Making a case for increasing annuities for inflation-protection




The one thing that is truly disastrous for a retiree’s portfolio is persistent inflation. And today’s inflation is definitely not transient. As of this writing (Oct 9th, 2022), fed funds are at 3.25%, US Treasury 2-year yield is at 4.30%, inflation at 8.3%, and unemployment rate at 3.5%. The last time we saw such a surge in inflation in the US, it persisted for 2 decades (1968-1990 approx.), and it took almost 4 business cycles for the inflation to be wrung out of the US economic system completely. The young workforce may revel in today’s globally synchronized surge in inflation, for they are getting a boost in their salaries, but retirees are living their nightmares. Retirees want inflation protection in their retirement years, in addition to protection from longevity risk. 


In this experiment, we consider a new product design composed of a whole life level annuity and an increasing annuity. The purpose of the increasing annuity is to mimic the effect of inflation

The simplicity of the increasing annuity design is quite evident. The annual benefit amount of the increasing annuity is k, 2k, 3k, 4k,… for year 1, 2, 3, 4,… and so on. On the other hand, the additional cash necessary to keep up with inflation would be [exp(f*t) - 1] where f is the inflation rate. For the whole life annuity, the annual benefit amount stays constant.
Using an inflation rate and a discount rate, we determine the level of k that will minimize the present value of the difference between the Inflation Coupon amount [exp(f*t) - 1] and the Increasing Annuity Benefit (k, 2k, 3k,...). For example, in the table below, the annual benefit of level annuity is $10,000, inflation rate is 5%, discount rate is 4% and the inflation protection runs for 25 years.

Table 1: Using the variables above (Inflation = 5%, Discount Rate = 4%, level benefit = $10,000), we determine k to be ~$770. The same is shown in Figure 1 below. Continuous compounding is used for this calculation (only).

  • Inflation (Coupon) is the additional cash (interest) that an annuitant would need to keep up with inflation. Simply, it is $10,000 *[exp(0.05*t) - 1]
  • Net.PV = (Inflation Coupon - Increasing Annuity Benefit)*vt
  • vt = exp(-0.04*t)
  • k is the initial benefit amount (of increasing annuity) determined by setting sum(Net.PV) =0.

Figure 1: Blue line shows Increasing Annuity benefit (k, 2k, 3k,…) over time. k = $769.5. Orange line shows the Inflation Coupon amount given inflation = 5%. Net.PV is a small fraction of the annual benefit amount. Sum of Net.PV = 0.

Figure 2: We run the same optimization (search for k) for different combinations of Inflation and Discount Rates. Blue line shows Increasing Annuity benefit (k, 2k, 3k,…). k is shown in each chart title. Orange line shows the Inflation Coupon amount given different inflation rates. Inflation rate is >= Discount rate, to reflect accommodative monetary policy stance. Sum of Net.PV = 0 for each chart.

Table 2: For different combinations of Inflation and Discount Rates, we determine the level of k that would be necessary to keep up with inflation. k runs over 25 periods. Continuous compounding is used.

Table 3: Finally, we compare the upfront premium (reserve) for an immediate annuity starting at age 60 or 70, and the annual pension amount set at $10,000 paid in arrears.


The premium (reserve) amount required for the Inflation Protected (IP) annuity is 1.7x - 1.8x times the premium required for a whole life immediate annuity. Another issue is that the benefit amount increases with time, leading to a higher mortality credit, and making the product less appealing for those who prefer bequest over insuring longevity+inflation risk. On the other hand, the IP annuity’s starting benefit is higher ($10,770 vs $10,000 for the rest). We believe that the simplicity of this product and the built-in inflation hedge will be appealing to annuitants and agents alike. For insurers, having this payout will add to the product assortment and will likely draw in customers.

Higher rates and better days ahead for the annuity market

Higher rates are unarguably the best thing to happen to the annuity market. Many of us don’t realize that the much larger size of the annuity market in the US, compared to UK or Europe, is very much a consequence of the high nominal interest rates American savers enjoyed from 1969 to 1990. Nothing attracts savers more than high nominal rates. Remember, FED’s Operation Twist program in 2011–2012 was specifically aimed at curbing the attractiveness of higher long term nominal interest rates.

