2004 Finance

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2004 Finance Investment Conference

• 27-29 June, Royal Windsor Hotel, Brussels

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Dynamic asset allocation to hedge cash
guarantees using revised option based portfolio
insuranceRachid Bouchaib
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Agenda

• Background
• Guaranteed Equity Bonds
• Adjusted option based portfolio insurance (OBPI)
• Decomposing Call option into equity and ZC
• Dynamic asset allocation to reduce volatility
• Extension to with-profits business
• Case study
• Conclusion

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Background

• Guarantees offered in life funds
• Guarantee charges relatively low
• Cost depends on the investment strategy
• Investment theory weak on A-L methodology
• Dynamic asset allocation could be derived from
  the profile of the gtees option pricing theory

A-L means asset allocation
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Guaranteed Equity Bonds

• Benefit linked to equity index performance
• Provide various levels of capital protection
• Tranche-based products
• Matching asset provided by investment banks
• Cost of the gtee implicit in the equity linkage
• Virtually zero risk for life office
• Life office plays an intermediary and admin role

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Matching assets

• ZC bond to meet the capital protection
• Call option provides equity exposure
• Investment - charges ZC Proportion Call
• Call proportion represents the level of
  participation in the equity index growth
• Participation in equity growth depends on gtee,
  equity volatility, swap rates, dividend, term...

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Participation in FTSE-100 growth
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Option based portfolio insurance

• OBPI provides protected equity exposure using
  options
• OBPI represents two possible strategies
• Hold equities and buy a Put option
• Hold ZC bond and buy a Call option
• OBPI tells how much money needed
• Not suitable strategy for life funds

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Adjusted OBPI for life funds

• Assets backing GEBs is an adjusted OBPI
• Equivalent strategy based on Put option
• Cost of the guarantee is implicit

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Life funds are not GEBs

• Life funds are open-ended
• No perfect matching assets
• Active management of the underlying assets
• Dividend income
• Guarantee charge applies
• Solution Replacing Call option by its
  replicating portfolio

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Participation in the FTSE-100 growth (including
income)
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Decomposing Call into equities and ZC bond

• Delta hedging is the tool
• Delta is the sensitivity of the option price
  relative to the underlying asset price
• Holding delta position in the underlying asset is
  equivalent to holding an option
• BS Call option formula gives the replicating
  portfolio

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Example of a Call replication
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Dynamic asset allocation

• Combined the adjusted OBPI Call replication
• Aggregates the ZC bonds with same maturity
• EBR
• EBR formula is similar to BS Call option price

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Calculated EBRs
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Sensitivity of the dynamic EBRs
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Two ways to recalculate the EBR
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Past performance 10-year guarantee
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Theoretical justification of an A-L

• Any A-L could be represented as an OBPI
• zero protection justifies 100 EBR
• High capital protection justifies 0 EBR
• Constant protection level requires dynamic A-L
• Implicit recommendations matching FI assets and
  tranche-based funds
• Compromise between structured products and
  traditional managed funds

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With-profits business Concept

• Single investment strategy for all generations
• Investment vehicle to achieve smoothed equity
  exposure by smoothing the payouts
• Concept was defeated by high equity volatility
• Managing the volatility of the portfolio is vital
• Tranche-based WP funds are more suitable

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Asset allocation for WP funds

• Set the EBR to the affordable level
• A/S could be invested to maximize EBR and
  minimize the cost of the guarantees
• Guarantees to be managed by dynamic EBR
• No-MVR guarantee (including maturity benefits)
• Minimum bonuses guarantees / Glide path
• Mortgage promises
• Guaranteed minimum pension

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Asset allocation for WP funds

• Guaranteed benefits to be covered by ZC bonds
• Intrinsic value of the guarantees
• Future regular bonuses
• Transfer to S/Hs, tax and future charges
• BRV(excluding GAOs) is a good candidate

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Dynamic EBR for WP funds

• FI assets to back the BRV
• Remaining assets are invested in Call option
• Replacing the ZC by the BRV gives
• EBR

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Numerical examples of the EBRs
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Case study modelling

• Single premium contribution
• Outstanding term of the guarantees 10 years
• 15 minimum return guaranteed (net of AMC)
• Fund at 95 of the face value of the guarantees
• AMC is 1 p.a
• No taxation (e.g. Trustee Investment Bond)
• Ignore lapses, mortality and new business

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Case study investment strategies
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Case study Expected cost and VaR
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Distribution of the cost of the guarantees
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Distribution of the cost of the guarantees
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Distribution of the fund performance
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Fund performance Floating Vs Dynamic EBR
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Case study Floating EBR
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Case study Dynamic EBRs
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Conclusion

• Dynamic A-L could be tailored to produce desired
  payout profile
• Clear methodology how EBR is linked to
• Gtee, Term, Equity volatility, FI rates, Tax,
  AMC
• Cost of the guarantee is under control
• Theoretical meaning of any A-L
• Tranche-based life funds are more suitable

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Thank you