Portfolio Hedging Strategies Alessandro Esposito
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CBOE
Optimising Portfolio Hedging Strategies
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• The case for Consistent Hedging
•Optimizing Hedging Strategies
• Sizing initial trades and managing positions over time
•Cross Asset Hedging
•Conclusions
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The Case for Consistent Hedging Hedging adds convexity to your portfolio
Mitigating the effect of adverse market moves justifies hedging across strategies
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Feb-08 Jun-08 Oct-08 Feb-09 Jun-09 Oct-09 Feb-10 Jun-10 Oct-10 Feb-11 Jun-11 Oct-11 Feb-12 Jun-12 Oct-12 Feb-13 Jun-13
SPXT SPXT + SPX 3M 95% Put
The Case for Consistent Hedging Buying puts simply won’t do the trick
Buying puts simply won’t do the trick Consistent hedging requires a more structured approach
SPX total return chart vs. 3m put hedged portfolio rolled monthly
Source: Bloomberg, Bank of America Merrill Lynch
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The Case for Consistent Hedging Hedging issues are multi-dimensional
• The Term the period over which one wishes to be protected
• The Strike the level from which one wishes to be protected
• Ranges the structure with which one wishes to be protected
• The Premium the optimal size of the hedge(s) versus the size of the portfolio
• The Frequency how often do you re-strike?
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• The case for Consistent Hedging
•Optimizing Hedging Strategies
• Sizing initial trades and managing positions over time
•Cross Asset Hedging
•Conclusions
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Optimising Hedging Strategies The avoidance of market timing risk
Straight Puts
Put Spreads
Calendars Collars
COMPLEXITY
PREDICTABILITY
The complexity of the payout increases the predictability of the hedged strategy
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Optimising Portfolio Hedging Strategies
In order to optimise portfolio hedging strategies, we need to be able to compare them : By evaluating the VaR of the hedged portfolio we are able to size different strategies by evaluating their impact on the risk of the portfolio
Q : How do you compare different strategies ? A : Look at their volatility
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I. COMPUTE VAR OF HEDGES
II. COMPUTE VAR OF
PORTFOLIO & HEDGES
III. SIZE THE TRADE BY REDUCING
HEDGED PORTFOLIO VAR
IV. SANITY CHECK !!
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Optimising Portfolio Hedging Strategies Sizing initial trades requires a four step process
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• The case for Consistent Hedging
•Optimizing Hedging Strategies
• Sizing initial trades and managing positions over time
•Cross Asset Hedging
•Conclusions
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Sizing Initial Trades and Managing Positions Over Time
Using the S&P 500 as our proxy portfolio we target a 10% risk reduction via a 3m 95%/85% put spread
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29-Feb-08 28-Feb-09 28-Feb-10 28-Feb-11 29-Feb-12 28-Feb-13
3m 95p-85p
Index
Hedged Strategy
SPX return chart vs. 3m put spread hedged portfolio rolled daily
Source: Bloomberg, Bank of America Merrill Lynch, Bluebay
• Sizing the put spread to 118% of its notional VaR goes from 0.42 to 0.38. • The Sharpe ratio improves from 0.13 to 0.15 • The high correlation between the portfolio and the hedged strategy indicates the ability to include • hedging as part of portfolio management
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SPX 1m95p 3m95p 12m90p 1m95-85ps 3m 95-85ps 1m95p-12m90p
Sharpe Ratio 0.134 0.16 0.16 0.15 0.15 0.15
Multiplier 0.55 0.40 0.33 1.14 1.18 VaR can't
be improved
• Hedge ratios diminish with longer time horizons for single put trades • Long Calendar put spreads additive to risk
Sizing Initial Trades and Managing Positions Over Time VaR Equivalent Hedging Strategies
Source: Bloomberg, Bank of America Merrill Lynch, Bluebay
Sharpe Ratio and Notional Hedge Ratio of SPX portfolio hedged with different strategies
