Adjusted Money’s Worth Ratios In Life Annuities

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.