Hedging Portfolio Risk
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Outline
Defining Tail Risk
Tail Risk Examples
Why Hedge Tail Risk?
Cost of Hedging Tail Risk
Not all Tail Risk Hedges are Priced Equally
Types of Tail Risk Hedging Strategies
Defining Tail Risk
Tail Risk can be defined as 3σ (occurs 0.13% of the time in a normal distribution)
S&P500 annualized volatility 18% so one month 3σ move is 15.6%
Financial asset returns are not normally distributed so large moves occur more frequently
Observed in recent history
Analytically shown by Markwat – estimates global market crashes are 15 times
more likely now vs. 1992
Tail event also defined as event perceived as unlikely by the market Probabilities can be implied from market prices
Example:
Greece CDS trading 50bps in Aug 2008 => Greek default is a tail event
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Tail Risk Examples
65 70 75 80 85 90 95
Mar-10 Apr-10 May-10 Jun-10
May '10 - Oil
WTI Jun-10 Future
5σ based on a 18% Historical Vol 3σ based on a 30% Implied Vol
-22.9% in 16 business days 1.6 2.1 2.6 3.1 3.6
May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11
Summer '11 - US Rates
10-year US Swap…
-89bps in 16 business days
4.6σ based on a 80% Historical Vol 3.4σ based on a 100% Implied Vol
600 700 800 900 1000 1100 1200 1300 1400 1500
Jun-08 Jul-08 Aug-08 Sep-08 Oct-08 Nov-08 Dec-08
Fall '08 - US Equities
S&P 500 Index
-40.1% in 44 business days
3.2σ based on a 30% Historical Vol 3.2σ based on a 30% Implied Vol
Data Source: Bloomberg and Geode Capital Management
Summer ‘07 – Equity Volatility
10 15 20 25 30
Mar-07 Apr-07 May-07 Jun-07 Jul-07 Aug-07
Summer '07 - Equity Volatility
VIX Sep-07…
4.5σ based on a 40% Historical Vol 2.25σ based on a 80% Implied Vol
+40.8% in 13 business days Summer ‘11 – US Rates Fall ‘08 – US Equities May ‘10 - Oil VIX In de x W TI ($ ) S& P I nd ex L ev el Yi el d % U S Tr ea su ry
Why Hedge Tail Risk
Why hedge tail risk if it may add negative expected value in your portfolio?
Reduce drawdowns - important for meeting constant liabilities Smoother return stream increases Sharpe ratio – asset allocation
decision
Survival and investor psychology
Frictional costs of large drawdowns
Investors more likely to make irrational decisions after large drawdowns
• Investors can become too risk averse
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Event Probabilities Implied by Option Prices
We can infer probability of “tail” events from market prices of options
Example – S&P500 put options
SPX down 10% in 1m SPX down 20% in 1m SPX down 30% in 1m Min 0.51% 0.01% 0.00%
Max 30.47% 18.13% 9.72%
Average 6.30% 1.37% 0.37%
as of 3-Aug-12 4.81% 0.61% 0.15%
%-ile as of 3-Aug-12 44.20% 41.50% 46.90%
Data Source: Goldman Sachs
0% 5% 10% 15% 20% 25% 30% 35%
Jan-96 Jan-99 Jan-02 Jan-05 Jan-08 Jan-11
Implied Probability of Tail Risk event
SPX down 10% in 1m SPX down 20% in 1m SPX down 30% in 1m
Implied Probability of Tail Risk Event
Pr
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Factors of Tail Risk Hedging Cost
Pricing of Tail Risk hedges reflected in traded risk premia across asset classes: Implied / Realized volatility premium (expensiveness of options)
Term structure (long dated vs. near dated options)
Skew (expensiveness of Out-of-The-Money puts vs. calls)
Convexity (expensiveness of Out-of-The-Money options vs. At-The-Money options) Corporate Credit Spreads (reflective of probability of default)
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Factors of Tail Risk Hedging Cost
Data Source: Bloomberg and Geode Capital Management
(35) (30) (25) (20) (15) (10) (5) 5 10 15 0 10 20 30 40 50 60 70 80
Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12