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1m95p 3m95p 12m90p 1m95-85ps 3m 95-85ps
Hedge Ratio Monthly Rolls
0.20 0.20 0.15 0.40 0.50
Hedge Ratio Daily Rolls 0.55 0.40 0.33 1.14 1.18
Sizing Initial Trades and Managing Positions Over Time
• Lower frequency dramatically reduces the hedge ratios • For shorter maturities, option strategies can be additive to VaR
Readily available data demonstrate the impracticality of rolling hedges daily We compare daily vs. monthly rolls
Impact of Re-Hedging over time
Notional Hedge Ratio of SPX portfolio hedged with different strategies, Daily vs. Monthly Roll
Source: Bloomberg, Bank of America Merrill Lynch, Bluebay
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Sizing Initial Trades and Managing Positions Over Time Re-hedging frequency and the impact on returns
• Lower frequency dramatically differentiates returns among strategies
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29-Feb-08 31-Aug-08 28-Feb-09 31-Aug-09 28-Feb-10 31-Aug-10 28-Feb-11 31-Aug-11 29-Feb-12 31-Aug-12 28-Feb-13
SPXT SPXT + SPX 1M 95% Put SPXT + SPX 1M 95%-85% Put Spread
SPXT + SPX 3M 95% Put SPXT + SPX 3M 95%-85% Put Spread SPXT + 12M 90% Put
SPXT + SPX 1M 95% Put - 12M 90% Put
Percentage Cumulative Returns of SPX hedged porfolios for a VaR reduction of 10%, using monthly rolls
Source: Bloomberg, Bank of America Merrill Lynch
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Can hedging become an integral part of your investment process ?
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Jan-00Jul-00Jan-01Jul-01Jan-02Jul-02Jan-03Jul-03Jan-04Jul-04Jan-05Jul-05Jan-06Jul-06Jan-07Jul-07Jan-08Jul-08Jan-09Jul-09Jan-10Jul-10Jan-11Jul-11Jan-12Jul-12Jan-13Jul-13
S&P500 TR
S&P500 TR + 3M 95% Zero Cost Collar
S&P500 TR + 3M 85%-95% Zero Cost Put Spread Collar
Source: Bloomberg, Bank of America Merrill Lynch
Return Risk Sharpe
SPX 1.18% 16.05% -0.07
95% Zero Cost Collar 2.78% 10.71% 0.05
85% - 95% Put Spread Collar 4.38% 12.48% 0.17
Zero Cost Collars can be used to improve Sharpe ratios and returns Hedging becomes part of the investment process
Sizing Initial Trades and Managing Positions Over Time
Percentage Cumulative Returns of SPX hedged portfolio using zero cost risk reversals
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• The case for Consistent Hedging
•Optimizing Hedging Strategies
• Sizing initial trades and managing positions over time
•Cross Asset Hedging
•Conclusions
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Cross Asset Hedging
For cross asset hedging regression analysis is used to compare the variables
VIX vs SPX returns over the past year give a Beta of 7.7
This is not a stable relationship over time Rolling correlations need to be monitored
Vix Linear regression regression on SPX returns
Source: Bloomberg
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Cross Asset Hedging
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Index
Hedged Strategy
• Cross asset hedging can be used in a systematic manner to improve the Sharpe ratio • Changes in correlation across variables make comparisons across hedging strategies more • complex
Using a 2m 100/150% call spread on the VIX we obtain a hedge ratio of 51% using a Beta of 7.7 The Sharpe ratio moves from 0.65 to 0.78
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60d Corr
30d Corr
Source: Bloomberg, Bank of America Merrill Lynch, Bleubay
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• The case for Consistent Hedging
•Optimizing Hedging Strategies
• Sizing initial trades and managing positions over time
•Cross Asset Hedging
•Conclusions
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CONCLUSIONS
• Hedging can become an integral part of the investment process
• VaR methodologies can be used to compare hedges, including cross asset hedges
• Frequency of re-hedging is a key factor sizing and comparing trades
• Systematic hedging requires more complex payoff
• Correlation changes affect cross asset hedges
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Disclaimer
V2 – Data end June 2013. Published 16 July 2013
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