Inflation-Indexed JGBs and BEI

Inflation-indexed JGBs are used by pension funds as a way to protect against rising prices, and as an input for reading the market's expected inflation from government bond prices.

Government bonds whose principal moves with prices

Japan's inflation-linked bonds, which the Ministry of Finance calls inflation-indexed JGBs, are government bonds whose principal rises and falls with prices. If prices rise after the bond is issued, the principal grows in proportion to the rise. The principal after this adjustment is called the inflation-adjusted principal amount. Interest is paid twice a year, and each payment is the inflation-adjusted principal on that payment date multiplied by the coupon rate. The coupon rate is set at issue and stays the same until maturity¹. On an ordinary fixed-rate JGB, neither the principal nor the amount of interest changes before maturity. On an inflation-indexed JGB, both the interest and the principal increase when prices rise¹. For this reason, these bonds give investors with long investment horizons, such as pension funds, a way to hedge the risk of rising prices².

Japan's inflation-indexed JGBs have a 10-year term and are linked to the nationwide consumer price index (all items, less fresh food)³. The first issue was on March 10, 2004⁴. Issuance stopped after the 2008 financial crisis and resumed in 2013. When issuance resumed, some features of the bonds were changed, including the addition of a floor on the principal at maturity, which the Ministry of Finance calls the deflation floor⁵.

Consider a hypothetical example in which an investor holds an inflation-indexed JGB with a face value of 10 billion yen and a coupon rate of 0.1% a year. The indexation coefficient is the ratio that shows how much prices have changed since issue (explained in the next section). If the indexation coefficient on a payment date is 1.02, the inflation-adjusted principal is 10.2 billion yen. If it is 0.97, the inflation-adjusted principal is 9.7 billion yen. The interest received on that payment date is as follows.

The interest rises and falls in the same proportion as the indexation coefficient. A fixed-rate JGB with the same coupon rate would pay 5 million yen on every payment date.

The indexation coefficient and the lag in the index

The inflation-adjusted principal amount is the face value multiplied by the indexation coefficient⁶.

$$\text{Inflation-adjusted principal} = \text{Face value} \times \text{Indexation coefficient}$$

The indexation coefficient is the Ref Index on a given day divided by the Ref Index on the 10th of the month of issue. The value on day $n$ of month $m$ is given by the following formula⁶.

$$\text{Indexation coefficient}(\text{day } n \text{ of month } m) = \frac{\text{Ref Index}(\text{day } n \text{ of month } m)}{\text{Ref Index}(\text{10th of the month of issue})}$$

The Ref Index is a daily value based on the consumer price index. The Ref Index on the 10th of each month is the consumer price index for the month three months earlier (for the 10th of month $m$, the index for month $m-3$). For days after the 10th, the value is found by drawing a straight line between the Ref Indices on the 10th of that month and the 10th of the following month, in proportion to the number of days that have passed. For days before the 10th, the value is found in the same way from the values on the 10th of the previous month and the 10th of that month⁶.

The index from three months earlier is used because the consumer price index is published with a delay, so the index for the current month is not yet known on a payment date or trade date. Daily values are needed to calculate accrued interest each time the bond is traded, so the monthly index is filled in day by day⁷. The indexation lag used in inflation swaps is covered in Inflation Swaps.

The deflation floor and the redemption amount

Inflation-indexed JGBs issued from fiscal 2013 onward are redeemed at face value rather than at the inflation-adjusted principal if the indexation coefficient at maturity is below 1. This lower limit is the deflation floor. Issues up to fiscal 2008 have no deflation floor⁹. Market participants call the issues with the deflation floor the "new type" and the issues up to fiscal 2008 without it the "old type"⁵.

The deflation floor applies only to the principal repaid at maturity, not to interest. If the indexation coefficient falls below 1 during the term, interest is lower than the amount calculated on the face value. Even when the indexation coefficient at maturity is below 1, the final interest payment is calculated on the inflation-adjusted principal found with that indexation coefficient below 1⁹. In the earlier example with a face value of 10 billion yen and a coupon rate of 0.1% a year, the amounts received at maturity are as follows.

