Guarantee Costs and Portfolio Selection in Guaranteed, Privatized Social Security Accounts, With and Without Inflation Indexing

This study demonstrates the practical application of option pricing theory to calculate the cost of providing guarantees for privatized social security accounts. We examine privatized social security from the perspective of a participant. If there are no guarantees, the participant is likely to invest in some diversified mix of stock and bond funds. Using an option pricing model we show that if the government guarantees the principal, rational participants will shift their entire contribution to the riskiest fund available for investment, which in turn will maximize the cost of providing the guarantee. We find that the cost of the guarantee is substantially lower for younger participants than for older participants if the guaranteed principal is not indexed for inflation, but the difference is small if the guaranteed principal is indexed for inflation. Our findings suggest that the government needs to offer only one mix of funds for investment in guaranteed accounts, and to minimize guarantee costs, it would guarantee only the principal. Alternatively, it could take a more age-neutral approach by guaranteeing the inflation-indexed principal.