol (rhs)
Fisher Black suggested at ZIRP bonds turn into options on future
policy rates
Say x(t) is the shadow rate1 and r(t) is the short rate.
),0max(
),(
tt
tt
xr
dWdttxdx
Hence, ZCB yield slope depends on the volatility:
TdsrEy sTT ~)])[exp(log(
)(~ 2121TTyy TT
Higher vol = higher rates and steeper curves
0
0.2
0.4
0.6
0.8
1
1.2
0 1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y 9Y 10Y
Yie
ld (%
)
ZCB Yield Curve Simulation
Volatility = 2%
Volatility = 1%
Optionality drives the outperformance of MBS
Mortgages (MBS) – also short volatility
Source: Citi Yieldbook, Nomura Research * Agency non-callables returns are adjusted to match the same duration as MBS.
7
-1%
0%
1%
2%
3%
4%
5%
MBS Decomposition
Ave
rag
e r
etu
rns (p
.a.)
MBS Returns Decomposition
Unexplained
Vega
Gamma
Credit
Duration
-10%
-5%
0%
5%
10%
15%
Ro
llin
g 1
y M
BS
re
turn
s
(an
nu
alize
d)
Unexplained 3y10y1m10y CreditDuration
* Sample period: Aug 2005 – Jul 2014
Duration is the main component in MBS returns
Duration and optionality help to replicate MBS returns MBS optionality replaced by iVRP outperforms
95
105
115
125
135
145
155
Cu
mu
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ve e
xces
s re
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s (b
ase
ind
ex
= 1
00
)
MBSAgency non-callablesAgency non-callables + 1m10y + 3y10y
90
110
130
150
170
190
210
Jan-02 Jan-04 Jan-06 Jan-08 Jan-10 Jan-12 Jan-14
Cu
mu
lati
ve e
xces
s re
turn
s (b
ase
ind
ex
= 1
00
)
MBS Agency non-callables + iVRP USD Select
9 Source: Wikimedia (http://commons.wikimedia.org/wiki/File:Warren_Buffett_KU_Visit.jpg) and WikiMedia (http://commons.wikimedia.org/wiki/File:Lehman_Brothers.svg)
Didn’t Buffett call Derivatives “Financial Weapons of
Mass Destruction”?
Wait a second!
Didn’t Lehman fall because they were
short vol?
10 Source: see Matt Levine, Lehman Brothers Maybe Sold Warren Buffett a Rainbow, Bloomberg View, 6 Feb 2014 and quoted sources.
Lehman Bought Vol
The insider’s story
$4.2bn
OTM puts “worst of”
(SPX, NKY,SX5E) basket
Buffett Sold Vol
Why did Buffett sell vol?
Source: Nomura Research 11
Our insurance-like derivatives contracts*, … are coming to a
close…….almost certain to realize a final ‘underwriting profit’
- Warren Buffett
“
”
Derivatives = Insurance!
* Equities puts, CDO Tranches, CDS, etc
Selling vol usually makes money
Source: Bloomberg, Nomura. The 1m10y swaption straddle implied volatility used in the above analysis is derived from the price of an ATMF 1m10y swaption, and the realised volatility is computed as being the actual realised volatility of the underlying 10y forward swap from the start date to the expiry date of the corresponding swaption straddle. The analysis is done on a daily basis and based on historical data from May1994 to Sep 2014.
13
0
50
100
150
200
250
300
Bas
is P
oin
t V
ola
tility
USD 1m10y
1m implied volatility
1m actual realised volatility
• Historically, implied volatility
tends to exceed realized volatility over the long term.
• In more than 70% of cases,
implied volatility was greater than realized volatility.
