# CFA Level 1 Exam: Callable bond vs Putable bond vs Convertible bond

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Bond Options

## Callable Bonds, Putable Bonds, Convertible Bonds

There are 3 types of options that can be embedded in bonds: call options, put options, and conversion options. Therefore, we distinguish 3 types of bonds with embedded options: callable bonds, putable bonds, and convertible bonds, respectively. The value of an option influences the value of the bond.

### Defining an Option

An option is a derivative instrument, which means that its value depends on the value of some underlying asset. The underlying asset can be a stock, a market index, an interest rate, and so on. If an option is embedded in a bond, the value of the option depends on the price of the bond, which means that it depends on interest rates.

An option gives one party a right to buy or sell an underlying asset in the future and the other party – an obligation to sell or buy the underlying asset in the future. This means that the latter party is obligated to sell or buy the underlying in the future if the former party requests it. If the option holder decides to use his right, we say that he exercises the option.

### Call Option vs Put Option

Depending on whether an option involves a right to buy or a right to sell the underlying, we distinguish two types of options:

- a call option, and
- a put option.

A call option gives the option buyer a right to buy an underlying asset in the future at a specified price from the option seller. In other words, the option seller is obliged to sell the underlying on the buyer's request.

A put option gives the option buyer a right to sell an underlying asset in the future at a specified price to the seller of the option. The seller of a put option is obliged to buy the underlying on the option buyer's request.

In the case of bonds, a put option is the right of the bondholder to sell back the bond to the issuer and the call option is the right of the issuer to buy back the bond from the bondholder.

### Conversion Option

Sometimes there is also a conversion option embedded in the bond.

The bondholder of a bond with a conversion provision can exchange the bond for a specified number of ordinary shares issued by the issuer. A conversion option is beneficial to the bondholder (exception: CoCos) because it gives him a right and not an obligation to exchange the bond for the shares.

The terms related to convertible bonds that you should know include:

- the conversion price,
- the conversion ratio,
- the conversion value,
- the conversion premium, and
- the conversion parity,

## How an Embedded Option Affects the Value of a Bond?

An embedded option usually has some value. So, if an option is embedded in a bond, it affects both the bond’s value and the required yield. Note that a put option and a conversion option are beneficial to the bondholder, while a call option is beneficial to the issuer.

So, a call option granted to the issuer results in a lower price of the bond. The bondholder is willing to pay less for the callable bond and requires a higher rate of return:

the value of the callable bond = the value of the bond without an embedded option – the value of the call option

If an option is granted to the bondholder, like in the case of a put option or a conversion option, he values the bond with the embedded option more and so is willing to pay a higher price for the bond. It also means that he requires a lower rate of return.

the value of the bond with an embedded option beneficial to the bondholder = the value of the bond without an embedded option + the value of the option

The current price of a bond with an embedded option is equal to USD 84. The price of the same bond without an embedded option is equal to USD 92. Is the option *most likely* beneficial to the bondholder or to the issuer?

- Issuer
- Cannot say
- Bondholder

**Answer: A**

Because the price of the bond without an embedded option is greater than the price of the bond with an embedded option it means that the option value is subtracted from the price of the bond without an embedded option. Such an option is not beneficial to the bondholder and is granted to the issuer.

The yield to maturity for a bond with an embedded option is equal to 9%. The YTM for the same bond without an embedded option is equal to 8%. Is the option beneficial to the bondholder or to the issuer?

- ...
- ...
- ...

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## Exercise Styles of Options:

American Style, Bermuda Style, and European Style

Generally, there are 3 exercise styles of options:

- American style,
- Bermuda style, and
- European style.

American call and American put can be exercised anytime between the first call date or the first put date, respectively, and the bond maturity date. Bermuda-style options can be exercised only on given dates. Finally, European style options can be exercised only on one given date.

## CFA Level 1 Exam Takeaways for Callable, Putable, and Convertible Bonds

- There are 3 types of options that can be embedded in bonds: call options, put options, and conversion options.
- A call option gives the option buyer a right to buy an underlying asset in the future at a specified price from the option seller.
- A put option gives the option buyer a right to sell an underlying asset in the future at a specified price to the seller of the option.
- The bondholder of a bond with a conversion provision can exchange the bond for a specified number of ordinary shares issued by the issuer.
- In the case of a put option, the bondholder will be eager to exercise the option if interest rates increase and the bond price decreases. In the case of a call option, the issuer will be willing to exercise the option if interest rates decrease and the bond price increases.
- Options usually have some values and these values affect bond prices. If the option is beneficial to the bondholder, we add the value of the option to the price of the option-free bond (aka. straight bond), and if the option is beneficial to the issuer, we subtract the value of the option from the price of the option-free bond.
- If the call value increases, the callable bond value decreases and YTM increases. If the put value increases, the putable bond value also increases and YTM decreases.
- If the volatility of the market discount rate increases, both the call value and the put value also increase.
- There are 3 exercise styles of options: American style, Bermuda style, and European style.