Figure description

The profit or loss on the principal, per 100 yen of face value, when an inflation-indexed JGB with the deflation floor is bought at a face value of 100 yen and held to maturity. Interest is not included. The horizontal axis is the indexation coefficient at maturity multiplied by the face value of 100 yen. The vertical axis is the redemption amount minus the purchase price of 100 yen. At or below 100 yen on the horizontal axis (an indexation coefficient of 1 or less), the redemption amount stays at 100 yen, so the profit or loss is 0. Above 100 yen, the profit rises one for one with the horizontal axis, reaching 10 yen at 110 yen. The figure shows that the principal does not fall below face value when prices fall, and increases by the amount that prices rise.

The inflation-indexed JGB can be seen as containing, in its redemption amount, a European option (an option that can be exercised only at maturity) with a strike price of 100 yen, the face value¹⁰. The shape of the profit or loss in the figure is the same as a long position in the inflation-indexed JGB plus a long put with a strike price equal to the face value. The deflation floor makes the price of the inflation-indexed JGB higher by its value¹¹. The option is worth less in three cases: when the current price of the inflation-indexed JGB (per 100 yen of face value) is well above 100 yen, when the price of the inflation-indexed JGB moves little, and when the time to maturity is short¹⁰. As of 2013, inflation-linked bonds issued by the governments of the United States, Germany, and France also had a deflation floor, while those in the United Kingdom did not¹².

The breakeven inflation rate (BEI)

The breakeven inflation rate (BEI) is the yield on a fixed-rate JGB (the nominal rate) minus the yield on an inflation-indexed JGB of the same maturity (the real rate)¹³. The real rate is the rate with the effect of prices removed, and it is calculated from the price of the inflation-indexed JGB¹³.

$$\text{BEI} = \text{Nominal rate} - \text{Real rate}$$

If inflation equals the BEI, investing in a fixed-rate JGB or an inflation-indexed JGB gives the same return. The BEI is called the breakeven rate because it marks this dividing line¹⁴. As of February 2024, the BEI published by the Ministry of Finance is the yield on the 10-year fixed-rate JGB closest in maturity to the most recent inflation-indexed JGB issue, minus the real rate on that issue¹⁵.

Consider a hypothetical example in which an inflation-indexed JGB and a fixed-rate JGB each have 1 year left to maturity. To keep things simple, assume the inflation-indexed JGB is the new type with the deflation floor and pays no interest, with a face value of 100 yen, a current indexation coefficient of 1 (an inflation-adjusted principal of 100 yen), and a price of 100 yen. The real rate is then 0%. If the yield on the fixed-rate JGB is 1.0%, the BEI is 1.0%. The amount received after 1 year from investing 100 yen, for each rate of inflation over that year, is as follows.

If inflation is above the BEI of 1%, the inflation-indexed JGB does better, and if it is below, it does worse. Even if prices fall 1%, the new-type inflation-indexed JGB is redeemed at 100 yen because of the deflation floor. Because the deflation floor supports the redemption amount even when prices are expected to fall, the BEI comes out higher than the inflation outlook by that amount¹⁶.

The BEI is used as a measure of the inflation rate the market expects, but it also contains elements other than the inflation outlook. The BEI can be broken down as follows¹¹.

$$\text{BEI} = \text{Expected inflation} + \text{Floor premium} - \text{Liquidity premium} + \text{Term premium}$$

The floor premium is the value of the deflation floor. The liquidity premium reflects how much harder inflation-indexed JGBs are to trade than fixed-rate JGBs. The term premium is the difference in risk premia between the two bonds¹¹. The lower the liquidity of inflation-indexed JGBs, the lower their price and the higher the real rate, so the BEI comes out lower.

Price changes and risks

If an inflation-indexed JGB is sold before maturity, its price changes with both the BEI and the nominal rate. Ignoring interest for simplicity, and assuming that prices are expected to rise at the BEI until maturity, the price $P$ of an inflation-indexed JGB with $n$ years to maturity (per 100 yen of current inflation-adjusted principal) can be written as follows¹⁷. Here $i$ is the nominal rate for the same maturity.

$$P = \frac{100 \times (1 + \text{BEI})^n}{(1 + i)^n}$$

Consider a hypothetical example in which the bond has 10 years to maturity, the BEI is 1.0%, and the nominal rate is 1.5%. The price is 95.18 yen. The price after the BEI and the nominal rate move is as follows¹⁸.

