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Back to the original question. I like to think in terms of "beta", i.e., exposures to risk factors. For many investors, portfolios likely have a negative inflation beta. A 1% shock on the inflation surprise side will likely subtract from your portfolio return. Bonds certainly have a negative inflation beta. Even stocks have a negative beta in the short-term due to Fed policy uncertainty, etc.
TIPS have a beta of 1.0. That's because you're guaranteed a real return and the TIPS return moves 1-for-1 with inflation.
So, right there you can derive your answer: You certainly cannot hedge the entire portfolio against inflation unless your entire portfolio is in TIPS. A perfect hedge would mean that your portfolio beta is 1, but mixing 95% of the portfolio with a negative beta with 5% with a beta=1 will not bring your overall beta to 1.
I agree about the portfolio, but could you hedge your annual consumption increases?
@chris-b That idea of "hedge your annual consumption increases" is nice in theory but difficult in practice. Because inflation shocks are normally permanent you have to hedge against not just your one-year increase in spending but all future consumption baskets. Not sure how to do that in practice.