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female mortality rates, as well as the differences between annuity sales and annuity quotes. However, it is noteworthy that our MWRs increase between 1999 and 2003 while the MWRs estimated by James, Iglesias and Martinez remain stable or even decrease. This stability of MWRs is at odds with the behavior of the risk-free rate – annuity rate differential in the same period. As shown in Figure 4, the relation between the risk-free rate and the annuity rate would only be consistent with MWRs lower than one in 1999 and higher than one in subsequent years, including 2003.

The main conclusion of James, Iglesias and Martinez, that Chilean MWRs are high by international comparison and that Chilean annuitants have got a good deal for their money is the same as the one reached here, but their numbers probably underestimate the true MWRs in March 2003. In addition to the use of an outdated mortality table, it is possible that their results are also being affected by a small and non-representative sample of annuity quotes. The risk-free yield curve used for discounting is probably different and may be also contributing to the different results.

# **7. Conclusions**

On any measure, the results in Chile indicate good value for consumers. In part, this can be explained by the larger supply of assets indexed to consumer prices in Chile, including higher yield indexed instruments such as mortgage, corporate, and infrastructure bonds. Rocha, Morales and Thorburn (2006) provide separate evidence that the annuity rate is positively correlated with the share of higher yield assets in the portfolios of providers, suggesting that MWRs are also positively affected by this factor. In other countries, providers are either exposed to inflation risk, due to the absence of indexed instruments, or can only access lower yield indexed instruments such as indexed government bonds.

The high MWRs may also reflect aggressive pricing behavior in a very competitive annuities market. It is interesting to note that the _structure_ of MWRs suggests efficient risk differentiation – MWRs are higher for customers that present relatively lower reinvestment and mortality risk to the provider. That is, annuities with a shorter expected duration tend to have higher ratios than those with a longer duration. However, the overall _levels_ of MWRs seem excessive, suggesting that providers may be either counting on future increases in interest rates, or deliberately accepting temporary losses to drive competitors out of the market and gain market share. Rocha, Morales and Thorburn (2006) provide separate evidence that the annuity rate increases with the level of competition, and decreases for larger firms with established market share, suggesting that the high degree of competition also explain the high MWRs.

The MWRs of the recent years probably cannot be sustained for a longer period, however, as they indicate very low spreads and profit margins and possibly losses in the annuity business for at least some companies in this period. The industry could absorb these losses, because of the strong capital buffer accumulated in the 1990s, and which was due to the introduction of a strict capital regulation early in that decade (Rocha and Thorburn (2006)). However, the continuation of aggressive pricing strategies could lead