Convertible Bonds (CB)

A CB is a bond that a company issues to raise funds, with a right to convert it into shares, and it is also traded by hedge funds and others who seek returns while removing share price risk.

A bond combined with the right to convert into shares

A convertible bond (CB), formally called a convertible bond with share options in Japan, is a corporate bond that can be converted into shares of the company that issued it. Under the Companies Act, a bond that carries share options is called a bond with share options¹. A CB is a bond with share options under which, when the share options are exercised, the full amount of the bond is redeemed in place of a cash payment for the shares². From the investor's point of view, the investor hands over the bond instead of paying cash and receives shares. A CB corresponds to the convertible bond that existed before the amendment to the Commercial Code.

With a bond with share options, you cannot transfer only the bond or only the share options³. A CB investor therefore always holds the bond together with a call option (call) to buy the issuing company's shares at a set price⁴. The price per share used when converting into shares is called the conversion price, and the number of shares you receive is the face value divided by the conversion price⁵.

Consider a hypothetical example in which Company F issues a CB on the following terms and an investor buys 1 million yen of face value. Company F's share price at issue is 800 yen.

The investor can ask Company F to convert the CB into shares at any time within a set period (the conversion period)⁶. In terms of when it can be exercised, the right is an American option.

Value and profit or loss at maturity

At maturity, a CB is worth the higher of the value of the shares received on conversion and the face value. If Company F's share price is above the conversion price of 1,000 yen, the investor converts into shares. If it is below, the investor does not convert and receives the face value⁷. However far the share price falls, the investor receives the face value of 1 million yen at maturity, as long as Company F remains able to pay.

The profit or loss depends on the price paid. Suppose that after the share price has risen, the investor buys this CB in the market at 110 yen per 100 yen of face value, paying 1.1 million yen for 1 million yen of face value. The amount received and the profit or loss for each share price of Company F at maturity are as follows.

Above a share price of 1,100 yen, the investor makes a profit, which is 500,000 yen at 1,600 yen. At 1,000 yen or below, the investor receives the face value of 1 million yen, and the 100,000 yen paid above face value is lost. Between 1,000 yen and 1,100 yen, converting into shares brings in less than 1.1 million yen, and the loss is smaller than 100,000 yen.

Figure description

The profit and loss from buying Company F's CB, with a conversion price of 1,000 yen, at 110 yen per 100 yen of face value and holding it to maturity, shown per share received on conversion. Per share, the investor pays 1,100 yen and receives either the face value of 1,000 yen or one share at maturity. At share prices of 1,000 yen or below, the profit or loss stays at −100 yen. Above 1,000 yen, it rises by 1 yen for each 1-yen rise in the share price, reaching 0 at 1,100 yen and a profit of 500 yen at 1,600 yen. The profit or loss on 1 million yen of face value (1,000 shares) is 1,000 times this.

This shape is the same as the profit and loss from buying a call with a strike price of 1,000 yen. Because a CB investor is on the buying side of the call, the loss when the share price falls is limited to the amount paid above face value. However, if the issuer becomes unable to pay, the investor may not receive even the face value.

Value before maturity: parity and the premium over parity

Before maturity, the price of a CB is set by looking at both the value of the shares received on conversion (parity) and the value of the CB as a bond. Parity is the value on conversion, expressed per 100 yen of face value⁸.

$$\text{Parity} = \frac{\text{Share price}}{\text{Conversion price}} \times 100$$

How far the actual price of a CB is from parity is expressed as the premium over parity⁸.

$$\text{Premium over parity (\%)} = \frac{\text{Market price of the CB} - \text{Parity}}{\text{Parity}} \times 100$$

Consider a hypothetical example in which Company F's CB has the share price and market price shown in the two cases below.

When the share price is well above the conversion price, the value of the CB moves toward parity, and the premium over parity becomes small. When the share price is well below the conversion price, the value of the right to convert into shares moves toward zero, and the value of the CB moves toward its value as a bond⁴. When the share price is low, then, the CB price is supported by the value of the bond rather than by parity, and the premium over parity becomes large. The CB price can also fall below parity, making the premium over parity negative. This is called a negative premium⁶.

