Asset Allocation and the Liquidity Premium for Illiquid Annuities

Academics and practitioners alike have developed numerous techniques for benchmarking investment returns to properly adjust seemingly-high numbers for excessive levels of risk. The same, however, can not be said for liquidity, or the lack thereof. This paper develops a model for analyzing the ex ante liquidity premium demanded by the holder of an illiquid annuity. The annuity is an insurance product that is akin to a pension savings account with both an accumulation and decumulation phase. We compute the yield (spread) needed to compensate for the utility welfare loss, which is induced by the inability to rebalance and maintain an optimal portfolio when holding an annuity. Our analysis goes beyond the current literature, by focusing on the interaction between time horizon (both deterministic and stochastic), risk aversion and pre-existing portfolio holdings. More specifically, we derive a negative relationship between a greater level of individual risk aversion and the demanded liquidity premium. We also confirm that, ceteris paribus, the required liquidity premium is an increasing function of the holding period restriction, the subjective return from the market, and is quite sensitive to the individuals endowed (pre-existing) portfolio.