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I-2 Hedging Tail Risk Committee on Investments/ Investment Advisory Group December 13, 2011

Agenda • Introduction to Tail Risk • Approaches to Tail Risk Hedging – Direct – Indirect • Implementation Choices – Strategic

– Tactical • Recommendation

• Appendix Office of the Treasurer of The Regents University of California

Hedging Tail Risk December 13, 2011 | 2

Introduction to Tail Risk • What is Tail Risk? • Why do “Tails” Occur? • Can Tail Risk be “Hedged”? R e t u r n s H is t o g r a m

Histogram of quarterly S&P 500 returns 1926-2011

IA S B B I S & P 5 0 0 T R U S D : D e c e m b e r 1 9 2 6 - S e p te m b e r 2 0 1 1 Number 40 38 36 34 32 30 28 26 24 22 20

The (left) “Tail”

18 16 14 12 10 8 6 4 2 0 - 4 0 .0 %

- 3 6 .0 % Mean

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- 3 2 .0 %

- 2 8 .0 %

- 2 4 .0 %

- 2 0 .0 %

- 1 6 .0 %

- 1 2 .0 %

- 8 .0 %

- 4 .0 %

0 .0 % R e tu r n

4 .0 %

8 .0 %

1 2 .0 %

1 6 .0 %

2 0 .0 %

2 4 .0 %

2 8 .0 %

3 2 .0 %

3 6 .0 %

4 0 .0 %

S t a n d a r d D e v ia t io n s

Hedging Tail Risk December 13, 2011 | 3

Introduction to Tail Risk • What is Tail Risk? – A large loss – An “unexpected” large loss – A loss outside the bounds of what normally occurs in the markets – A loss greater than 2 (3?) standard deviations – A sudden and severe increase in risk aversion – Unexpected large losses in multiple asset classes and across the globe – Losses beyond what can be mitigated by diversification alone Office of the Treasurer of The Regents University of California

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Introduction to Tail Risk • Why do “Tails” Occur? – The other side of the business cycle (cyclical) – Market liquidity “dries up” (1987, 2007-8) • Liquidity is inversely proportional to perceived uncertainty • The other side of a credit bubble (secular) • In extreme (bad) events, risk asset markets move together (down) as fear gathers momentum – Since equity risk dominates most institutional portfolios, diversification does not protect against extreme events – Regime change (but these cannot be “hedged”) Office of the Treasurer of The Regents University of California

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Introduction to Tail Risk • Can Tail Risk be “Hedged”? – Yes: many liquid assets have derivatives markets – No: contractual hedges are expensive; not recommended as a static strategy – Maybe • Risk is not eliminated (counterparty, operational, basis, regulatory,…) • Terms of insurance may not correspond to actual events (e.g., slow decline in market)

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Hedging Tail Risk December 13, 2011 | 6

Approaches to Tail Risk Hedging • Direct / Exact Approaches – Buying portfolio protection, e.g., options – Know what will be hedged and by how much over what period – Costly, especially if used as strategic policy – All strategies have better performance when applied selectively

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Hedging Tail Risk December 13, 2011 | 7

Approaches to Tail Risk Hedging - Direct • Equity Options – Buying volatility: Puts – Buying / Selling volatility • Put-Call Collars • Put-Spread Collars – Selling Tail Insurance • Dynamic Rebalancing – Use futures to increase / decrease risk exposures, always maintaining a “floor” value in safe assets

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Put Options • If one expects a positive equity risk premium over time, then most options will expire out of the money (worthless) • Chart below shows cumulative cost (P/L) of buying and exercising put options •

Source: Bridgewater Asset Management

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Hedging Tail Risk December 13, 2011 | 9

Passive Put Options = Reduce Equity Exposure • A passive program of always buying 7% OTM puts has the same impact as a reduction in equity exposure of 22%! – US conventional balanced portfolio has same return, volatility, and drawdowns •

Source: Bridgewater Asset Management

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Hedging Tail Risk December 13, 2011 | 10

How Much Protection Does 1% Buy? • Suppose we have $600 Equity, $1,000 total (60/40) portfolio • The bar graph below shows the percent of equity notional value which could have hedged by buying 10% out of the money puts, using no more than 1% of the total portfolio value to buy hedges • On most days – but not when the VIX gapped up - a 1% risk budget would have been more than adequate Source: Bloomberg, Treasurer’s Office

