Traditional treasury bills and TIPS

TIPS----Treasury Inflation-Protected Securities.

As its name implies, TIPS' major property is that the principal is adjusted to nation's price level, usually measure as CPI. For example, suppose the coupon rates of a ten-year TIPS and a ten-year traditional treasury bill are both 3 percent. If investors buy them at par and hold to maturity, and average inflation is 2.5 for the next 10 years, then the real return of the traditional treasury bill is only 0.5 percent while that of the TIPS is still 3.5 percent. (WHY? Because the principal coupon rate is automatically adjusted to be 2.5+3=5.5 percent) So TIPS keeps the purchasing power.

Ideally, the return yield between TIPS and traditional treasury bill is the average market participants' inflation expectation, which can give us valuable information in inflation forecasting. In real life, however, some other factors also play roles in this yield spread.

(1) Inflation risk:
TIPS is inflation-risk free, while traditional treasury bill is subject to inflation effect, so investors bear more risk buying the latter bond. Based on economic theory, investors should be compensated by some amount to buy the bond, and we call this amount of pecuniary compensation as Inflation Risk Premium.

(2) Liquidity risk:
Based on finance theory, value of a certain type of asset is related to its liquidity. If the asset takes significant time and effort to sell at fair price, then investors might have to lower price to sell it when time constraint is tight. Traditional treasury bills are supposed to be the most liquid assets in financial market, and thus investors of these bonds don't have such worries. TIPS are relatively more illiquid and thus liquidity premium might exist to attract investors to buy TIPS. (TIPS have higher liquidity risk)

To summarize, the yield spread can be expressed as:

y^(n) - y^(r) = inflation expectation + inflation risk premium - liquidity risk premium,

where  y^(n) denotes nominal return of traditional treasury bills, and y^(r) denotes real return of TIPS.

From this equation it is clear that the spread conveys accurate info about inflation expectation only when inflation risk premium is of the same size as liquidity risk premium. However, if both premium are significant smaller than inflation expectation, then the spread still has a good approximation of inflation expectation. Furthermore, if premiums are roughly constant over time, then we can know change of inflation expectation by tracking change of spread rate.