An investor holding an inflation-indexed JGB gains when the BEI rises, and loses when the BEI falls or the nominal rate rises. An investor who wants exposure only to moves in the BEI buys the inflation-indexed JGB and sells a fixed-rate JGB of the same maturity, which offsets the nominal rate risk. As of February 2024, hedge funds and others are described as taking positions that combine the two in this way¹⁷. As the last row of the table shows, if the BEI and the nominal rate move by the same amount, the price hardly changes.

Besides changes in market rates, there are the risks of falling prices and of low liquidity. When prices fall, interest and the principal of old-type issues decrease, as described in the section on the deflation floor. Inflation-indexed JGBs are also traded less than fixed-rate JGBs, so it can be hard to find a buyer when you want to sell. In the 2008 financial crisis, some overseas investors, who had been major buyers, turned to selling, and the prices of inflation-indexed JGBs fell sharply¹⁹. As of January 2024, the Ministry of Finance buys back and cancels inflation-indexed JGBs to improve the balance of supply and demand and to raise liquidity²⁰.

The gap between the inflation swap rate and the BEI

An inflation swap is a trade that exchanges an amount linked to the rate of inflation for an amount based on a fixed rate. Because the payments on an inflation-linked bond can be replicated with a combination of inflation swaps, in a perfect market the fixed rate on inflation swaps and the BEI calculated from government bonds would be equal²¹.

In practice, the two differ. Assuming there is no liquidity premium on nominal government bonds and no premium for a deflation floor, the difference between the inflation swap rate (IS) and the BEI is the sum of the liquidity premium on inflation swaps, $\delta_{IS}$, and the liquidity premium on inflation-linked bonds, $\delta_R$²².

$$IS - \text{BEI} = \delta_{IS} + \delta_R$$

A 2006 Bank of England analysis finds that the main reason for the difference is that arbitrage between the two markets does not work fully. If inflation-linked bonds are seen as hard to trade, their prices fall and the BEI comes out lower. A feature often noted in the inflation swap market is that there are more parties who want to be inflation receivers (the side that receives the inflation-linked amount) than inflation payers, which, other things being equal, pushes up the fixed rate on swaps. Also, distortions in the yields on nominal government bonds affect the BEI calculated from government bonds, but do not affect the inflation swap rate²³.

Derivatives such as inflation swaps often require less collateral than buying the bonds themselves, and so tend to have smaller liquidity premia. Several empirical studies in the United States find that the liquidity premium on inflation swaps is much smaller than that on inflation-linked bonds, and that most of the difference between IS and the BEI comes from the liquidity premium on inflation-linked bonds²². According to a 2013 paper from the Federal Reserve Bank of New York, in the United States the inflation swap rate was almost always higher than the BEI, and the difference exceeded 100bp around the time of the 2008 financial crisis²⁴.

According to a 2020 Bank of Japan working paper, inflation swaps in Japan are thinly traded, so depending on market conditions, a liquidity premium that cannot be ignored may arise on the swap side as well²⁵. Because the BEI on Japan's new-type inflation-indexed JGBs also includes the premium for the deflation floor, the same working paper estimates three factors together from the BEI and IS: the deflation floor, liquidity, and risk premia²⁶. Inflation-indexed JGBs are issued only with a 10-year term, and issuance was suspended for a time, so government bonds alone do not give a continuous series of real rates across a wide range of maturities. The paper therefore combines inflation swap rates with the prices of inflation-indexed JGBs to estimate the term structure of real rates²⁷.