Even though rates have increased significantly in the last quarter, and although the short end of the yield curve continues to imply rate cuts in 2023 (more on that later), we think there is room for higher rates in the coming quarters. To help annuity providers prepare for higher rates, we have prepared a brief cheat-sheet. Essentially, we have attempted to determine the impact of higher option budgets on various popular product designs (payoffs) for fixed indexed annuities using S&P 500 Index as the model case.

Primary Assumptions:
We have anchored our option budgets to the cost of the hedge for S&P 500 Point-to-Point 1 year Cap Rate of 7.50% with an approximately 5 year long surrender charge. We determined that the option cost for such a payoff is 4.14%. While keeping the option budget fixed at 4.14%, we determine the base case caps and participation rates for other payoffs. Then we model the impact of increasing option budgets by 10 bps, 25 bps, 50 bps and 75 bps.

Option Budget at a glance

Next, we present a more detailed analysis of higher option budgets on cap and participation rates. While higher interest rates (higher budget) push cap and par rates higher, they also make the overall option more expensive (due to higher cost of capital), all things equal. Hence we have modeled the impact of higher interest rates and higher caps separately, and then together.

Expected Option Costs for Point to Point Cap Rate payoff

Expected Option Costs for Monthly Averaging Cap Rate payoff.

Expected Option Costs for Performance Trigger Payoff


  • All interest rates reset annually on policy anniversary date. Negative index return results in a zero interest credit.
  • Based on market data of S&P 500 Index as of the close of Friday, August 19, 2022.

Below is a quick summary of different payoffs.

  • PTP CAP: Interest is credited annually based on the annual point-to-point return of an index such as the S&P 500 Index, up to a maximum rate called the cap rate.
  • Participation Rate: Interest is credited annually based on the annual point-to-point return of an index such as the S&P 500 Index, times a participation rate.
  • Performance Trigger: A declared interest rate is credited if the index return is positive or flat.
  • Monthly Averaging: Index return is calculated using a monthly arithmetic average of an index since inception. Index return is capped at a cap rate and floored at zero.

Asset returns are the primary driver of insurers' income from Fixed Annuity and Fixed Indexed Annuity businesses.

Table 1: Comparison of Base Case (Current Regime) with a Low Interest Rate macro environment. 

Table 2: Two adverse scenarios (AS) are shown. AS#1: Low Equity Returns. AS#2: Low Asset and Equity Returns.


  • Our base case scenario is that of high nominal rate (5 YR Corporate AA yield 4%), average asset income (5.75%) and single digit equity returns (7-9%).
  • Our analysis suggests excellent Fixed Annuity and Fixed Indexed Annuity returns for both policyholders and insurers in the base case scenario.
  • We also present two adverse scenarios. 
  • Adverse Scenario #1: Average Asset Returns (5.74%) and Low Equity Returns (4%), FA ROE is 9.78% and FIA ROE is 7.4%.
  • Adverse Scenario #2: Low Asset Returns (4.5%) and Low Equity Returns (4.5%) 

Our analysis clearly shows that asset income is the primary determinant of insurers ROE for both FA and FIA. The current regime of high rates and average asset and equity returns present excellent conditions for both policyholder and insurers. While low equity returns reduce policyholders' payoffs, they do not affect insurers' income as long as spread income is sufficient. Finally, spread income lower than 75 bps spells doom for FA and FIA insurers alike, while policyholders continue to earn average payoffs.

Assumptions and Analysis

  • In this analysis, we compare the expected policyholder payoffs and business returns for Fixed Annuity (FA) and Fixed Indexed Annuity (FIA) providers. We ignore the impact of taxes (Bermuda, ahem). The first year’s premiums are called a New Money (NM), and subsequent renewals are called as R1, R2, R3… and so on, somewhat like vintage years (borrowed from PE).
  • We also model policy lapses in the later years, which reduce the asset balance of the insurer. The lapse rates we have used are 0%, 2%, 3%, 3%, 4%, 5%, 5%, 20%, 12%, 8% for years 1 to 10, respectively. The surrender charge goes away after 7th year, which leads to a much higher lapse rate (20%) in the 8th year.
  • Option Budget is determined using the current 5-year US corporate A rated yield. We set fixed annuity rates equal to option budget, determined using 5 year US Corporate yield. Option budgets further determine FIA caps. So, a 2.25% option budget sets the cap at 4.5%, while a 4% option budget sets the cap at 7%. These caps are based on European Vanilla (point-to-point) options on S&P 500 Index.
  • We set book leverage to 10x. A 10x leverage means the ratio of 'Assets' to 'Shareholder Equity' is 10. Acquisition cost is 60 bps per year, and expenses are 25 bps per year.
  • Another key assumption that applies to Asset Income, Option Budgets and Option Payoffs is that all these rates are flat and fixed at a constant level (unchanging).
  • Finally, for further simplicity, we assume that credit income determines asset income; and the performance of S&P 500 determines equity returns.