Notional Percent of 60/40 Portfolio Hedged with 1% of total capital, 10% OTM Puts

100

100

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Notional Percent

VIX Index

8/31/11

1/31/11

6/30/10

11/30/09

4/30/09

9/30/08

2/29/08

7/31/07

12/31/06

5/31/06

10/31/05

0 3/31/05

0 8/31/04

20 1/31/04

20 6/30/03

40

11/30/02

40

4/30/02

60

9/30/01

60

2/28/01

80

7/31/00

80

12/31/99

•

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What Risk Budget is Required for 100% Hedge? • Suppose we have $600 Equity, $1,000 total (60/40) portfolio • The bar graph below shows the percent of Total Fund value which would have been used to hedge 100% of equity by buying 10% out of the money puts • The average cost was 63 bp / median cost was 41 bp. For days where the cost was over 1.0%, the average cost was 1.88% Source: Bloomberg, Treasurer’s Office

Percent of total fund required to hedge equity portion of 60/40 Portfolio with 10% OTM Puts

7%

100

6%

80

5% 4%

60

3%

40

2%

20

1%

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8/31/11

1/31/11

6/30/10

4/30/09

9/30/08

2/29/08

VIX Index

11/30/09

option cost / total fund

7/31/07

12/31/06

5/31/06

10/31/05

3/31/05

8/31/04

1/31/04

6/30/03

11/30/02

4/30/02

9/30/01

2/28/01

0 7/31/00

0% 12/31/99

•

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Approaches to Tail Risk Hedging 2 • Indirect / Approximate Approaches – More efficient diversification, or – Indirect (i.e., cross) hedges – “Actual results may vary” from what was intended – Opportunity cost and/or cost of hedges usually less than direct approaches

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Hedging Tail Risk December 13, 2011 | 13

Approaches to Tail Risk Hedging - Indirect • Diversification – by asset class – Reduce equity allocation (de-risk) – Gold, Treasuries, Cash • Diversification – by risk factor – Risk Parity / Risk Balanced – “Exotic Beta:” risk factors other than equity • Cross-Asset Hedges – Volatility Products (e.g., VIX-based) – Credit Default Swaps (CDS) • Active Management – Dedicated Tail Risk Hedging Funds Office of the Treasurer of The Regents University of California

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Balanced Risk Portfolio Strategies (“Risk-Parity”) • Risk Parity is a portfolio construction method that provides superior diversification potential • Most institutional portfolios are heavily weighted to equity risk (even if “diversified”) • A “risk balanced” portfolio buys assets so the contribution to risk from different risk sources is roughly equal – Scaled to the same overall volatility as the conventional portfolio • Result: better diversification, but with leverage • This is approach used by Treasurer on a limited basis for portfolio protection during past 2 years Office of the Treasurer of The Regents University of California

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Implementation Choices • First: what is the goal? – Avoid loss greater than X or reduce impact of specific event(s)? – Level of protection, cost / budget, horizon? • Second: strategic or tactical? – Strategic • E.g., always buy puts, zero cost collars, etc. • Not necessarily static, but less discretion – Tactical • Use discretion (signals) to decide when, what, and how much insurance to buy Office of the Treasurer of The Regents University of California

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Implementation Challenges • Investors are used to being paid to take risk • Investors need to pay to avoid risk – Directly (by buying insurance) – Indirectly (by reducing risk assets) • Fiduciaries – Willingness to occasionally underperform peers • For Investment Staff / Investment Managers – Hard to buy protection only when needed – Hard to buy the right protection for uncertain outcomes

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Recommendation • Establish pilot “Tail Hedging” program for TRIP • Recommend use of dedicated “tail risk” manager(s) to purchase an optimal portfolio of tail hedges • Recommend revising fund Policy/Guidelines to permit investing in tail risk hedging strategies on an opportunistic basis – Range of 0-2% (capital used to buy hedges) – No change to policy benchmark • Tail risk hedging program becomes part of the asset allocation decision