VIX Term Structure Premium
VIX Fut 5th Contract (LHS) VIX Fut 1st Contract (LHS) Spread (RHS) VI X cu rve slo pe
VIX Term Structure Premium
VI X Fu tu re s (15) (10) (5) 5 10 15 0 10 20 30 40 50 60 70 80 90
Feb-05 Feb-06 Feb-07 Feb-08 Feb-09 Feb-10 Feb-11 Feb-12
SPX Volatility Premium VIX Index (LHS) SPX 1m Realized Volatility (LHS) Spread (2m Avg) (RHS) Vo la til ity (% ) SPX Volatility Premium Vo lat ilit y Sp re ad (% )
Not All Tail Hedges Are Priced Equally
Supply/Demand imbalances cause many tail risks to be overpriced
SPX crash protection, VIX upside are among assets that generally have a
natural bid from:
Dealers who need to reduce their crash risk
Systematic tail risk hedging funds
Some tail risks in FX and Rates seem cheap
Low absolute levels of volatility and low implied/realized premium Flatter term structures mean lower roll down cost or minimal decay
Active Tail hedging strategies can take advantage of this Buy protection only if the cost is reasonably cheap
Volatility arbitrage funds can sell expensive protection and hedge with cheap
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Different Types of Tail Risk Strategies
Tail risk hedging strategies vary by philosophy, approach, and expertise
Systematic vs. Active
Proponents of systematic strategies (often dealers) advocate that one cannot time
the market
Proponents of active strategies advocate that market conditions should be taken
into account when trading (consider varying leverage, asset selection, structures, tenors, etc.)
Listed vs. OTC
For listed, counterparty risk is with the exchange and structures are limited to
shares, futures and vanilla options
OTC subject to more counterparty risk, but much richer investment universe
New Dodd-Frank regulation will move more derivatives to exchanges
Single asset focused vs. multi-asset class (depth vs. breadth?)
Single asset class allows deep focus, but greatly constrains investment universe Multi-asset class provides much larger flexibility in investment universe
Preferred Tail Risk Hedging Approach
Buy tail protection that is the cheapest available across global markets and across asset classes – assumption that correlations will rise in global crash
Buy protection only if the cost is reasonable (i.e., it’s priced as a true tail risk)
Diversify across:
Asset classes: Equities, FX, Rates, Credit, Commodities Assets within classes
Tenors
Strikes or “moneyness” Structures
Puts, put spreads, volatility swaps, variance swaps, options on variance, VIX
futures/options, forward volatility agreements (FVA), swaptions
Counterparties
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Lessons Learned
Don’t wait too long to monetize hedges
Allow leverage to vary to keep decay rates more stable
Worry about correct marking to market and collateral
Counterparty diversification on OTC trades
Avoid some counterparties on specific trades
e.g., trade that insures against Euro break-up better traded with large US bank than
French bank
Ladder tenors to have capital available when attractive tail hedges become
Examples
Long Bovespa Put Spread to benefit from upward-sloping forward and moderate
implied volatility / skew
Long EURHUF Forward Volatility Agreement (FVA)
100 200 300 400 500 600 700 800 10 15 20 25 EURHUF 6m6m FVA (LHS) Hungary 5y CDS (RHS) Sovereign Credit Still Elevated
FX Implied Vol DOWN
45000 50000 55000 60000 65000 70000 IBOV Index
BVSP Futures Curve at Inception Put Spread Long Strike
Put Spread Short Strike BVSP Forward 6.8% ann. higher than spot
Dec-12 80%/70% BVSP Put Spread bought for 70bps (14.3x) – impact of the forward is a 40% discount BS VP In de x L ev el (BR L) FX vo la til ity (% ) Hung ary C DS ($ )
