**Equity Indexed Annuity Definition **

An Equity Indexed Annuity (EIA), often referred to as a fixed indexed annuity or simple indexed annuity, is a type of unconventional financial asset that is typically considered as an alternative to conventional investment assets such as fixed-rate and variable-rate annuities. Equity Indexed Annuities are especially suitable for conservative investors that typically prefer securities that involve lower risks. These securities are unique in the sense that their interests, yields and returns are partly based on equity indices, such as the Standard & Poor’s 500 Index (S&P 500).

**A Little More on What is an Equity Indexed Annuity**

An Equity Indexed Annuity (EIA) is a popular investment vehicle for funding retirement. It offers a guaranteed minimum investment return along with the opportunity to share in stock-market gains. However, these annuities do not directly invest the money put down by the investor in the stock market. On the contrary, the money accumulated via EIAs is invested partially based on an equities index, and the investor is offered a percentage of the index gains over a stipulated period of time, or a guaranteed minimum return in the event of a stock market decline.

**Calculation of the Index-linked Interest Rate of an EIA**

An Equity Indexed Annuity may use different combinations of indexing features in order to determine the index-linked gain. These indexing features have a significant impact on the return on investment. Below are some common indexing features employed by EIAs.

: Participation rates determine what portion of the increase in the index will be used to calculate index-linked interest for the EIA.*Participation Rates*: Several EIAs use spread, margin or asset fees in lieu of participation rates, while some others use a combination of participation rates and spread, margin or asset fees.*Spread, Margin and Asset Fees*: A cap is an upper limit that certain EIAs apply to the return. Expressed as a percentage, the cap rate is the maximum rate of interest that the annuity will draw.*Interest Rate Caps*

**Indexing Methods of EIAs**

There are six primary indexing methods employed by Equity Indexed Annuities. They are:

This method is the simplest of the six and involves a division of the index on the maturity date by the index on the issue date, followed by the subtraction of ‘1’ from the result. This method essentially records the change in the index from the beginning of the term to the end of the term.*The European Method (Point-to-Point Method):*This method averages several index points in order to derive the beginning index or the ending index, or both. The Asian method safeguards investors from the risk of a market decline on the date of maturity.*The Asian Method:*This method records index levels on each policy anniversary and assigns the highest of these as the index level on the date of maturity.*The High-water Mark Method:*This method records index levels on each policy anniversary before maturity and assigns the lowest of these as the index level on the date of issue.*The Low-water Mark Method:*This method is also known as the*The Ratchet Method:**Annual Reset Method*and is one of the most complicated methods of the lot. It calculates the increase in the index each policy year by comparing the indices on the beginning as well as ending anniversaries. It then calculates appreciation by adding or compounding the increases for each policy year. However, the Ratchet Method completely ignores any resulting decreases.This method calculates the increase in the index for the term or the policy year in consideration and then subtracts a percentage from that change*The Spread Method:***.**

**Advantages of Equity Indexed Annuities**

An EIA typically combines the attributes of both a fixed annuity as well as a variable annuity with a view to incorporate the benefits of both types of annuities. The low-risk attributes of an EIA, coupled with a guaranteed minimum return, calculated on around 90 percent of the premium paid at an annual interest rate of 1% to 3%, have made it a popular type of annuity. Moreover, since the return of an equity indexed annuity is tied to the performance of a benchmark equity index, the investor is very likely to derive higher gains when the stock market rises. Conversely, in the event of a fall in the stock market, the investment is still hedged by the guaranteed minimum return, which means that investors are less likely to lose their principal. Thus, EIA are best suited for conservative investors that are willing to trade in some potential returns for a more secure investment.

**Disadvantages of Equity Indexed Annuities**

There are certain limitations of Equity Indexed Annuities as well. To begin with, EIAs are complex investment vehicles and are available in a wide variety of formats. This complexity often results in investors misinterpreting the operating mechanisms of EIAs. Secondly, there are instances where EIAs do not match the entire return of the market index they are tied to. This is because different EIAs employ different methods for calculating gains. Lastly, Equity Indexed Annuities carry surrender charges that may be as high as 20%. Since, most EIAs last 15 years or more, investors seldom have the option of accessing their money without paying steep penalty charges for years.

### Academic Research on** Equity indexed Annuity**

*https://www.investopedia.com › Retirement › Retirement Savings**https://en.wikipedia.org/wiki/Equity-indexed_annuity**https://money.usnews.com › Money › Investing**https://smartasset.com/investing/equity-indexed-annuities**https://money.cnn.com/retirement/guide/annuities_equityindexed…/index.htm*

**Academic Research on Equity Indexed Annuity**

Optimal design of a perpetual **equity**–**indexed annuity**, **Moore, K. S., & Young, V. R. (2005). ***North American Actuarial Journal***, ***9***(1), 57-72. **The authors evaluate the following attributes of a perpetual equity-indexed annuity (EIA) that appeal most to buyers: Participation rate; Guaranteed death benefit; Guaranteed surrender benefit; Initial and maintenance fees. The objective is to find an equilibrium between maximizing the buyer’s bequest and enabling the EIA issuer to achieve a positive net income, going by the expected discounted value of the issuer’s payout.

