siamond wrote:
The process you're suggesting starts from a nominal quantity, goes to a real quantity by subtracting 'expected inflation', churns over real numbers, and then we come back to a nominal quantity by adding the current year's inflation. It wasn't fully obvious to me that subtracting expected inflation at the beginning of the year, then adding current inflation at the end of the year, is the right thing to do.

So, if this is how TIPS work in the real world, then I guess this is how the risk of unexpected inflation is captured? Starting by subtracting expected inflation, then adjusting for actual inflation along the way?

In the real world, assuming that a TIPS is bought at par, one is guaranteed to receive the stated coupon in inflation-adjusted dollars, and the principal back in inflation-adjusted dollars. TIPS have a special feature in case of deflation: a TIPS will never pay back less than its initial principal in nominal dollars (and I think this applies to coupons, too). I call this a special feature, because Canadian

*real return bonds*, on which TIPS were partly modeled, have no such deflation bonus; they simply pay their coupons and return their principal in inflation-adjusted dollars, which might be lower nominal amounts than the original nominal amounts on the day of issue.

Let's look at a small example. Imagine that I bought a hypothetical 1% 5-year $100 TIPS

at par. Each year, this bond will pay me $1 in inflation-adjusted dollars and, at maturity, it will pay me back $100 in inflation-adjusted dollars:

(All amounts, below, are in nominal dollars).

**End of Year 0:** I invest $100.00 into a 1% 5-year TIPS.

**During Year 1:** Inflation is 2.5%.

**End of Year 1:** The principal is now $100.00 + 2.5% = $102.50. The 1% coupon is paid and I receive $102.50 X 1% =

**$1.03**.

**During Year 2:** Inflation is 3%.

**End of Year 2:** The principal is now $102.50 + 3% = $105.58. The 1% coupon is paid and I receive $105.58 X 1% =

**$1.06**.

**During Year 3:** Inflation is

-1%.

**End of Year 3:** The principal is now $105.58 - 1% = $104.53. The 1% coupon is paid and I receive $104.53 X 1% =

**$1.05**.

**During Year 4:** Inflation is 2%.

**End of Year 4:** The principal is now $104.53 + 2% = $106.62. The 1% coupon is paid and I receive $106.62 X 1% =

**$1.07**.

**During Year 5:** Inflation is 2.5%.

**End of Year 5:** The principal is paid and I receive $106.62 + 2.5% =

**$109.29**. The 1% coupon is paid and I receive $109.29 X 1% =

**$1.09**.

As you can see, there's no such thing as "subtracting expected inflation at the beginning of the year, then adding current inflation at the end of the year". A single TIPS works exactly like a nominal bond (if you exclude the deflation bonus), except that its principal and its coupons are adjusted to inflation.

All the talk about "expected inflation" is just speculation about TIPS pricing, like people do with the pricing of stocks and nominal bonds. A bond is a contract to be paid certain amounts of money at specific times. When one buys a bond (nominal or TIPS) at par, premium, or discount, one knows its exact future cash flows in nominal or inflation-adjusted dollars, depending on the type of bond (excluding any deflation bonus). In other words, one knows the future

*internal rate of return of the investment at maturity* as long as the bond is held until maturity and coupons are not reinvested (in nominal or inflation-adjusted dollars, depending on the type of the bond, and excluding any deflation bonus). Note that this does

not tell us the future

*total return* of the investment over the same period if coupons were reinvested in the same bond, which would require knowing the

*future market prices* of the bond on coupon pay dates (or

*future yields*, if you prefer).

What I am proposing is to 1) try constructing a synthetic

*real* yield curve*, then 2) model a TIPS fund similarly to how we modeled a nominal bond fund based on a nominal yield curve, except for the implementation of the annual inflation increments on coupons and principal amounts. Assuming exact investment-maturity and sell-maturity

*real* yields, cash flows of the modeled fund would be exact, leading to self-correcting returns. Of course, we won't have exact

*real* yields, so the quality of our synthetic returns will be dependent on the quality of our synthetic

*real* yields.

* This will require speculating on TIPS pricing in a world where they didn't exist.