#### Discover more from Paper Alfa - Macro & More

Inflation-linked bonds, linkers, or TIPS (US version) are commonly used terms in macroeconomics. I came across them in my earlier days and was intrigued by the differentiating characteristics compared to ordinary nominal bonds. There is no real magic to it, just a few basic concepts that need to be understood. The goal here is to tackle the basics and give you a first solid foundation and understanding of this niche fixed-income asset class.

Linkers are way less liquid than their nominal counterpart, I learned this heavy lesson in the fall-out of the GFC when I had a small allocation to Japanese inflation-linked bonds. Real yields (see further below) spiked and with it the bond’s valuation. I wasn’t even able to sell those at any reasonable price until the Ministry of Finance and ultimately also the Bank of Japan stepped in.

Here is the chart of said security. It only took about 2 years to reach the same price level. Total return wise I recovered quicker as I was earning some carry. Still, it was in all things probably one of my worst-ever investments.

Ironically, I came across many seasoned investors who didn’t really understand the profile and properties of linkers. The major misconception was and probably still is that they will protect you in high inflation regimes.

Didn’t work out in 2022 that way, and that’s just as it should be. Those things are equally sensitive to rates rising as their nominal counterparts. Real yields are what drives them.

So much for the intro into the asset class, let’s dig into the details. Oh, before that a really, really bad pun, you ready? It goes with the inflation theme.

My love for you isn’t nominal, it’s real.

Ok, with that out of the way, off we go!

Linkers are securities whose **principal is tied** to a consumer price index, and the interest they pay is based on a fixed rate applied to the **inflation-adjusted principal** (whereas a nominal bond pays interest based on a fixed rate applied to the bond’s face value).

At maturity, the linker holder is paid back the inflation-adjusted principal. The frequency of the interest payments can differ across countries but is usually **semiannual or annual**. Linker bonds offer protection against inflation in the specific price index they track; these price indices follow a specific subset of goods and services and may not capture broad trends in consumer prices.

Let’s look at the components of the bond in more detail:

**Principal:**

The principal of a linker is directly linked to the underlying price index.

The principal increases when the index increases (i.e., inflation) and, generally, decreases when the index falls (i.e., deflation).

At

**maturity**, if inflation has been positive over the life of the bond, the issuer pays the owner the inflation-adjusted principal. On the other hand, if deflation occurred, typically, the issuer pays the owner the original face value of the security. As such, linkers usually provide a “**deflation floor**”, i.e., the investor gets back par even if there is deflation over the life of the bond.The

**tricky**thing with the floor is really depending on when you bought the bond. If you, say, bought a bond which already had 10% of inflation accrued you are buying at 110 inflation-adjusted. If you now have deflation until maturity you’d be at worst been losing 10% back to 100. Most inflation-linked bonds have a floor. Have a guess whether the Japanese one in ‘08 had one although I think they come with floors these days.

**Interest:**

Interest payments on linkers are usually made on a semiannual or annual basis.

The coupon rate is constant over the lifetime of an inflation-linked bond.

The interest payment is determined by multiplying the inflation-adjusted principal by the coupon rate. Therefore, the interest payment varies over the life of the security. While the principal payment at maturity is guarded by a deflation floor, the individual coupon payments are not. During deflationary periods, if the principal of the linker goes below the original face value, the coupon payments can be lower than the original coupon rate.

Nothing better than an **example** to home in those above points:

So for Year 2, when there is 2% annual inflation. The principal appreciates to 1’020 $ and the 2% coupon gives an all-in compensation of 2% * 1’020 = 20.4 $ of which 0.4 $ is the inflation compensation.

Important to know that linkers are traded on a real basis. This means that the price you see on the screens is only half the story. After that, you will need to adjust the price by how much inflation has been accrued from the purchasing reference index compared to the base index from when the bond was issued.

**Example**: Say you buy a bond at 100. The reference index is 115 (15% of inflation has been accrued) while the base index is 100. The “**dirty**” price for settlement purposes will be 115 (100 * 115/100).

**Why would you buy a real bond rather than a nominal bond?**

Buying a linker rather than a nominal bond is effectively taking a view that inflation will be higher than what is currently priced, which is the difference between the nominal yield and the linker yield.