Valuation of **equity**–**indexed annuity **under stochastic mortality and interest rate, **Qian, L., Wang, W., Wang, R., & Tang, Y. (2010). ***Insurance: Mathematics and Economics***, ***47***(2), 123-129. **An equity-indexed annuity (EIA) contract offers two discrete benefits: An equivalent participation in the return on a specified equity index. An assured return on the single premium. This paper scrutinizes the valuation of equity-indexed annuities under stochastic mortality and interest rate, both of which are presumed to be interdependent factors. The authors use the change of measure technique to introduce pricing formulas in closed form for the point-to-point and the annual reset product designs. Lastly, the authors perform a series of numerical experiments in order to determine the correlation between certain parameters and the pricing of EIAs.

Optimal surrender strategies for **equity**–**indexed annuity **investors, **Moore, K. S. (2009). ***Insurance: Mathematics and Economics***, ***44***(1), 1-18. **This paper samples an investor in an equity-indexed annuity (EIA) contract who pursues both the surrender strategy as well as the post-surrender asset allocation strategy in order to maximize the expected discounted utility of bequest. The author constructs a variational inequality which governs the optimal surrender strategy as well as a Hamilton–Jacobi–Bellman equation that controls the post-surrender asset allocation strategy. The paper scrutinizes the optimal strategies and establishes their reactions to the product features, model parameters, and mortality assumptions.

The problem with current accounting: A critique of SFAS 115 and SFAS 133 using an **equity**–**indexed annuity **example, **Wallace, M. (2006). ***North American Actuarial Journal***, ***10***(1), 11-29. **This article employs a simple equity-indexed annuity (EIA) in order to demonstrate the drawbacks associated with historical cost accounting as well as with the various remedial measures that have been adopted. The author goes on to advocate the adoption of a full fair value accounting system for all assets and liabilities on the company’s books as the only permissible method to reflect risk accurately on a company’s accounting statements.

Optimal surrender strategies for **equity**–**indexed annuity **investors with partial information, **Wei, J., Wang, R., & Yang, H. (2012). ***Statistics & Probability Letters***, ***82***(7), 1251-1258. **This paper scrutinizes an equity-indexed annuity (EIA) investor looking to evaluate the optimal time of surrendering the EIA so as to maximize his logarithmic utility of the wealth at the time of surrender. The authors employ a geometric Brownian motion with regime switching in order to model the dynamics of the index. They also consider a finite time horizon with an unobservable Markov chain in order to derive more realistic outcomes.

The **equity indexed annuity**: A Monte Carlo forensic investigation into a controversial financial product, **Carver, A. B. (2013). ***Decision Sciences Journal of Innovative Education***, ***11***(1), 23-28. **Equity Indexed Annuities (EIAs) are often considered contentious as financial products since their payoffs are based on complex, and mostly incomprehensible formulas. This article scrutinizes the role played by the Monte Carlo simulation in demonstrating the actual returns deliverable by an EIA, as well as the underlying risks involved. The analysis provided in this article can be employed to illustrate the potential of the Monte Carlo simulation in solving problems that involve uncertainty and nonlinear payoffs.

Improvements on the **equity indexed annuity **market, **Sachelarie, V. (2002). (Doctoral dissertation, The Ohio State University). **This paper discusses certain desirable attributes of Equity indexed annuities (EIAs) such as: A minimum guaranteed return; Tax deferral; A locked-in interest rate; Participation of each EIA customer in the stock market. However, of late, increased volatility as well as slower growth of the stock markets has been severely affecting the EIA market. As a result, there has been a drastic reduction in the participation rates offered by insurers, which directly translates to lower sales figures.

Pricing of **equity indexed annuity **under fractional Brownian motion model, **Xu, L., Shen, G., & Yao, D. (2014). In ***Abstract and Applied Analysis*** (Vol. 2014). Hindawi. **This paper seeks to address the valuation of equity indexed annuity (EIA) designs in a fractional Brownian motion-driven market. The authors offer an explicit pricing expression for point-to-point equity indexed annuity design and pricing bounds of high-water-marked EIA design. They present a few numerical examples to elucidate the influence of the parameters involved in the pricing problems.

Analyzing **equity**–**indexed annuity **using Lee-Carter model, **Li, H. Y. (2010). (Doctoral dissertation, Concordia University). **This paper demonstrates ways to compute the closed-form pricing formula of a point-to-point financial guarantee, by utilizing the Black-Scholes framework. The author also creates a replicating portfolio in order to hedge a point-to-point financial guarantee. However, because companies only trade discretely, this replicating portfolio generates errors in hedging. The paper demonstrates the distribution of the present values of hedging errors and introduces the Lee-Carter stochastic mortality model.

Risk-minimizing hedging strategy for an **equity**–**indexed annuity **under a regime switching model, **Qian, L. Y., Wang, W., & Wang, R. M. (2015). ***Acta Mathematicae Applicatae Sinica, English Series***, ***31***(1), 101-110. **Besides offering an assured return on the single premium, the equity-indexed annuity (EIA) contract also provides a proportional participation in the performance of a stated equity index. However, it becomes essential to work out ways to manage the risk of the EIA. This article takes into account the hedging of the equity-indexed annuity. The authors presume that the financial model parameters rely on a continuous-time finite-state Markov chain. The Markov chain is observed and its state is interpreted as the state of the economy. The risk-minimizing hedging strategy for the EIA is obtained under the Markov regime switching model.