A Comparison of Index-Linked Annuities

Abstract

In recent years, index-linked annuities (ILAs) have gained considerable popularity in the U.S. retirement savings market, reflected by rapidly increasing sales and new product developments. These products offer investors some equity exposure while also providing financial protection against downside risk. The products differ primarily based on how much the investor could potentially lose (and gain) year over year. A second (and related) differential is that some products are considered “fixed annuities” (due to their principal protection) and, as such, they face fewer regulations, among other benefits, compared to “variable annuities.” We describe the most common types of ILAs, discuss their differences, and compare them from the perspective of a typical investor by numerically solving dynamic optimization problems. When calibrating the model to current market conditions, we find that the newly introduced fixed index-linked annuity is the preferred product for investors with moderate to high levels of risk aversion, particularly if carriers can convert the lighter regulatory framework into moderately higher cap rates. On the other hand, investors who are only mildly risk averse or even risk-loving would generally prefer a traditional mutual fund investment or a registered index-linked annuity with a buffer feature. Our insights should prove useful for actuaries working on product development as well as for insurance agents and retirement planners.

ACKNOWLEDGMENTS

The authors thank Co-Editor Mike Sherris and two anonymous reviewers for their helpful comments.

Notes

1 Notably, nearly all of these sales (98% in 2019) were from “new” premiums, as opposed to 1035 exchanges. Source: LIMRA (2020).

2 As Moenig (2022) points out and as we discuss below, the products are likely still profitable for carriers, even under small or negative costs. This is because the insurer earns a credit spread from investing the funds, with fixed annuities providing a higher level of discretion in this regard.

3 The sole exception to this is for RILAs with significant downside risk exposure (as discussed further below). Here, a 100% participation rate may not be sufficient for the product to be priced actuarially fair, even without a cap. In this case we remove the cap and choose a participation rate in excess of 100%.

4 At the end of each crediting term, the policyholder can choose a different downside specification and market index, among the firm’s available offerings.

5 Formally, the utility specification (3)(3) $$u(A_T)=u_c(A_T)+v\left(u_C(A_T)-u_C(P)\right),$$(3) requires that $v(0)=0$ and that v(x) is continuous everywhere, strictly increasing, and twice differentiable for all $x\ne 0$. Loss aversion is captured by the requirement that for $y>x\ge 0$ we must have $v(y)+v(-y)<v(x)+v(-x)$. See Kőszegi and Rabin (2007) and Macé and Peter (2021) for further discussions.

6 Probability weighting refers to individuals who either ignore or greatly overvalue the likelihood of extreme outcomes, a phenomenon observed and modeled (first) by Tversky and Kahneman (1992) but that has found a lot of support in both lab and field experiments (see, e.g., Bernedo Del Carpio, Alpizar, and Ferraro [2022], and references therein).

7 Moenig (2022) estimates—using empirical contract offerings—that for RILAs $\overline{c}$ is only around 0.2%. We find similar figures below. The author further explains that insurers are able to offer the product at such a low cost because they benefit from the ability to invest the funds in corporate bonds and earn a spread, as discussed above (while protecting their RILA account liabilities with options). For comparison, for an MF or a variable annuity contract, this cost would be the product’s annual fee rate, which can be much higher.

8 The GHQ nodes and weights can be easily and efficiently obtained in many common programming languages. Note, however, that the original GHQ nodes have to be multiplied by $\sqrt{2}$ and the weights have to be divided by $\sqrt{\pi }$ to be representative of a standard Normal distribution. For a more detailed discussion of the methodology—including its application to multiple Normal random variables—we refer the interested reader to Moenig (2021).

9 For instance, consider a FILA contract with offerings described by set ${\mathbb{S}}_1$ and a single premium of 100. If at the beginning of a crediting term the account value is 104, the investor can only choose either F = 0 or $F=-2.5\%$ as potential floor levels for the upcoming crediting term, because a floor of –5% could potentially lead to an end-of-term account value of $104·(1-0.05)=98.8$, which is less than the initial investment.

10 In July 2021, the Alternative Reference Rates Committee recommended the use of the CME Group’s forward looking secured overnight financing rate term rates as a replacement for the London Inter-Bank Offered Rate (LIBOR).

11 We want to point out that this pricing approach works well for ILAs with one-year crediting terms, because the insurer can fully hedge the embedded equity risk by trading options. However, such options are not generally sold in the markets for guarantees with longer crediting terms, such as variable annuity products, and other pricing approaches are necessary (see, e.g., Feng 2018; Barigou, Chen, and Dhaene 2019).

12 Because the equity portion of an MF investment is based on the total return of the fund, we use δ = 0 for contract [6].

13 According to Statista (2022), the average market risk premium in the United States has varied from 5.3% to 5.7% between 2011 and 2021. Moreover, between 1954 and 2021, the S&P 500 price index exceeded the one-year constant maturity treasury rate by an average of 4.7% to 6.1% p.a., depending on whether one accounts for the relatively larger average dividend rates during this time frame compared to our model assumptions. We therefore consider 5.5% as a reasonable long-term average for the equity risk premium on our index.

14 Results for longer crediting terms ($\tau =3\mathit{\text{or}}6$ years) are more ambiguous. To our knowledge, FIAs with crediting terms longer than one year are not currently offered in the marketplace.

15 Under myopic loss aversion, the investor not only considers the terminal payout from the investment but her utility is reduced when she experiences a short-term loss. That is, the investor would strictly prefer a path of the account value that never falls below the initial investment $P$ over a path that falls below $P$ at some point but recovers and ends up at the same terminal value $A_T$. Under the model specifications in the present study, the investor would be indifferent between the two paths because only the value of $A_T$ matters to her preferences, not any account values $A_{t}f\mathit{\text{ort}}<T$.

16 In Section 3.1 we provide a way to elicit the investor’s approximate risk aversion level by answering a single question.