In other words, investors are better off buying the linker rather than the nominal bond if realized inflation turns out to be higher than what was priced in the linker market at the time of purchase, and vice versa. Note that the linker yield is also known as real yield and that the difference between the nominal and real yield is known as breakeven inflation; we discuss more details on this below. Important to remember that much of the discussion is a relative one, i.e. are linkers better vs. nominals or vice versa.

### Fisher equation

The relationship between inflation expectations, real yields, and nominal yields was summarized by economist Irving Fisher in his 1896 publication “Appreciation and Interest.” The original Fisher equation can be expressed mathematically as:

**1 + r(nominal) = 1 + r(real) * (1 + inflation expectation)**

In simple terms, the equation states that the real rate is equal to the nominal interest rate minus the expected inflation rate (breakeven rate).

If investors think realized inflation will be more than the expected inflation, they are better off buying inflation-linked bonds, as the principal on linkers will be adjusted by realized inflation. If, on the other hand, investors think inflation expectations in the market are fairly priced, they should be indifferent between linkers and nominals as the return on both would be identical when held to maturity (hedging considerations aside).

So below chart, you see the 5-year nominal yield of US treasuries of around 4% (orange), as well as the 5-year breakeven rate of 2.1% (blue). This means 5-year real yields are 1.9%. Which one would you buy and hold?

Over the lives of bonds, if realized inflation exceeds breakeven inflation, the inflation-linked bond would outperform a similar-maturity nominal bond, as the combined yield from principal appreciation (which is equal to the realized inflation) and the real yield would be higher than the nominal yield, which is the sum of real yield and expected inflation (i.e., breakeven inflation). Conversely, if realized inflation is less than breakeven inflation, the nominal bond would provide higher returns.

**Nerdy corner:**

It is worth pointing out here that there is a small nuance in how the linker principal tracks the changes in the underlying index: there tends to be a lag in the principal adjustment. For example, let us assume that an investor purchased 100 mio $ of the on-the-run 5y TIPS bond on Feb 1st, 2023. The trade settles on Feb 2nd, 2023. If the investor sells the bond on March 1st, 2023, the percentage change in the principal is not equal to the per cent change in CPI from Feb 2nd to Mar 2nd. It is equal to the per cent change in the CPI index from Dec 2nd to Jan 2nd. Say what?

This is because, in the case of TIPS, the principal mirrors the changes in the inflation index with a **two-month lag**. Note that this lag may vary across countries. For now, it is important to understand that the calculation period of the underlying breakeven inflation starts prior to the day of the purchase. In the case of TIPS, it denotes inflation expectations during the period starting two months prior to the purchase and ending two months prior to the maturity date. Easy right?

Trading breakevens is one of the most common **investment strategies** in the TIPS market. This strategy allows investors to hedge their TIPS position with comparable Treasuries in order to build a portfolio that is potentially insensitive to the movement in interest rates. Trading breakevens is most suitable for those investors who have a specific view on future inflation but have no view on broader interest rates. The strategy would involve buying TIPS and hedging the duration via futures on the maturity equivalent nominal bond (treasury) in order to be duration neutral. If market expectations increase you make money.

### Inflation Swaps

In the interest of not overwhelming you with information, I will just briefly highlight the main properties of inflation swaps here. As usual, if you want more information on any particular subject just comment and I will try to accommodate where I can.

A zero-coupon inflation swap is an over-the-counter product related to linkers that allow investors to take a view on inflation with a single contract. In the contract, the swap receiver receives at maturity, the cumulative change of the reference inflation index, in exchange for an annually compounded fixed rate at maturity. There are no coupon payments, as the name suggests.

As there is no seasonality and carry implications nor liquidity premium, zero-coupon inflation swaps are a cleaner expression of expected inflation between the starting date and the maturity date The convention for determining the value of the CPI index for a given date is similar to that of linkers in the US—i.e., there is a lag in calculating the reference value of the inflation index.

The fixed rate can be thought of as the breakeven inflation rate of the swap. This is comparable to the breakeven inflation rate in inflation-linked bonds in that it is the average inflation rate needed over the period in order for the swap to have zero value when it expires. Swap and cash breakevens can be roughly compared, but because the swap is zero coupon, it would have to be adjusted to compare directly to the breakeven on a coupon-paying instrument.

Conceptually the swap works as shown in the below picture.

Hope you enjoyed this little interlude into the real world!

Your,

Paper Alfa

## Inflation-linked Bonds & Swaps

Amen to that!

Great overview. Not my cuppa, but ideal for a friend who likes TIPS.