This relationship becomes clear if you split the value of a CB into the value of the bond and the value of the option⁴.

$$\text{Value of the CB} = \text{Value of the bond} + \text{Value of the option to convert into shares}$$

The value of the bond is the present value of the future payments, discounted at the interest rate plus a margin (spread) that reflects the issuer's credit. The value of the option is found by treating it as a call with parity as the price of the underlying asset and the face value as the strike price⁴.

In practice, however, the two parts cannot be separated and traded, and they affect each other, so this split is only an approximation to aid thinking. The value of the bond handed over on conversion changes with interest rates and the spread, and when the share price falls, the issuer's credit spread tends to widen, which also tends to lower the value of the bond⁹. To reflect in the valuation the fact that the CB can be converted into shares at any time, practitioners use lattice methods such as binomial trees¹⁰.

Benefits and costs for the issuer

In return for attaching the right to convert into shares, the issuer can keep the coupon low. The coupon on a CB is generally lower than on a straight bond⁵, and many of the CBs that Japanese companies have issued carried no interest¹². If the share price does not rise above the conversion price and the CB is not converted, the issuer pays almost no interest and only repays the face value at maturity, so its funding cost is lower than with a straight bond¹².

On the other hand, if the CB is converted into shares, the issuer's cost can become large. In Company F's example, if the share price at maturity is 1,500 yen, the investor converts, and Company F, which raised only 1 million yen, delivers 1,000 shares worth 1.5 million yen at market value. The 500,000-yen gap between the 1.5 million yen it could have raised by issuing the same shares in the market and the 1 million yen it actually raised can be seen as Company F's effective cost¹². If the company issues new shares to deliver, the number of shares increases and the value of each share is diluted (this is called dilution). Because the CB is converted only when the share price is above the conversion price, this is the same as issuing shares below the market price. As conversion becomes more likely, this puts downward pressure on the share price¹³.

The issuer and investors reach agreement on the terms of issue mainly through the level of the conversion price. With other terms unchanged, the higher the conversion price, the less likely conversion becomes, which favors the issuer and works against investors. How far the conversion price is set above the share price at issue is called the conversion premium (in Japan, the up rate)¹⁴.

$$\text{Conversion premium} = \frac{\text{Conversion price}}{\text{Share price when the conversion price is set}} - 1$$

In Company F's example, the conversion price was set at 1,000 yen when the share price was 800 yen, so the conversion premium is 1,000 ÷ 800 − 1 = 25%. As of 2025, many of the yen-denominated CBs of Japanese companies are Euroyen CBs issued overseas, in London and elsewhere. Their main investors are said to be overseas CB funds and hedge funds, and the terms are fixed within a few hours, starting in the evening Japan time, by setting the conversion premium¹⁵¹⁴.

A CB can also carry clauses other than the right to convert into shares. One is a downward reset clause, which lowers the conversion price at a set time after issue by a method set in advance (an upward reset clause raises it)⁵. Another is a soft call option, which lets the issuer redeem the CB early at face value when the share price reaches a level such as 125% or 130% of the conversion price. Because investors are better off converting into shares than being redeemed at face value, a soft call prompts investors to convert¹⁶.

Hedged investors and gamma trading

Some CB investors hold CBs without hedging the share price and issuer credit risks, and others hedge them. Investors who hedge, mainly hedge funds and similar investors, buy CBs and sell a number of shares that matches the delta of the option component¹⁷. Delta shows how much the value of an option moves when the share price moves. Delta itself changes as the share price moves, and this rate of change is called gamma. Having removed the risk from share price movements, these investors buy and sell shares each time the share price moves to bring delta back to zero, and seek returns from this trading (gamma trading)¹⁸.

Consider a hypothetical example in which an investor holds 1 million yen of face value (1,000 shares' worth) of a CB with a delta of 0.5. The investor sells 500 shares to bring delta to zero. Suppose the share price falls from 1,100 yen to 1,000 yen and delta falls to 0.4. The investor buys back the 100 shares it has oversold at 1,000 yen. If the share price returns to 1,100 yen and delta returns to 0.5, the investor sells the 100 shares again at 1,100 yen, earning the difference of 100 yen × 100 shares = 10,000 yen from the trades¹⁹. If the value of the option falls by less than this over the same period as time passes, the investor makes a net profit. Conversely, if the share price barely moves from 1,100 yen, this trading hardly happens. If the value of the option falls by 10,000 yen over the same period as time passes, the investor makes a net loss of 10,000 yen.

