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“Selling Vol” or Earning a Risk Premium?

May 2015

Vol Risk Premia in Equities

Dr Nick Firoozye

Derivative Research

+44-207-102-1660

Nick.Firoozye@nomura.com

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

Everyone is short vol

But not everyone is getting paid for it!

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

turn

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

Smart money sells vol!

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

Vol as Insurance

When should you sell it and which vol should you sell?

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 are Pervasive

Diversification and outperformance

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

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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

Closing thoughts

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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