This paper considers the possibility of letting a pay-go pension system mimic a fully funded pension system. Generically, it turns out to be impossible to make a less than fully funded pension system actuarially fair on average. But a non-funded pay-go pension system can provide an actuarially fair implicit return on the margin, which increases economic efficiency. The benefits of this fall entirely on current pensioners as a windfall gain unless compensating transfers are implemented. Such a system can be thought of as a pay-go system that mimics a fully funded pension system in combination with lump transfers to current pensioners from current and future workers.