Ok, lets assume, for the sake of illustration, that the coupon of the TIPS you own is 1% and then the fed raises interest rates to 10%. The question is, is the coupon of your TIPS indexed with the fed interest rates movements or not ? If the answer is no, than I can clearly see a market risk upon TIPS, just like any other bond.
There's no real inflation hedge that is perfect. Inflation-linked bonds are one option, stocks are another, real estate is another, commodities also work to a degree, but each one has its own factors which influence price, quite apart from inflation. Probably the best option is to own a diversified portfolio of the above assets. Also, remember that commodities have negative long-run real returns, as they have storage costs, whereas stocks, real estate, and bonds have positive long-run returns. As for hedging against forex movements, this is very easy - spread your cash into the other major currencies, namely the Euro and the Yen. Maybe add some Sterling and Swiss Francs too.
No. They are indexed against inflation. You're not trying to beat Fed Rates, you're trying to beat inflation.
In the MAY 04 issue of 'Futures" magazine (a surprisngly superb issue!) there's an article called "Inflation is everywhere and nowhere" which is pertinent to our discussion.