Whether the investor gains or loses depends on how much the share price moves. The time value part of an option's value falls over time, so if the share price moves little, the amount earned from trading does not cover that fall, and the result is a loss. If the actual volatility of the share price is greater than the implied volatility in the CB price, the result is a profit¹⁸. Even with the risk from share price movements removed, the issuer credit and interest rate risks remain¹⁹.

When a CB is issued, it is not unusual for overseas investors such as hedge funds to buy the option component, while the remaining bond component is packaged into a bond called a CB repackaged bond and sold to banks and others²⁰.

Risks

The issuer's credit risk and the difficulty of selling before maturity are covered in general on the What Are Structured Products? page. With a CB too, receiving the face value at maturity however far the share price falls depends on the issuer being able to pay. If the issuer goes bankrupt, the investor may receive neither the interest nor the face value²¹.

What is specific to CBs is that the price before maturity can be strongly affected by the issuer's share price, and also depends on the time to maturity and on movements in interest rates²¹. When the share price falls, the value of the bond also tends to fall, in addition to parity⁹. As in the example in the profit-and-loss table at maturity, if you buy above face value and the share price stays below the conversion price until maturity, the amount you paid above face value is lost.

As more CBs are converted into shares, the amount outstanding falls, and they can become harder to sell (liquidity risk)²¹.

How CBs differ from exchangeable bonds

A CB and an exchangeable bond (EB) are both bonds that may turn into shares, but the option points the opposite way²². A CB investor is on the buying side of a call and chooses whether to convert into shares. With an exchangeable bond, if the price of the underlying shares falls below a set price, the investor receives shares of a company other than the issuer instead of the face value²³. How an exchangeable bond investor is on the selling side of an option is covered on the Exchangeable Bonds (EB) page.

Notes

1. "会社法" (Companies Act, in Japanese), Article 2, item 22 (bonds with share options). ↩

2. Japan Exchange Group, "転換社債型新株予約権付社債" (Convertible bonds with share options), glossary (in Japanese). ↩

3. "会社法" (Companies Act, in Japanese), Article 254, paragraphs 2 and 3. ↩

4. Fuminobu Otake, Nobuyuki Oda and Toshinao Yoshiba, "転換社債の市場価格分析とリスク管理" (Market price analysis and risk management of convertible bonds), Institute for Monetary and Economic Studies, Bank of Japan, Discussion Paper No. 98-J-15, August 1998 (in Japanese): "イ．シンプル・モデル" (A. The simple model) in "2.（2）プライシング理論" (2.(2) Pricing theory), pages 5–6, and footnote 7. ↩ ↩² ↩³ ↩⁴

5. Japan Exchange Group, "転換社債型新株予約権付社債（CB）とは" (What are convertible bonds with share options (CB)?), CB overview (in Japanese): the main text, note 2 (conversion price), and "特徴" (Features). ↩ ↩² ↩³

6. Fuminobu Otake, Nobuyuki Oda and Toshinao Yoshiba, "転換社債の市場価格分析とリスク管理" (Market price analysis and risk management of convertible bonds), Institute for Monetary and Economic Studies, Bank of Japan, Discussion Paper No. 98-J-15, August 1998 (in Japanese): "2.（1）転換社債の商品性" (2.(1) Product features of convertible bonds), pages 2–3. ↩ ↩²

7. Takahiro Hattori, "転換社債（CB）入門―発展編―" (Introduction to convertible bonds (CB): advanced), Ministry of Finance, "ファイナンス" (Finance), April 2025 issue (in Japanese), "2.1 投資家の立場から" (2.1 From the investor's standpoint), page 19. The source notes that the parts expressing opinions are the author's personal views and not the views of the organization the author belongs to. ↩

8. Japan Exchange Group, "CBの価格（パリティと乖離率）" (CB prices (parity and premium over parity)), CB overview (in Japanese): "パリティ（理論価格）" (Parity (theoretical price)) and "かい離率" (Premium over parity). ↩ ↩²

9. Fuminobu Otake, Nobuyuki Oda and Toshinao Yoshiba, "転換社債の市場価格分析とリスク管理" (Market price analysis and risk management of convertible bonds), Institute for Monetary and Economic Studies, Bank of Japan, Discussion Paper No. 98-J-15, August 1998 (in Japanese): item ① of the limits of the simple model in "2.（2）" (2.(2)), page 7. ↩ ↩²