Issuance and trading in practice

Inflation-indexed JGBs are issued through auctions held by the Ministry of Finance. Since fiscal 2013, both new issues and additional issues of existing bonds (reopenings) have been sold in Dutch-style auctions in which bidders compete on price²⁸. In a Dutch-style auction, all successful bidders buy at the same price²⁹. The Ministry of Finance sets the coupon rate when it announces the auction. The rate is generally set in steps of 0.1%, and the lowest rate is 0.005%²⁸. When issuance resumed in 2013, real rates were negative, and the coupon rate cannot be set below zero. The Ministry of Finance therefore adopted a method in which it sets a positive coupon rate and bidders bid on price³⁰. The highest accepted yield shown in the auction results represents the real rate²⁹.

The minimum face value is 100,000 yen, and transfers are made in whole multiples of 100,000 yen of face value. Interest is paid on the 10th of the month every 6 months (on the next business day if the 10th is a bank holiday). The bonds are not eligible for STRIPS, which separate principal and interest for trading³¹.

Notes

1. Ministry of Finance, "物価連動国債の商品設計" (Product design of inflation-indexed JGBs, in Japanese), the introductory explanation. An English overview is available: "10-year Inflation-Indexed Bonds (JGBi)." ↩ ↩²

2. Takahiro Hattori, "物価連動国債入門－基礎編－" (Introduction to inflation-indexed JGBs: basics), Ministry of Finance, "ファイナンス" (Finance), January 2024 issue (in Japanese), "２.１　物価連動国債のキャッシュ・フロー" (2.1 Cash flows of inflation-indexed JGBs). ↩

3. Ministry of Finance, "物価連動国債の商品設計" (Product design of inflation-indexed JGBs, in Japanese), the items "満期" (Maturity) and "連動する物価指数" (Price index linked to) under "具体的な商品設計" (Detailed product design). ↩

4. Bank of Japan, "わが国物価連動国債の商品性と役割について～米英における経験を踏まえて～" (The features and role of inflation-indexed JGBs in Japan, in light of experience in the United States and the United Kingdom) (Bank of Japan Review, 2004, in Japanese), page 1, "はじめに" (Introduction). ↩

5. Takahiro Hattori, "物価連動国債入門－基礎編－" (Introduction to inflation-indexed JGBs: basics), Ministry of Finance, "ファイナンス" (Finance), January 2024 issue (in Japanese), "２.２　物価連動国債の導入の経緯" (2.2 How inflation-indexed JGBs were introduced). ↩ ↩²

6. Ministry of Finance, "物価連動国債の商品設計" (Product design of inflation-indexed JGBs, in Japanese), the items "想定元金額の計算方法" (Calculation of the inflation-adjusted principal amount) and "利子額の計算方法" (Calculation of interest) under "具体的な商品設計" (Detailed product design). ↩ ↩² ↩³ ↩⁴

7. Takahiro Hattori, "ブレーク・イーブン・インフレ率（BEI）入門－物価連動国債から算出する期待インフレ率－" (Introduction to the breakeven inflation rate (BEI): expected inflation calculated from inflation-indexed JGBs), Ministry of Finance, "ファイナンス" (Finance), February 2024 issue (in Japanese), "４.２　連動係数はなぜ複雑になるのか" (4.2 Why the indexation coefficient is complicated). ↩

8. Ministry of Finance, "物価連動国債（１０年）の適用指数及び連動係数" (Ref Index and Indexation Coefficient applicable to Inflation-Indexed Bonds, in Japanese), the explanations of how the indexation coefficient is calculated and of the revision of the consumer price index base (from the 2020 base to the 2025 base), and the caution on using the published values. An English version is available: "Ref Index and Indexation Coefficient applicable to Inflation-Indexed Bonds," which gives the same calculation method and the 2025-base revision, and notes that the published figures are offered for information only. ↩ ↩²

9. Ministry of Finance, "物価連動国債の商品設計" (Product design of inflation-indexed JGBs, in Japanese), the introductory explanation, the note to "元本保証（フロア）のイメージ" (Illustration of the deflation floor), and the items "物価が下落した場合の元本保証" (The deflation floor when prices fall) and "償還金額" (Redemption amount) under "具体的な商品設計" (Detailed product design). An English overview is available: "10-year Inflation-Indexed Bonds (JGBi)," including the conceptual diagram of the deflation floor and its note. ↩ ↩²

