Investors often hedge their liabilities against nominal interest rate risk. However, inflation risk also plays an important role for real wealth outcomes, especially in the long-run. If both risks follow a bivariate mean-reverting process, optimal allocations in nominal bond strategies typically turn out to be extreme, in particular when the bond maturities lay close to each other. We show that this makes the investment strategy sensitive to small changes in the mean-reversion parameters and the feedback parameter that takes into account the impact of the inflation rate level on the nominal interest rate drift. We perform a numerical analysis to demonstrate that small estimation errors of these parameters might have a large impact on terminal real wealth. A range of values of the feedback parameter is applied to compare the resulting investment strategies to Brennan and Xia (2002), Van Bilsen et al. (2020), and Munk et al. (2004). We find that the optimal two bond strategies involve one medium term bond and one very long-term bond, but these strategies are very sensitivity to parameter uncertainty. One bond strategies are more robust, but cannot completely hedge inflation risk, which results in a large loss in the Certainty Equivalent Wealth of a risk averse investor.