I think MrSmart, who is usually extremely helpful, might have gotten a bit mixed up on this one–‘priced at par’ does indeed mean at 100% face value, no more, no less. The par curve is a theoretical concept, and our closest example of this is the US Treasury term structure of only on-the-run bills, notes, and bonds. Their superior credit quality, liquidity, and recent coupon print means they are by far our best indicator of what said theoretical concept would be. So, we can hold these factors constant to focus on the time value of money. I could imagine a practical use by a trader in the mid-1960s at one of the Fed’s primary dealer investment banks (there’re about 22 desks today). They buy directly from the government and make markets in Treasuries. On the buy side, as the magician noted here and on his incredibly insightful and thoughtfully constructed web page, the par curve is the starting point to derive the spot (zero) and forward (breakeven) term structure. All these curves are packed with the information we need to unwrap to get some arb-free analysis going. We can only (kind of) see the par curve (the US does have a solid zero market, but other countries often don’t). Practically, we want to move from the observed to the unobservable in a risk-reward tradeoff. Total reward = price, (compounded) average reward = spot, and marginal or incremental reward = forward rate. (In reality, as we already know, not all Treasuries always trade at par, even if they’re the new print, so fixed income analysts might use computers to fit a par curve, adjusting the current one a bit, but the USA curve is usually pretty close; I only mention this so you’re not too confused, that minutia is outside the scope of this exam). By plotting the par curve, you use price (the PV) and cash flows over time (the FVs @ t’s) to unwrap the discount rate, which is also known as the YTM. We’re now at a critical juncture; for a 3 or 6 month T-bill, this is the YTM and the spot rate and the f0,1 forward rate. Next, after plotting the the T-bills, which are basically freebies (although they can have liquidity problems–again, minutia), you remove the coupons, except for the final big one, which is the principal, for each maturity point, bootstrapping or creating the spot curve, or zero-coupon curve. With one variable for price, another for the face value, and all the data behind that maturity in the term structure, you finish it off with the last piece of the puzzle, which is also the the forward rate that gets you back home.
The compounded average of the previous maturity’s spot rate, along with this new building block/forward rate, creates the spot rate, which is a geometric link of your (implied) forward rates for a given maturity. It’s also the rate that should price a zero coupon bond at 100par, or face value. Once you go out as far as you want along the term structure, you can use that data and some geometric averaging to find the implied forward term structure, as you slice up the spot curve based on the start of the forward rate you are interested in and its maturity.
But since everyone robotically states that the three curves “all contain the same information,” assuming I’ve got this understood properly, the par curve, with a (not stale) print determined by the primary market and quickly evaluated by the secondary market, is the only one of these we can really see and trust, is really where it all begins. And I think that’s the point.