10. Takahiro Hattori, "物価連動国債入札－発展編（フロア・オプション、流動性等）－" (Auctions of inflation-indexed JGBs: advanced topics (floor option, liquidity, and others)), Ministry of Finance, "ファイナンス" (Finance), March 2024 issue (in Japanese), "２.３　オプションという観点でみた元本保証" (2.3 The deflation floor seen as an option). ↩ ↩²

11. Takahiro Hattori, "ブレーク・イーブン・インフレ率（BEI）入門－物価連動国債から算出する期待インフレ率－" (Introduction to the breakeven inflation rate (BEI): expected inflation calculated from inflation-indexed JGBs), Ministry of Finance, "ファイナンス" (Finance), February 2024 issue (in Japanese), "３.３　BEIのバイアス：フロア・オプションとリスク・プレミアム" (3.3 Biases in the BEI: the floor option and risk premia). ↩ ↩² ↩³

12. Takahiro Hattori, "物価連動国債入札－発展編（フロア・オプション、流動性等）－" (Auctions of inflation-indexed JGBs: advanced topics (floor option, liquidity, and others)), Ministry of Finance, "ファイナンス" (Finance), March 2024 issue (in Japanese), "２.４　先進国における物価連動国債の元本保証" (2.4 Deflation floors on inflation-linked government bonds in advanced economies) and Chart 3 (as of 2013). ↩

13. Takahiro Hattori, "ブレーク・イーブン・インフレ率（BEI）入門－物価連動国債から算出する期待インフレ率－" (Introduction to the breakeven inflation rate (BEI): expected inflation calculated from inflation-indexed JGBs), Ministry of Finance, "ファイナンス" (Finance), February 2024 issue (in Japanese), "２.１　期待インフレ率とは" (2.1 What expected inflation is) and "２.２　実質金利の計算方法" (2.2 How the real rate is calculated). ↩ ↩²

14. Takahiro Hattori, "物価連動国債入門－基礎編－" (Introduction to inflation-indexed JGBs: basics), Ministry of Finance, "ファイナンス" (Finance), January 2024 issue (in Japanese), "２.４　物価連動国債を利用した期待インフレの測定：ブレーク・イーブン・インフレ率（BEI）" (2.4 Measuring expected inflation with inflation-indexed JGBs: the breakeven inflation rate (BEI)). ↩

15. Takahiro Hattori, "ブレーク・イーブン・インフレ率（BEI）入門－物価連動国債から算出する期待インフレ率－" (Introduction to the breakeven inflation rate (BEI): expected inflation calculated from inflation-indexed JGBs), Ministry of Finance, "ファイナンス" (Finance), February 2024 issue (in Japanese), "２.３　期待インフレ率の期間構造" (2.3 The term structure of expected inflation). ↩

16. Takahiro Hattori, "物価連動国債入札－発展編（フロア・オプション、流動性等）－" (Auctions of inflation-indexed JGBs: advanced topics (floor option, liquidity, and others)), Ministry of Finance, "ファイナンス" (Finance), March 2024 issue (in Japanese), "２.２　フロア・オプションによるBEIと期待インフレの乖離" (2.2 The gap between the BEI and expected inflation caused by the floor option). ↩

17. Takahiro Hattori, "ブレーク・イーブン・インフレ率（BEI）入門－物価連動国債から算出する期待インフレ率－" (Introduction to the breakeven inflation rate (BEI): expected inflation calculated from inflation-indexed JGBs), Ministry of Finance, "ファイナンス" (Finance), February 2024 issue (in Japanese), "３.２　物価連動国債の価格の変動：BEIと名目金利" (3.2 Changes in the price of inflation-indexed JGBs: the BEI and the nominal rate). ↩ ↩² ↩³

18. Prices are calculated with the formula and rounded to 2 decimal places. The change in price is the difference from the price before the move, 95.18 yen. ↩

