Learn how to get extra savings in hedging costs for point-to-point cap payoffs using strike-averaging.
This result applies only to FIAs that have point-to-point “capped” payoffs.
In this analysis, we show that buying one point-to-point hedge (call spread) at the weighted average strike (cap) is far more advantageous than buying multiple hedges at different strikes. Using historical market data for S&P 500 index, we prove that this result holds true in every scenario of liability weights.
Let’s understand by example.
Let us assume that the risk manager is looking to hedge three FIA liabilities, each of $100,000 notional (principal) at caps of 5%, 7% and 9%. The weighted average strike of the single composite hedge will be 7% for $300,000.
If the cost of buying three individual hedges is the same as the cost of buying one composite hedge, the risk manager may presume that it is advantageous to buy three different hedges, since the three hedges will ‘mimic’ the liabilities exactly and will have zero basis risk and full hedge effectiveness. In practice, most risk managers do some averaging of the strike, but still buy many point-to-point cap hedges, rather than just one single hedge. We propose that they will benefit from buying just one hedge per index (and tenor) on their hedging day.
This single PTP hedge will be struck at the weighted average strike and will hedge all the policy allocations linked to a particular index and renewing on a particular date. We have determined that this single hedge will be 3 to 6 bps costlier than the sum of costs of the individual hedges, but will have a far higher realized payoff than the individual hedges. This single hedge will have zero additional basis risk, and will not decrease the hedge effectiveness either.
The reason behind this advantage is that this ‘averaging’ of strikes (caps) brings down the required return of the index. So, considering our sample case mentioned above, if the index returns 7%, buying one composite hedge will have a payoff of $21,000 (7% payoff), while the three individual hedges (struck at 5%, 7% and 9%) will have a payoff of $19,000 ($5000 + $7000 + $7000 ; 6.33% payoff). So, our single composite hedge returns a full 66 bps higher return than the individual hedges. Moreover, this 66 bps advantage is a ‘profit’ for the insurer since the interest credited to the policyholder’s account is still $19,000.
Mathematically, if the index return is higher than the minimum strike and lower than the maximum strike, the average strike hedge performs better than the individual hedges. As it is the case today, insurers have policies issuing and renewing at caps ranging from 4% to 12%, and this strategy is particularly effective.
To help you understand and test this result better, we are providing an Excel file.
There must be some catch!
Yes, there is a catch, which is, that the composite Weighted Average Strike Hedge will be 3-6 basis points more expensive than the sum of costs of Individual Strike Hedges. However, it is quite likely that traders will be able to avail a 3-6 bps discount from a single best counterparty (seller of OTC call spread) in return for awarding them a ‘bulk’ trade. We determined this range (3-6 bps) by analyzing last 10 years of S&P 500 equity volatility data and the following equally weighted strikes: 5%, 6%, 7%, 8%, 9% and 10%. Further, we show, via Table 1, that this (3-6 bps) range holds true in all practical strike ranges.
Final Thoughts
We think this strategy is extremely effective because it boosts savings and simplifies the hedging program at the same time. Policies or policy allocations need to be first grouped together by starting (issue) dates and renewal dates. For most insurers, FIA policies are issued on a weekly or bi-weekly basis, and for them, this strategy works really well. We see that most insurers today are buying call spreads at a wide range of strikes (5% to 10%), and if the index return falls within this range, the benefit from a higher payoff of the composite Weighted Average Strike Hedge will surely exceed the negligibly higher cost.
In Summary
Risk managers at annuity (life insurance) companies hedge the financial risk of derivatives embedded within their fixed-indexed annuity policies using call spreads. Often there are dozens, if not hundreds of policies that need to be hedged on a particular day. So, the risk manager typically chooses to buy a limited number of hedges (call spreads) at a few ‘averaged’ strikes, simply because buying a call spread for each individual strike is practically unfeasible given the limited amount of time available to the trader. In this analysis, we show that the risk manager will benefit from buying just one call spread struck at the weighted average strike of the individual liabilities, provided all the grouped liabilities have the same starting and renewal dates.
Using historical option trade data of the S & P 500 index, we determine that the cost of the single Weighted Average Strike Hedge is only 3-6 bps higher, on average, than the cost of Individual Strike Hedge. However, the payoff of the single Weighted Average Strike Hedge is always higher than the total payoffs of Individual Strike Hedge whenever the index return is between the minimum and the maximum strikes.
Individual Strike Hedge = A set of Call Spreads struck at the cap rates of respective annuity policies
Weighted Average Strike Hedge = One Call Spread struck at the weighted average cap rate of a group of liabilities.
Weighted Average Strike = sum(Si * Ni) / sum(Ni)
Where Si = Strike (cap) of individual policy and Ni = Notional of individual policy