Here is an overview of the questions I will try to answer in this short article:

• Briefly, what is inflation?
• How do central banks maintain inflation?
• How can investors protect their cash flows against inflation?

By definition, inflation is an increase in the general price of goods and services over a time period. Its converse is deflation. Inflation reduces the purchasing power of money as each unit of the currency buys fewer goods and services.
To put it another way around, 1€ is worth less than it was before. This website shows this effect as it displays the value of a dollar in 1920 across the years due to inflation.
It can have several causes but the main is the supply and demand.

#### How it’s measured?

Inflation within a country is measured monthly by the local Consumer Price Index (CPI) in which each product has its own weight. The following chart shows the weights of different goods in different CPI :

Weights of goods in different local indexes

#### Inflation and central banks

Inflation plays an important role in setting economic policies. The main task of the European Central Banks (ECB) is to maintain price stability and thus to maintain inflation. It performs this task by changing interest rates. Here is the logic :

• High interest rates make people more willing to put money on bank accounts and discourage people from borrowing which slows down the demand.
• Low interest rates encourage consumption as saving accounts are no longer attractive and borrowing is cheaper.

Example: Earlier in November, the Bank of England (BoE) raised its interest rates by 25bp (0.25%) to 0.5% in order to reduce its current 3% inflation to the 2% initial target.

## How to hedge your return against inflation?

Suppose you buy a nominal bond with 3% yield and annual inflation is 2%, this inflation erodes your return. The real story (return adjusted for inflation) is indeed 0.98%:

$R_{real} = \frac{1.03}{1.02} - 1$

Inflation Linked Bonds (ILBs) are similar to a nominal bond with coupon and/or principal indexed on inflation. Two structures are possible:

• Capital indexed: Both coupon and principal are indexed on inflation.
• Coupon indexed: Only coupon is indexed on inflation.

I will only deal with capital indexed linkers here as the other structure is a scam.

#### Who issue ILBs?

Mainly governments. For example, French government issues OATi and OATei. The first is indexed on the French CPI and the second on HICP (Eurozone inflation). Italy issues BTPi and BTPei, UK issues inflation-linked GILTs, US issues TIPS and so on. Most linkers guarantee at least 100% of the par value at maturity (except from UK, Canada and Japan) as a protection against deflation: deflation floor.

#### Quotation

Linkers are quoted using the Canadian Model, they are always quoted in term of fixed real rate. The approximated Fisher equation tells us that :

$Real Rate \approx Nominal - Inflation$

To illustrate this, here is a screenshot I took this morning on Bloomberg:

Yield and Spread Analysis on 2.1 OATi 2023 – {YAS} on Bloomberg

This french Linker has a real yield of -1.309% if you buy as of now for 120.21 + accrued interest.

#### Daily Inflation Reference

The DIR fixing used to compute coupons has a 2 months-lag since it’s computed with the $CPI_{m-2}$ and $CPI_{m-3}$. The ratio:

$Index Ratio = \frac{DIR_T}{DIR_{T0}}$

is the ratio to multiply to the fixed coupon to get the indexed coupon that has to be paid.

#### Cash flows in pratice

Let’s buy a 1.5% 2Y Linker. Suppose $DIR_0 = 100$, $DIR_1 = 104$ and $DIR_2 = 107.5$.

At the end of year 1:

Index Ratio is $\frac{104-100}{100} = 4\%$. The coupon is therefore:

$1.5*(1+4\%) = 1.56$

At the end of year 2:

Index Ratio is $\frac{107.5-100}{100} = 7.5%$. The coupon is therefore:

$1.5*(1+7.5\%) \approx 1.61$

and the principal is $100*(1+7.5\%) = 107.5$. This add up to 109.11€ for the final payment.

Linker has a higher credit risk than its nominal comparator due to the heavily skewed cash flow structure. Inflation-linked bonds have little coupons that grow up each year and a huge principal payment at the end. I made a little schema to show it:

Comparison of cash flows structure between nominal and inflation-linked bond

This higher credit risk can be measured with the IOTA spread defined as

$IOTA = ASW_{Linker} - ASW_{Nominal}$

and is normally positive. Also, the cash flow profile implies a higher duration (see the duration as the Roberval Balance comparing coupons to principal) for linkers and are consequently more sensitive to any change in yield.

#### Possible scenarios

What is the breakeven inflation? This is the future inflation that would equalize the returns on a linker and its nominal comparator (i.e the closest fixed rate bond).

• If the realized inflation is equal to the breakeven, then the linker return is the same as the nominal bond.
• If the realized inflation is greater (lower) than the breakeven, the linker outperforms (underperforms) the nominal bond.

#### Strategy example: Steepener

When the gap between the yields on short-term and long-term bonds increases, the curve is steepening. It happens when short-term yields decrease whereas long-term yields increase. When one anticipates a steepening curve, he usually goes short on short-term rates and long on long-term rates.
Have a short positive position on short-term yield means being long on the bond as a downward movement in yield will make the associated bond price goes up! Similarly, be long on long-term yield means being short on the associated bond.

#### Swap market: Inflation swaps

In this section, I will give an insight into the inflation derivatives market by introducing 3 widely traded inflation-swaps. Swaps are regulated by the International Swaps and Derivatives Association and daily margin calls are made to a clearinghouse to erase counterparty risk.

#### Zero Coupon Inflation Swaps

These swaps are the most liquid inflation derivatives. This kind of swap naturally involves two counterparts: the inflation receiver and the inflation payer, and a single cash flow at maturity (after N years). The following diagram presents the rates exchanged at maturity:

Zero-coupon inflation swap exchanged rates

The fixed rate is usually called the swap breakeven and is calculated so the expected payment is the same for the payer and the receiver. For example, for a 1Y Z.C inflation-swap, the fixed rate is exactly the inflation expected by the market for the next year!

#### YoY inflation-swap

This swap is similar to the Z.C inflation-swap but has annual payments. The inflation payer pays each year the rate : $R = \frac{CPI_n}{CPI_{n-1}}-1$. A YoY swap is nothing but several Z.C swaps together! Here is how they are quoted with this Bloomberg screenshot I took today:

Z.C and YoY UK inflation-swap – {SWIL} on Bloomberg

As inflation-swaps reflect the future inflation expected by the market, there is something pretty interesting here. BoE raised up its rates to lower local current 3% inflation but the market doesn’t believe in an instantaneous drop in UK-inflation but rather in a progressive one.

#### 5y5y YoY inflation swap forward

A 5y5y inflation swap forward is a 5 years swap in 5 years from now. Its rate is really useful for central banks as it tells what the market thinks the long-term impact of its policies will be on inflation. Here is the current quotation of few 5y5y inflation swap forward on Bloomberg:

5y5y inflation swaps forward for UK, EU, JY and US – {ALLX} on Bloomberg

### Conclusion

I said inflation reflects the rising in price of a basket of goods and services due to supply and demand but what about the change in the quality of products? Inflation indexes such as the European HICP take it into account as they subtract the change in price that is due to quality.

In reality, linkers are not used to protect against inflation on a trading floor but inflation-swaps are since they are much more secured thanks to ISDA and are zero-cost at inception!

Inflation market is a recent and growing market with more and more participants such as corporates, bank ALM, funds, asset managers, pension funds…

### Thank you!

##### References:

Frank J. Fabozzi: Fixed Income Analysis – Second Edition.