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Adjusted Money's Worth Ratios In Life Annuities

Jaime Casassus and Eduardo Walker

The Money’s Worth Ratio (MWR) measures an annuity’s actuarial fairness.
It is calculated as the discounted present value of the annuity’s expected
future payments divided by its cost. We argue that, this measure may
overestimate the value‐for‐money obtained by annuitants, since it does not
adjust for liquidity or risk factors. Measuring these factors is challenging,
requiring detailed knowledge of the annuity provider’s assets, liabilities, and
of the stochastic processes followed by them. Using a multi‐factor
continuous‐time model and option pricing theory, we propose a simple
solution for an Adjusted MWR (AMWR), which does consider illiquidity and
default risk. We implement this solution for the competitive Chilean annuity
market, which offers unadjusted MWRs above 1, finding that indeed these
ratios are biased upward 7 percent on average. We also present estimates
of default option values, asset insufficiency probabilities and implied credit
spreads for each annuity provider.

Keywords: Money's worth ratios, annuities, insurance companies, credit risk, liquidity premium,
default probability, multi‐factor continuous time models, option pricing, Emerging Markets, Chile