• Average gain is 11.3bp and
positive as well
-100
-80
-60
-40
-20
0
20
40
60
80
100
1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014
Bas
is P
oin
t V
ola
tility
1m implied volatility - 1m actual realised volatility
Underwriting Profit
Payout on Policy
0%10%20%30%40%
<-80
(-80,-60)
(-60,-40)
(-40,-20)
(-20,0)
(0,20)
(20,40)
(40,60)
(60,80)
(80,100)
Observations (%)
Positive risk
premia
Simple indicators improve the short gamma performance consistently
When should you sell vol?
Source: Nomura Research. The global portfolio consists of 33% S&P 500, 33% EuroStoxx and 33% Nikkei. The sample period is Jan 2002 to Dec 2014. For comparison purpose, the volatility of returns are rescaled to 5%.
14
99
100
101
102
103
104
105
2002 2004 2006 2008 2010 2012 2014
Cu
mu
lative e
xcess
re
turn
Global Equity Volatility Risk Premia
Short only Short using Indicator A Short using Indicator B Short using Indicator C
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Short only Short using Indicator A Short using Indicator B Short using Indicator C
Sh
arp
e r
atio
S&P 500
EuroStoxx
Nikkei
Global
Styles make everything better!
Source: Nomura Research. The sample period is Jan 2001 to Jan 2015. The iVRP Aggregate index sells straddles on 1m/3m expiries + 2y/5y/10y/20y/30y tails across USD/EUR/JPY, and delta-hedged until expiry. The FX VRP Aggregate index. The FX VRP Aggregate index sells straddles on 1w/1m/3m/6m expiries and delta-hedged until expiry.
15
0
0.5
1
1.5
2
USD iVRP EUR iVRP JPY iVRP Global iVRP
Sh
arp
e r
atio
Aggregate Select
Styles without timing improves diversified portfolio in rates
Styles without timing improves diversified portfolio in FX
75
85
95
105
115
125
135
145
155
165
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15
Cu
mu
lati
ve e
xces
s re
turn
s
Global FX VRP Select Index
Global FX VRP Aggregate Index
85
95
105
115
125
135
145
155
165
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15
Cu
mu
lati
ve e
xces
s re
turn
s
Global iVRP Select Index
Global iVRP Aggregate Index
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
EURUSD VRP USDJPY VRP GBPUSD VRP Global VRP
Sh
arp
e r
atio
Aggregate Select
80
81
82
83
84
85
86
87
88
89
90
91
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-50 -25 0 25 50
Imp
lied
Vol (b
ps)
Sh
arp
e R
atio
s
Strike
Short Receiver Sharpe Ratio (LHS)
Short Payer Sharpe Ratio (LHS)
Short Straddle Sharpe Ratio (LHS)
Implied Vol (RHS)0%
5%
10%
15%
20%
25%
30%
0.00
0.20
0.40
0.60
0.80
1.00
90 95 100 105 110
Imp
lied
Vola
tility
Sh
arp
e R
atio
Strike
Short Calls Sharpe Ratio (LHS)
Short Puts Sharpe Ratio (LHS)
SPX Sharpe Ratio (LHS)
Average Implied Vol (RHS)
S&P 500 OTM call outperformed
Which vol should you sell?
Source: Nomura Research. The sample period for equities vol/ underlying is1998 to 2015. The sample period for rates vol/ underlying is 2010 to 2015. 16
OTM Puts
USD 1m10y ATM straddle swaption outperformed
OTM Receivers OTM Payers OTM Calls
Do NOT sell vol when vol is high!
