**DISCUSSION PAPER PI-1303**

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