*The Business Professor*, updated March 7, 2020, last accessed October 20, 2020, https://thebusinessprofessor.com/lesson/assumed-interest-rate-definition/.

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### Assumed Interest Rate (AIR) Definition

The assumed interest rate (AIR) refers to an interest rate or growth rate used by an insurance company to calculate the value of an annuity contract and its payout. An insurance company determines AIR and it serves as the benchmark for the annuityās periodic income payment that an annuitant would receive at the due time.

When calculating the payout of an annuity contract, the assumed interest rate is a crucial metric. There are diverse factors that are considered when an insurance company is o determine AIR, these include the age of the annuitant upon annuitization, the type of annuity coverage, the coverage options, and others.

### A Little More on What is an Assumed Interest Rate

The assumed interest rate (AIR) as used by an insurance company determines the minimum rate of return that a variable annuityās separate account must realize during the payout so as to maintain a steady annuity payment to the annuitant. It refers to the minimum interest rate that the insurer must earn on the cash value of the annuitantās policy that will help the insurance company cover its costs and also maintain an expected profit margin. This means the higher the AIR, the higher monthly income an annuitant would receive and the higher the profits that the insurance company would make.

The AIR is determined by insurance companies, it is the target rate of return they set on annuity separate accounts in order to have steady payments and also pay all costs.

The AIR is not a guaranteed rate of return given that there is no fixed return that annuityās separate accounts record. However, if an annuity account performs above the AIR, the annuitant would receive higher payments but the reverse is the case when the account performs below the AIR. The AIR takes into account the value of an annuity, the type and the annuitantsā age at the time he would begin to receive monthly income payments.

### Reference for āAssumed Interest Rate (AIR)ā

https://www.investopedia.com/terms/a/assumedinterestrate.asp

https://investinganswers.com/financial-dictionary/debt…/assumed-interest-rate-4807

www.businessdictionary.com/definition/assumed-interest-rate.html

https://www.nasdaq.com/investing/glossary/a/assumed-interest-rate

https://financial-dictionary.thefreedictionary.com/Assumed+interest+rate

### Academics research on āAssumed Interest Rate (AIR)ā

The timing of annuitization: Investment dominance and mortality risk, **Milevsky, M. A., & Young, V. R. (2007). The timing of annuitization: Investment dominance and mortality risk.Ā ***Insurance: Mathematics and Economics***,Ā ***40***(1), 135-144. **We use preference-free dominance arguments to develop a framework for locating the optimal age (time) at which a retiree should purchase an irreversible life annuity, as a function of current annuity prices and mortality tables. Then, using the institutional characteristics of annuity markets in the US, we show that annuitization prior to age 65ā70 is dominated by self-annuitizationĀ evenĀ in the absence of any bequest motives. And, for retirees who are willing to accept some financial risk in exchange for retaining the benefits of liquidity and bequest, the optimal age can be even later. In addition to the normative implications, these results should help shed light on the so-called annuity puzzle which has been much debated by economists, by focusing attention on theĀ specific agesĀ for which a puzzle can actually be said to exist.

Optimal asset allocation in life annuities: a note, **Charupat, N., & Milevsky, M. A. (2002). Optimal asset allocation in life annuities: a note.Ā ***Insurance: Mathematics and Economics***,Ā ***30***(2), 199-209. **In this note, we derive the optimal utility-maximizing asset allocation between a risky and risk-free asset within aĀ *variable annuity*Ā (VA) contract, which is a US-based savings and decumulation investment product. We are interested in the interaction between financial risk, mortality risk and consumption, towards the end of the life cycle. Our main result is that for constant relative risk aversion (CRRA) preferences and geometric Brownian motion (GBM) dynamics, the optimal asset allocation during the annuity decumulation (payout) phase is identical to the accumulation (savings) phase, which is the classical Merton [J. Econ. Theory 3 (1971) 373] solution.

Variable payout annuities and dynamic portfolio choice in retirement, **Horneff, W. J., Maurer, R. H., Mitchell, O. S., & Stamos, M. Z. (2010). Variable payout annuities and dynamic portfolio choice in retirement.Ā ***Journal of Pension Economics & Finance***,Ā ***9***(2), 163-183. **Many retirees hope to continue earning capital market rewards on their saving while avoiding outliving their funds during retirement. We model a dynamic utility maximizing investor who seeks to benefit from holding both equity and longevity insurance. She is free to adjust her portfolio allocation of her financial wealth as well as of the annuity over time, and she can purchase variable payout annuities any time and incrementally. In this setting, we show that the retiree will not fully annuitize even without bequests; rather, she will combine variable annuities with withdrawals from her liquid financial wealth so as to match her desired consumption profile. Optimal stock exposures decrease over time, both within the variable annuity and the withdrawal plan. Welfare gains from this strategy can amount to 40% of financial wealth, depending on risk parameters and other resources; additionally, many retirees will do almost as well as the fully optimized outcome if they hold variable annuities invested 60/40 in stocks/bonds.

Mortality risk, inflation risk, and annuity products, **Brown, J. R., Mitchell, O. S., & Poterba, J. M. (2000).Ā ***Mortality risk, inflation risk, and annuity products***Ā (No. w7812). National Bureau of Economic Research.**

Lifecycle portfolio choice with systematic longevity risk and variable investmentāLinked deferred annuities, **Maurer, R., Mitchell, O. S., Rogalla, R., & Kartashov, V. (2013). Lifecycle portfolio choice with systematic longevity risk and variable investmentāLinked deferred annuities.Ā ***Journal of Risk and Insurance***,Ā ***80***(3), 649-676. **This article assesses the impact of variable investmentālinked deferred annuities (VILDAs) on lifecycle consumption and portfolio allocation, allowing for systematic longevity risk. Under a selfāinsurance strategy, insurers set premiums to reduce the chance that benefits paid exceed provider reserves. Under a participating approach, the provider avoids taking systematic longevity risk by adjusting benefits in response to unanticipated mortality shocks. Young households with participating annuities average oneāthird higher excess consumption, while 80āyearāolds increase consumption about 75 percent. Many households would prefer to participate in systematic longevity risk unless insurers can hedge it at a very low price.