The Vanguard and Fidelity web sites report durations similar to what you do: 8.5 for Vanguard as of 12/31/2012 and 5.3 for Fidelity as of 1/31/2013. (See Vanguard Inflation-Protected Securities Fund Investor Shares (VIPSX)
and Spartan® Inflation-Protected Bond Index Fund - Fidelity Advantage Class FSIYX
.) The notes explaining duration say:
Vanguard wrote:The duration estimates the fund's percentage change in price for a given change in the real interest rates in the TIPS market.
Fidelity wrote:Duration estimates how much a bond fund's price will change with a change in comparable interest rates.
I suspect that by "comparable", Fidelity means interest rates on nominal
Treasury bonds, not the real interest rates on TIPS. For example, assume that for every 1% point change in nominal rates, real interest rates change 5/8% point. Then you'd expect Vanguard's fund price to fall 8.5% X 5/8 = 5.3% for a 1% rise in nominal rates.
The problem with this is that there is no fixed relationship
between nominal and real interest rates. In fact quite often they will move in the opposite direction. This makes an estimated "nominal" duration for a TIPS fund useless, in my opinion.
So I would ignore the duration reported by Fidelity. Since both funds probably have about the same holdings, I'd just use the duration reported by Vanguard for both of them. Or you could use the 8.76% I calculated (as of 2/8/2013) for the weighted average duration of all TIPS with maturities over 1 year. (See my post, Re: Consistent Yield & Duration to Help Choose TIPS Fund