The demo models individual tontine account (ITA) outcomes using Monte Carlo simulation of portfolio returns and the tontine pool's mortality experience. Both are modeled using random draws from a simple normal distribution (nothing fancy, we know, but remember that this is just a prototype). Payout ranges are provided for selected percentile ranges and are approximate. Random scenarios illustrate that payouts will vary randomly from month to month. Payout levels are not insured and not guaranteed.
The Accounting Ledger shows expected values at the mean. This can also be interpreted as the result in the case that the portfolio achieves its expected return each year and the mortality experience is exactly as expected. The plot at the right shows the approximate range of payouts given portfolio and mortality volatility.
The model assumes that investments are always made on the first day of the month. Investment returns and mortality credits are applied at the end of each month, and payouts likewise occur on the last day of the month. A second owner is only modeled if the Joint Account? box was checked, in which case mortality credits and payouts are made base on the life of both owners. If one owner dies, the surviving owner continues to receive payouts based on that owner's selected survivorship percent.
Payouts continue until the earlier of 1) X number of months after the member's death (or the second to die in the case of joint accounts), where X is defined by the mortality credit processing lag (explained further below), and 2) X months after the owner reaches age 119 1/2.
The demo models mortality using the 2012 IAM Basic mortality table projected forward using scale G2, available from the Society of Actuaries. The maximum age in this table is 120. The Monte Carlo simulation models idiosyncratic mortality risk, but not systematic mortality risk. The level of residual idiosyncratic mortality risk can be modeled using the Tontine pool membership size parameter, which influences a heuristic that approximates the level of idiosyncratic risk. A larger membership pool size results in a lower degree of pool mortality risk. To see the effect of systematic changes in mortality, use the Tontine pool mortality experience ratio parameter. A value of 1 means that actual mortality experience aligns with the expected experience as defined by the model's mortality table, on average. A value greater than 1 means that members systematically die at a rate faster than expected by the mortality table. A value less than 1 means that members systematically die at a rate slower than expected by the mortality table.
The Mortality credit processing lag parameter determines the "lag period" that the ITA provider might employ to allow time to verify which members have died during any given month. For example, a value of '3' means that the provider waits 3 months to verify deaths and allocate mortality credits to survivors--in this case, the mortality credits for February, for example, would be granted in May.
Notice: Demos are prototypes, provided for illustration only. All information is provided in good faith, however we make no representation or warranty of any kind, express or implied, regarding the accuracy, validity, reliability, availability, or completeness of any information associated with this site or any other demo or prototype.
This demo computes the statistical properties of a tontine with given charactistics. It uses a closed-form three-factor model and does not rely on simulation.