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APPENDIX • • • •

What is hedging? Options and Insurance Risk disclosure Direct Approaches – Put Options – Zero Cost Collars – Put Spread Collars • Indirect Approaches – Gold, Treasuries, Cash – Risk balanced diversification (risk-parity) – Exotic Beta – Cross Asset Hedges (VIX, CDS) – Active Management Office of the Treasurer of The Regents University of California

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What is Hedging? • Hedging = taking an opposite or offsetting position to temporarily neutralize the fluctuation in value of a risky portfolio – Futures • A short futures position + the underlying index = no gains (losses) if the index rises (falls) • Minimal trading cost only

– Options • An option’s payout is contingent on the market index exceeding a given level by a given time • Premium (cost to purchase contract) can be material

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Hedging Tail Risk December 13, 2011 | 20

Options and Insurance • Buying put options on an equity portfolio is like buying fire insurance on a primary home • Option premium is like insurance premium – If the fire doesn’t occur, the premium is “lost” – On average, buying insurance is a bad “investment” – Yet for most people, the certain loss of a small premium is worth avoiding the catastrophic loss of a home – Do you feel the same way about your investments?

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Options and Insurance - 2 • The level of loss protection of an equity option is like the deductible in an insurance contract • Differences – Fires are random events, distributed over space – Equity market losses, like hurricanes, happen at the same time to everyone

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Hedging Tail Risk December 13, 2011 | 22

Risk Disclosure • Static Strategic Policy Allocation – Simple to manage and understand – Ignores changing environment; no longer “best practice” • Dynamic Strategic Policy Allocation – May include Tail Risk Hedging component – More complex to manage and evaluate • Counterparty risk for OTC instruments • Timing / Manager risk (investment decisions) • Regret risk

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Put Options • Cost of insurance (buying puts) is a significant drag on performance – 7% OTM: average cost 2.4% of portfolio value • 15% OTM: average cost 1.5% of portfolio value • Insurance costs more after market has fallen •

Source: Bridgewater Asset Management

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Hedging Tail Risk December 13, 2011 | 24

Zero Cost Collars: Limit Downside + Cap Upside • Example shows naïve use of zero cost collars on a 60/40 portfolio • Two different floors: 5% loss and 10% loss, quarterly • Strategy underperforms unhedged portfolio •

Source: State Street Associates

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Application of Market Timing • Use of a risk aversion index can be profitable in determining when to use protection strategies • This filter is based on a “Systemic Risk Index” which indicates increased likelihood of potential losses when market indexes begin to move together •

Source: State Street Associates

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Zero Cost Collars with Timing • Selective use of insurance strategies outperforms an unhedged portfolio •

Source: State Street Associates

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Hedging Tail Risk December 13, 2011 | 27

Put Spread Collars • A Put Spread Collar (PSC) is an option strategy in which one purchases an out of the money and sells a call (like a zero-cost collar) but then also sells another put further out of the money • Like a collar, it limits upside and protects on the downside. Unlike a collar, the downside protection is limited to the range between the two put strikes • The investor collects a volatility premium and “self-insures” beyond the second put strike

•

Source: State Street Associates Office of the Treasurer of The Regents University of California

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Put Spread Collars • A Put Spread Collar (PSC) is a Zero Cost Collar plus the sale of an out of the money put. This strategy provides premium income (from the short put) and effectively “self-insures” below its strike • It thus loses less than a collar in rising markets, while protecting against moderate losses • When applied selectively, the results are even better

•

Source: State Street Associates Office of the Treasurer of The Regents University of California

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Dynamic Hedging (Portfolio Insurance) • Another approach to portfolio protection is Dynamic Hedging, also called Constant Proportion Portfolio Insurance (CPPI) • This is successful at avoiding losses but at the cost of losing most of the upside •

Source: State Street Associates

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Hedging Tail Risk December 13, 2011 | 30

Dynamic Hedging, with Timing • Selective use of insurance strategies outperforms an unhedged portfolio •

Source: State Street Associates

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Hedging Tail Risk December 13, 2011 | 31

Gold: Not a Consistent Hedge • Gold has provided a hedge against equities during select periods – 7/1972 thru 8/1974 – 3/2000 thru 12/2002 – 7/2007 thru 2/2009