Base Case Scenario: The Current Macro Environment of High Rates and Average Asset and Equity Returns bodes well for annuity providers and policyholders alike. 
Now that we are decidedly in a regime of higher interest rates, let’s call it the "Base Case" macro environment. Equity returns of 7%-9% are low relative to the recent history, but sufficient to max out the FIA caps. Likewise, we (conservatively) expect moderate credit income and asset returns at 5.75%. Thus, this macro environment creates ideal conditions for both policyholders' (maxed out caps) and insurers' returns from FA and FIA products.

Base Case: Policyholders's payoffs and Insurers' returns in the current environment of High Interest Rates and Moderate Asset Returns

Base Case: (Table) High Interest Rates and Moderate Asset Returns

Low Rate Environment: Low Interest Rates and moderate asset and equity returns

Chart: Low rate macro environment

Low rate macro environment: For better comparative analysis, we show how the previous conditions of low rates and high equity returns impacted policyhoders' and insurers' returns. High equity returns boosted general account balances for FIAs, but not enough to make up for the low asset incomes.

Adverse Case Scenario: Asset Income (not equity returns) is the primary determinant for insurers' income from FA and FIA products.
We study two different scenarios. 
Adverse Scenario #1: Low Equity Returns.
The only difference between the Base Case scenario and the Low Equity Return scenario is that of Option Payoff (reduced from 7% to 4%). Based on last 20 years' of historical data, annualized equity returns of 5% or less represent cumulative frequency of less than 25%. Meaning there is a 75% chance that equity returns will be higher than 5%. So, a 4% equity return is a reasonable approximation of low EQ return scenario. The main effect is on policyholders' payoffs. Secondarily, because of lower growth in general account, the insurers' FIA incomes also suffer.

Chart: Adverse Scenario # 1

Table: Adverse Scenario # 1

Adverse Scenario #2: Low Asset Returns and Low Equity Returns
Here, we assume lower asset income (5.75% -> 4.5%) and lower equity returns (7.0% -> 4.5%) compared to our Base Case scenario. Our reason for combining low equity returns with low asset returns in this scenario is that, we think going forward, it will be very unlikely to see a combination of low credit income (low asset returns) and high equity returns. A significant Central Bank easing could achieve such a scenario (low asset income, high equity income), but we would like to exclude that possibility. In a realistic Adverse Case scenario, credit losses will invariably spill off to equity markets, lowering equity returns. Since insurers are quite conservative in their asset book, they will still earn an average of 50 bps over 5 year US Corporate A yield despite significant credit losses stretching over 2-4 years. Here, we see that while policyholders earn average payoffs, the insurers' return are deeply negative. The main reason for this outcome is the low spread earned by insurers (4.5% - 4% = 0.5%), which is not enough to pay for acquisition costs and expenses. This result highlights two key phenomena: 1) FA and FIAs are invariably “spread products” as long as insurers' incomes are concerned. 2) Policyholders will continue to earn decent interest incoem from both FA and FIA in most scenarios.

Chart: Adverse Scenario #2

Table: Adverse Scenario #2

It is quite natural to assume that insurers will lower credited rates and option budgets in an environment of low or negative business returns. Yes, that is quite possible - however, disintermediation risk will limit insurer's ability to move down rates. Also, many FA products have multi-year guarantees. Also, let's not forget that in a scenario of severe cash drain, insurers can just discount their policies to earn a whole lot of new money (new policies) in a short amount of time, and later perhaps pierce bailout rates or staple free GLWB riders to those discounted policies. Who doesn't like this business!

Would you like to run a few scenarios of your own? Go ahead and try our tool: Annuity Business Return Calculator