Source: Nomura Research, Bloomberg. The sample period is Jan 2006 to Jan 2015 across equities, rates and FX. Sharpe ratio is calculated by monthly data. 17
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Low-vol Bucket Mid-vol Bucket High-vol Bucket
Sh
ap
re r
ati
o
Performance of USD 1m10y Swaption (Rates) VRP
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
Low-vol Bucket Mid-vol Bucket High-vol Bucket
Sh
arp
e r
ati
o
Performance of EURUSD 1m (FX) VRP
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Low-vol Bucket Mid-vol Bucket High-vol Bucket
Sh
arp
e r
ati
o
Performance of Equities VRP
Moderate vol does best
Now:
• FX is High
• Rates is Mid
• Equities is Low
Vol risk premia exist across equity markets
Source: Nomura Research, Bloomberg. For comparison purpose, the volatility of returns are rescaled to 1%. 19
In Europe as well, VRP outperformed significantly
95
100
105
110
115
120
Mar-01 Mar-03 Mar-05 Mar-07 Mar-09 Mar-11 Mar-13
EuroStoxx 50
Vol Risk Premia Long Only
Vol risk premia exist across equity markets
Source: Nomura Research, Bloomberg. For comparison purpose, the volatility of returns are rescaled to 1%. 20
Short gamma strategies outperformed across equity markets (vol scaled and centered indices)
95
100
105
110
115
120
Cu
mu
lati
ve e
xce
ss r
etu
rns
S&P 500
Vol Risk Premia
Long Only
95
100
105
110
115
120EuroStoxx 50
Vol Risk PremiaLong Only
96
98
100
102
104
106
108
110
112Nikkei 225
Vol Risk Premia
Long Only
98
100
102
104
106
108
110
Kospi 200
Vol Risk Premia
Long Only
97
101
105
109
113
Cu
mu
lati
ve e
xce
ss r
etu
rns
Hang Seng
Vol Risk Premia
Long Only
96
98
100
102
104
106
108
Nifty 50
Vol Risk Premia
Long Only
96
101
106
111
116
ASX 200
Vol Risk Premia
Long Only
98
99
100
101
102
103
104
105
106
Mar-11 Mar-12 Mar-13 Mar-14
MSCI EM
Vol Risk Premia
Long Only
Equity vol premia truly diversify
Source: Nomura Research. The sample period is Feb 2001 to Apr 2015. 21
Equity vol risk premia outperformed traditional equity factors
eVRP Growth Value Quality Mmtm Low Vol S&P 500
eVRP 100%
Growth 22% 100%
Value 2% -61% 100%
Quality -34% 10% -21% 100%
Momentum
-7% 43% -70% 48% 100%
Low Vol 50% 0% 32% -40% -17% 100%
S&P 500 59% 4% 24% -57% -35% 88% 100%
90
95
100
105
110
115
120
Feb-01 Feb-03 Feb-05 Feb-07 Feb-09 Feb-11 Feb-13 Feb-15
Cu
mu
lati
ve e
xces
s re
turn
s
Equity Vol Risk Premia (eVRP)GrowthValueQualityMomentum
95
97
99
101
103
105
107
109
111
113
115
May-03 May-05 May-07 May-09 May-11 May-13
Cu
mu
lati
ve e
xces
s re
turn
s
Equity Vol Risk Premia (eVRP)
Barra Low Vol
S&P 500
eVRP Growth Value Quality Mmtm Low Vol S&P 500
Ret (p.a.) 20.6% -4.7% 3.6% -3.7% -3.7% 5.8% 4.0%
Vol (p.a.) 20.4% 8.2% 8.6% 8.4% 13.4% 11.7% 15.2%
Sharpe 1.01 -0.57 0.42 -0.44 -0.27 0.49 0.27
MDD -55.6% -71.3% -32.9% -64.6% -72.2% -57.8% -75.8%
Calmar 0.37 -0.07 0.11 -0.06 -0.05 0.10 0.05
Vol risk premia exist across asset classes
Source: Nomura Research. G10 FX Carry is the Nomura G10 FX Carry Index. Correlation is calculated based on Jan 2001 to Jan 2015. 22
Short gamma strategies outperformed across asset classes and are decorrelated
40
400
01 02 03 04 05 06 07 08 09 10 11 12 13 14
Cu
mu
lati
ve e
xces
s re
turn
s (l
og-
scal
ed
)
eVRP S&P 500
90
120
150
180
210
240
270
300
95 97 99 01 03 05 07 09 11 13 15
Cu
mu
lati
ve e
xces
s re
turn
s
iVRP (USD) US 10Y Treasury
90
100
110
120
130
140
150
10 11 12 13 14 15
Cu
mu
lati
ve e
xces
s re
turn
s
FX Global VRP
G10 FX Carry
Correlation eVRP iVRP (USD) FX VRP S&P 500 Treasury FX Carry
eVRP 100%
iVRP (USD) 16% 100%
FX VRP 23% 28% 100%
S&P 500 52% 16% 25% 100%
Treasury -20% 3% -16% -35% 100%
FX Carry 21% 9% 27% 23% -18% 100%
Performance of cross-asset VRP
Source: Nomura Research. The sample period is Feb 2001 to Mar 2015. Cross-asset VRP Aggregate portfolio consists of 33.3% Global iVRP Aggregate + 33.3% Global FX VRP Aggregate + 33.3% eVRP. Each component is leveraged to 10% vol. Cross-asset VRP Select portfolio consists of 33.3% Global iVRP Select+ 33.3% Global FX VRP Select + 33.3% eVRP. Each component is leveraged to 10% vol.