• But Gold had a negative return from 6/1980 thru 3/2000 (20 years!) • For monthly equity losses of - 10% or more, the value of holding gold is questionable •

Source: Bloomberg

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Hedging Tail Risk December 13, 2011 | 32

Treasuries: Benefit from “Flight to Quality” • When the S&P 500 had a negative return, its mean monthly return was -3.44% versus 0.36% for a 10 year US Treasury Bond • The correlation of negative equity periods with Treasuries was -0.10 • Most importantly, Treasuries never had significant losses during large equity drawdowns • Hence sovereign debt has historically been the “hedge” component of institutional portfolios

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Cash: the Ultimate Tail Hedge • Cash always has a positive return, and almost always a positive real return (but not now) • It has value as a tail hedge only given superior market timing ability • Except for the inflationary 1970’s and early 80’s, it has failed to keep up with equities, so it can only be used tactically •

Source: Bloomberg, Morningstar

Negative real cash return

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Balanced Risk portfolio strategies - example •

Cumulative Return 250% 200%

•

150% 100%

50% 0%

University of California

5/1/2010

7/1/2008

9/1/2006

1/1/2003

11/1/2004

3/1/2001

5/1/1999

Conventional Portfolio

5/1/2010

7/1/2008

9/1/2006

11/1/2004

1/1/2003

3/1/2001

5/1/1999

7/1/1997

9/1/1995

11/1/1993

1/1/1992

3/1/1990

5/1/1988

9/1/1984

11/1/1982

1/1/1981

3/1/1979

5/1/1977

7/1/1986

9/1/1995

7/1/1997

0% -5% -10% -15% -20% -25% -30% -35% -40% -45% -50%

7/1/1975

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Drawdown

9/1/1973

•

Drawdowns were substantially reduced during 1973-74 and 20002002, and somewhat mitigated during 2008-09 The strategy suffered during the interest rate spikes of 1980 and 1981-82

11/1/1971

•

•

Risk Balanced Portfolio

1/1/1970

Conventional Portfolio

11/1/1993

1/1/1992

3/1/1990

5/1/1988

7/1/1986

9/1/1984

11/1/1982

1/1/1981

3/1/1979

5/1/1977

7/1/1975

9/1/1973

11/1/1971

1/1/1970

-50%

Annualized return is 2.4% higher in the risk balanced portfolio The Return to Risk ratio (Sharpe ratio) of the risk balanced portfolio is 0.64 versus 0.37 for the conventional portfolio Leverage of about 2:1 is used in this example

Hedging Tail Risk

Risk Balanced Portfolio December 13, 2011 | 35

“Exotic” Beta = Risk Factors other than Equity • There are many risk factors uncorrelated with equity • A portfolio of these strategies can be an efficient return source, while lowering overall volatility • Not a direct hedge, but a more efficient use of risk • Examples: Value, Momentum, Carry, Volatility, Liquidity •

Source: Kepos Capital

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Hedging Tail Risk December 13, 2011 | 36

Cross-Asset Hedges • • •

•

Some assets are strongly related to equity on the downside, and thus can be effective as indirect - and potentially inexpensive - hedges The two most widely used are VIX derivatives and corporate Credit Default Swaps (CDS) As shown below, when protection is most needed, these markets move opposite to equity

Source: Bloomberg

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Hedging Tail Risk December 13, 2011 | 37

Active Tail Risk Management • Passive use of equity puts has been a poor long run strategy • Even naïve active strategies would have produced superior results • Both strategies shown below spend 1% of fund value per year to buy tail hedges • Rather than just buy and roll” puts, the active strategy monetizes (i.e., exercises) the puts when they increase in value, generating liquidity during equity drawdowns Source: PIMCO

S&P Index + Tail Hedging Potential Payoffs Since Jan 1950 1

1000

Active 5x Strategy (Model)

2

No Tail Hedge3

C umulative Returns (Unit Values)

•

Passive Expire/Roll Strategy (Model)

100

82.79 64.32 54.18

10

1 1950

1955

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4

1960

1966

1971

1977

1982

1987

1993

1998

2004

2009

Hedging Tail Risk December 13, 2011 | 38