19. Takahiro Hattori, "物価連動国債入門－基礎編－" (Introduction to inflation-indexed JGBs: basics), Ministry of Finance, "ファイナンス" (Finance), January 2024 issue (in Japanese), "BOX　金融危機時における物価連動国債の暴落" (Box: The collapse in inflation-indexed JGB prices during the financial crisis). ↩

20. Takahiro Hattori, "物価連動国債入門－基礎編－" (Introduction to inflation-indexed JGBs: basics), Ministry of Finance, "ファイナンス" (Finance), January 2024 issue (in Japanese), "３.３　買入消却の仕組み" (3.3 How buybacks work). ↩

21. Matthew Hurd and Jon Relleen, "New information from inflation swaps and index-linked bonds" (Bank of England, Quarterly Bulletin Spring 2006), page 29. ↩

22. Kazuhiro Hiraki and Wataru Hirata, "ブレークイーブン・インフレ率から抽出される日本の市場参加者の長期インフレ予想" (Long-term inflation expectations of market participants in Japan extracted from breakeven inflation rates) (Bank of Japan Working Paper Series No.20-J-6, September 2020, in Japanese), page 14, "3.3 流動性プレミアムの識別方法と定式化" (3.3 Identifying and specifying the liquidity premia), and footnote 15. ↩ ↩²

23. Matthew Hurd and Jon Relleen, "New information from inflation swaps and index-linked bonds" (Bank of England, Quarterly Bulletin Spring 2006), page 29, "Practical differences." ↩

24. Michael J. Fleming and John R. Sporn, "Trading Activity and Price Transparency in the Inflation Swap Market" (Federal Reserve Bank of New York, Economic Policy Review, May 2013), page 45. ↩

25. Kazuhiro Hiraki and Wataru Hirata, "ブレークイーブン・インフレ率から抽出される日本の市場参加者の長期インフレ予想" (Long-term inflation expectations of market participants in Japan extracted from breakeven inflation rates) (Bank of Japan Working Paper Series No.20-J-6, September 2020, in Japanese), pages 14–15. ↩

26. Kazuhiro Hiraki and Wataru Hirata, "ブレークイーブン・インフレ率から抽出される日本の市場参加者の長期インフレ予想" (Long-term inflation expectations of market participants in Japan extracted from breakeven inflation rates) (Bank of Japan Working Paper Series No.20-J-6, September 2020, in Japanese), page 4. ↩

27. Kazuhiro Hiraki and Wataru Hirata, "ブレークイーブン・インフレ率から抽出される日本の市場参加者の長期インフレ予想" (Long-term inflation expectations of market participants in Japan extracted from breakeven inflation rates) (Bank of Japan Working Paper Series No.20-J-6, September 2020, in Japanese), pages 7–8. ↩

28. Ministry of Finance, "物価連動国債の商品設計" (Product design of inflation-indexed JGBs, in Japanese), the items "発行方法" (Method of issuance) and "表面利率" (Coupon rate) under "具体的な商品設計" (Detailed product design). ↩ ↩²

29. Takahiro Hattori, "物価連動国債入門－基礎編－" (Introduction to inflation-indexed JGBs: basics), Ministry of Finance, "ファイナンス" (Finance), January 2024 issue (in Japanese), "４.１　入札結果の事例" (4.1 An example of auction results). ↩ ↩²

30. Takahiro Hattori, "物価連動国債入門－基礎編－" (Introduction to inflation-indexed JGBs: basics), Ministry of Finance, "ファイナンス" (Finance), January 2024 issue (in Japanese), "３.２　物価連動国債の入札" (3.2 Auctions of inflation-indexed JGBs). ↩

31. Ministry of Finance, "物価連動国債の商品設計" (Product design of inflation-indexed JGBs, in Japanese), the items "最低額面金額及び振替単位" (Minimum face value and unit of transfer), "利払日" (Interest payment dates), and "ストリップス化" (STRIPS) under "具体的な商品設計" (Detailed product design). ↩

32. Ministry of Finance, "物価連動国債の商品設計" (Product design of inflation-indexed JGBs, in Japanese), the item "入札時における受入経過利子額の計算方法" (Calculation of accrued interest received at auction) under "具体的な商品設計" (Detailed product design). ↩