23
50
100
150
200
250
300
350
400
450
500
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15
Cu
mu
lati
ve e
xce
ss r
etu
rns
Cross-asset VRP Select Cross-asset VRP Aggregate
Cross-asset VRP Aggregate Cross-asset VRP Select
Since
Feb-2001 5Y 1Y
Since
Feb-2001 5Y 1Y
Annualized Return 7.3% 9.3% 5.4% 10.8% 11.8% 8.0%
Volatility 6.9% 7.0% 3.6% 6.9% 7.7% 4.0%
Sharpe Ratio 1.06 1.33 1.49 1.58 1.54 1.97
Max Drawdown 34.7% 11.8% 2.9% 25.2% 12.6% 3.4%
Calmar ratio 0.21 0.79 1.87 0.43 0.93 2.31
Cross-Asset VRP using Style-based investing gives superior performance
25
Conclusions
Volatility = Insurance
Everybody is short – not everybody is getting paid for it.
Not a question of whether to sell vol, but when to sell it
Some vols are better than others
Vol Risk Premia are pervasive
Vol is an asset class you should not ignore
Appendix: Vol Risk Premia – Selling Gamma
Source: Nomura Research 26
We can sell options, and delta hedge, mark-to-market regularly
This is called “shorting Gamma” or obtaining the Volatility Risk Premia
Effectively, we sell insurance to the market – tail-risk insurance. In general, it is commensurate with the risk.
Note that Gamma, 𝛤 𝑡 = 𝜕2𝐶(𝑆,𝑡)
𝜕𝑆2 is positive for a long call or put position, and negative for a short position.
According to the Black-Scholes robustness theory, a short variance swap
position has the following theoretical PnL (right)
Hence, selling variance swap allows to capture the Volatility Risk Premia.
For a variance swap 𝛤 𝑡 =constant, so it captures the pure vol risk premium.
For other markets where variance swaps do not exist, we have to carefully
balance risk across entry points (although we cannot alter positions after entry
due to transaction costs).
Black-Scholes Theory
Gamma:
Risk/Exposure
Volatility Risk Premia
VRP
Selling vol—short gamma strategies,.
𝐸[𝑃&𝐿] = 1
2Γ 𝑡 𝜎𝐼𝑚𝑝
2 𝑡 − 𝜎𝑅𝑒𝑎𝑙2 𝑡 𝑑𝑡
𝑇
0
Appendix A-1
Analyst Certification
I, Nick Firoozye, hereby certify (1) that the views expressed in this Research report accurately reflect my personal views about any or all of the subject securities or issuers referred to in this Research report,
(2) no part of my compensation was, is or will be directly or indirectly related to the specific recommendations or views expre ssed in this Research report and (3) no part of my compensation is tied to any
specific investment banking transactions performed by Nomura Securities International, Inc., Nomura International plc or any other Nomura Group company.
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