The diversifying power of inflation‐linked (IL) bonds relative to traditional asset classes has changed significantly. In this paper, we study the dynamics of conditional volatilities and correlations for three asset classes, IL bonds, nominal bonds and equities, in the USA and Europe. Using a DCC‐MVGARCH for the period 1997–2007, we highlight the change that took place in 2003. Although IL bonds once had definite diversification power, they are now highly correlated with nominal bonds and have reached similar volatility levels. As a result, the two asset classes are practically substitutable. This seems to be due to more stable inflation expectations and to a more liquid IL bond market. Although diversification was a valuable reason for introducing IL bonds in a global portfolio before 2003, this is no longer the case. Dynamic portfolio optimisation using our estimates of conditional correlations and volatilities clearly demonstrates that the optimal weight of IL bonds in a portfolio decreased sharply in 2003 in favour of nominal bonds and equities.