Hedging inflation-linked liabilities without inflation-linked instruments through long/short investments in nominal bonds

In the absence of inflation-linked bonds or inflation swaps, no perfect hedging strategy exists for inflation-linked liabilities, and nominal bonds are often used as substitute hedging instruments. This paper provides a formal analysis of the problem of hedging inflation-linked liabilities with nominal bonds in the presence of real rate uncertainty as well as realized and expected inflation risks. While a long-only position in nominal bonds will always have a negative exposure to unexpected inflation, our analysis suggests that long-short nominal bond portfolio strategies can in principle be designed to achieve a zero exposure to changes in unexpected inflation (required to hedge inflation-linked liabilities), while having a target exposure to changes in real rate equal to that of liabilities. The practical implementation of such long-short replication strategies, however, is not a straightforward task in the presence of parameter uncertainty. We explore several non-exclusive solutions to the estimation risk problem, including the use of conditional parameter estimation methodologies as well as the introduction of robust restrictions on input parameters or portfolio weights. These approaches lead to substantial improvements in out-of-sample hedging performance.