# TIPS (Treasury Inflation Protection Security) Information

I've recently been learning about TIPS and their role as an inflation protection instrument. If you buy a TIP even when it has a negative real yield-to-maturity, is it still possible to have a profitable position?

Since as inflation occurs, the face value would also increase which is ultimately returned to you at the end. EX: you buy 10Y - 1000 dollar TIP for 1100 dollars . At the end of 10Y (face value + coupon payments) > \$1100.

If so, why don't people load up on TIPS to protect purchasing power since you're guaranteed at least par value or greater. I'm having trouble understanding the downside and hence break-even inflation rate.

Recently issued TIPS have negative real yields, meaning that they are issued at a price P>100. The payment at maturity will be 100*cpi(maturity)/cpi(issue date). The latter expression may or may not be greater than P. So if your definition of ‘profitable’ is in terms of nominal dollars, it is unclear.

I ignored the fact that newly issued TIPS have a coupon of 0.125% which ought to be taken into consideration also. But essentially, if the real yield at issuance is say -0.5%, then this is a nominal yield of inflation-0.5%, so the securities actually do not keep up with inflation nowadays. Neither does your money in the bank, which pays zero while inflation is around 1.5-2%.

TIPS is two instruments in one - a bond whose principal is linked to the Consumer Price Index for All Urban Consumers CPIAUCNS published by the BLS, and a put option with strike set to par value. The par value protection offered by the Treasury is not free and is paid by the bond investor. Also, not all investors may agree with BLS methodology for measuring the inflation, the BLS may choose to adjust the methodology down the road, and the calculation itself is not verifiable. While all these items could be seen as minor obstacles, the biggest barrier to adoption was the long period of low inflation and low nominal yields.

I've recently been learning about TIPS and their role as an inflation protection instrument. If you buy a TIP even when it has a negative real yield-to-maturity, is it still possible to have a profitable position?

Absolutely. Let's consider two scenarios:

### 1. You are not holding the bond to maturity:

In this case, recall that Canadian-style linkers, such as US TIPS, are quoted using the following formula: $$\text{Dirty price} = (P + AI) \times \frac{I_\text{settlement date}}{I_\text{base date}},$$ where $$P$$ is the real clean price, $$AI$$ is the real accrued interest, $$I_\text{settlement}$$ is the index ratio as of the settlement date, and $$I_\text{base}$$ is the index ratio on the base date (at issuance). The index ratio is essentially interpolated from lagged CPI. Furthermore, $$P + AI$$ is computed using the conventional price-yield formula:

$$P + AI = \frac{c/2}{(1+y/2)^w} + \frac{c/2}{(1+y/2)^{w+1}} + \cdots + \frac{100 + c/2}{(1 + y/2)^{w + N}}.$$ where $$c$$ is the real coupon rate (i.e., as quoted) and $$y$$ is the quoted real yield.

So how would dirty price change, thus generating P&L for you?

1. The real yield, $$y$$, can change. If it declines, then the dirty price goes up, all else equal. Since the real yield has no lower bound, the -0.6% real yield might feel low, but it could go to -5% (theoretically) and generating a ton of capital gains...
2. $$AI$$ naturally increases with time, giving you real coupon income.
3. $$I_\text{settle}$$ can change; e.g., it increases as CPI increases, giving you inflation protection.

### 2. You are holding the bond to maturity:

In this case, your investment return is roughly the initial real yield plus realized inflation. I use the word "roughly" because there's a ton of subtleties (e.g., compounding, reinvestment, etc.), but it's broadly true. To see this, let's consider a stylized one-year linker with just one cash flow; we'll also assume annual compounding for simplicity. Let's assume that today, this stylized one-year TIPS gets issued, and you pay a full price of $$P$$ for it at a real yield of $$y$$:

$$P_0 = \frac{c + 100}{1 + y}\times\frac{I_\text{settle}}{I_\text{base}} = \frac{c + 100}{1 + y}.$$

Then at maturity, ignoring the deflation floor, you receive $$P_1 = (c + 100) * \times \frac{I_\text{maturity}}{I_\text{base}}.$$

Your return over the year is $$\frac{P_1}{P_0} - 1 =(1 + y)\frac{I_\text{maturity}}{I_\text{base}} - 1 = (1 + y)(1 + \text{realized 1-year inflation}) - 1 \approx \text{real yield} + \text{realized 1-year inflation}.$$

The analysis above ignores the deflation floor; i.e., the final principal payment must be at least 100. A detailed discussion of the deflation floor likely complicates things too much, but broadly speaking, the deflation floor is not particularly valuable for old issues since there's a lot of inflation accruals already. Even for new issues, say the most recently issued 10-year TIPS, my calculation is that the embedded deflation floor is worth only 3 basis points... And in the environment we're likely headed, deflation floor is even less of a concern.

If so, why don't people load up on TIPS to protect purchasing power since you're guaranteed at least par value or greater. I'm having trouble understanding the downside and hence break-even inflation rate.

The breakeven inflation is simply the difference between the nominal bond yield and the real yield. Roughly speaking, you'd prefer TIPS over a comparable nominal Treasury issue if you think subsequently realized inflation will be higher than the initially priced breakeven inflation.

Again, let's consider a stylized 1-year nominal bond and a 1-year TIPS. So the breakeven inflation (BEI) is $$\text{BEI} = \text{1-year nominal yield} - \text{1-year real yield}.$$ Over the course of one year, the nominal bond will return exactly its yield, aka the 1-year nominal yield, and we've established above that the 1-year TIPS will return "1-year real yield + 1-year realized inflation." So if 1-year realized inflation is equal to the initial breakeven inflation, then the nominal bond will have the same return as the TIPS. If realized inflation is higher (or lower), then TIPS outperforms (underperforms) the nominal bond.