10. The same material, item ② of the limits of the simple model and "ロ．二項ツリー法による計算方法" (B. Calculation using the binomial tree method), pages 7–8. ↩

11. Fuminobu Otake, Nobuyuki Oda and Toshinao Yoshiba, "転換社債の市場価格分析とリスク管理" (Market price analysis and risk management of convertible bonds), Institute for Monetary and Economic Studies, Bank of Japan, Discussion Paper No. 98-J-15, August 1998 (in Japanese): the abstract, and in "2." (2.), item ② of the results of measuring market risk and items ① and ② of the features of the simple method, page 21. ↩

12. Takahiro Hattori, "転換社債（CB）入門―発展編―" (Introduction to convertible bonds (CB): advanced), Ministry of Finance, "ファイナンス" (Finance), April 2025 issue (in Japanese), "2.1 投資家の立場から" (2.1 From the investor's standpoint) and footnote 6, page 19, and "2.2 発行体の立場から" (2.2 From the issuer's standpoint), page 20. ↩ ↩² ↩³

13. Fuminobu Otake, Nobuyuki Oda and Toshinao Yoshiba, "転換社債の市場価格分析とリスク管理" (Market price analysis and risk management of convertible bonds), Institute for Monetary and Economic Studies, Bank of Japan, Discussion Paper No. 98-J-15, August 1998 (in Japanese), footnote 13, page 8. ↩

14. Takahiro Hattori, "転換社債（CB）入門―発展編―" (Introduction to convertible bonds (CB): advanced), Ministry of Finance, "ファイナンス" (Finance), April 2025 issue (in Japanese), "2.3 CBのプライシングのイメージ：アップ率" (2.3 A picture of CB pricing: the up rate) and "アップ率が決められるプロセス" (The process by which the up rate is set), pages 20–21. ↩ ↩²

15. Takahiro Hattori, "転換社債（CB）入門―投資家編―" (Introduction to convertible bonds (CB): investors), Ministry of Finance, "ファイナンス" (Finance), May 2025 issue (in Japanese), "1．はじめに" (1. Introduction) and "2.1 ユーロ円CBとは" (2.1 What are Euroyen CBs?), page 66. The source notes that the parts expressing opinions are the author's personal views and not the views of the organization the author belongs to. ↩

16. Takahiro Hattori, "転換社債（CB）入門―発展編―" (Introduction to convertible bonds (CB): advanced), Ministry of Finance, "ファイナンス" (Finance), April 2025 issue (in Japanese), "（1）ソフトコール・オプション" ((1) Soft call options) in "3.2 各種オプション" (3.2 Types of options), pages 22–23. ↩

17. Takahiro Hattori, "転換社債（CB）入門―投資家編―" (Introduction to convertible bonds (CB): investors), Ministry of Finance, "ファイナンス" (Finance), May 2025 issue (in Japanese), "2.2 CBの投資家の分類" (2.2 Types of CB investors), page 67. ↩

18. The same material, "2.4 ガンマ・トレーディング" (2.4 Gamma trading), pages 68–69. ↩ ↩²

19. The same material, "BOX1 ガンマ・トレーディングの具体例" (Box 1: A worked example of gamma trading), pages 69–70. The figures here are replaced with a fictional example. ↩ ↩²

20. The same material, "2.3 CBに含まれるオプションの性質" (2.3 The nature of the option embedded in a CB), pages 67–68. ↩

21. Japan Exchange Group, "リスク" (Risks), CB overview (in Japanese): "信用のリスク" (Credit risk), "価格変動リスク" (Price fluctuation risk), and "流動性リスク" (Liquidity risk). ↩ ↩² ↩³

22. Financial Services Agency, "投資信託等の販売会社による顧客本位の業務運営のモニタリング結果について" (Results of monitoring customer-oriented business conduct by distributors of investment trusts and other products, in Japanese) (June 2022), page 29, the paragraph beginning "こうした EB 債の商品性は" (The product characteristics of such exchangeable bonds) and note 27. ↩

23. Japan Securities Dealers Association, "EB債（他社株転換可能債券）の特徴やリスクとは？" (What are the features and risks of exchangeable bonds?, in Japanese), page 1, "１．そもそもＥＢ債とは？" (1. What is an exchangeable bond?). ↩