Callable, putable and convertible bonds

Which embedded option helps whom?

A contingency provision allows an action if an event occurs. The most common ones give a right, not an obligation, to either the issuer or the bondholder. They are called embedded options because they behave like option contracts but cannot be traded apart from the bond. Their value is the price of the bond with the provision minus the price of an otherwise identical bond without it.

Contingency provisionsa clause that allows an action if an event occurs

• Benefit the issuer Memorize the issuer holds the option
  • Callable bond Memorize issuer may redeem early; higher yield, price capped
    • Fixed-price call Memorize schedule of call prices after a protection period
    • Make-whole call Use it price from a government yield plus a spread; rarely used
• Benefit the investor Memorize the bondholder holds the option
  • Putable bond Memorize sell back at the put price (usually par); lower yield, price floor
  • Convertible bond Memorize swap for shares at the investor's choice; much lower coupon
  • Contingent convertible (CoCo) Memorize bank bond; converts automatically on a capital trigger; higher yield
• Warrant Use it attached, not embedded: trades separately

	Callable	Putable	Convertible
Option held by	issuer	investor	investor
Used when	rates fall (refinance cheaper)	rates rise or credit weakens	share price rises
Value vs straight bond	straight − call	straight + put	straight + conversion option
Yield vs straight bond	higher	lower	much lower
Price behavior	capped near the call price when yields fall below the coupon	floored at the put price when yields rise above the coupon	tracks the shares when they are well above the conversion price

How do callable bonds work?

A callable bond lets the issuer redeem all or part of the bond before maturity. The issuer wants the flexibility to refinance if rates fall.

A bond usually has a call protection period in which it cannot be called, followed by a call period with a schedule of call price s that usually steps down towards par. This is a fixed-price call .

Investors bear call risk : the maturity is uncertain, price gains are capped and, when the bond is called, they must reinvest at lower rates. They are paid for it with a higher yield than on an equivalent bond that cannot be called.

How much the call matters depends on the yield. If the yield to maturity (YTM) is above the coupon, refinancing would cost more than the current coupon, so the issuer has no reason to call and the bond moves much like a straight bond. As the YTM falls below the coupon, the callable bond’s price is effectively capped at the call price while the straight bond’s price keeps climbing.

A make-whole call is different: the issuer pays a price based on the yield of a government bond of similar maturity plus a small spread. That price is usually well above the market price, so make-whole calls are rarely used and have little economic effect on either side.

How do putable bonds work?

A putable bond gives the investor the right to sell the bond back to the issuer at a set price, usually par, on set dates. If rates rise and prices fall, the investor can put the bond and reinvest at higher yields. The issuer must then refinance earlier, at worse terms.

Because the put has value to the investor, a putable bond costs more and yields less than an equivalent straight bond. When the YTM is below the coupon, the put is not worth using and the bond behaves like a straight bond. When the YTM rises above the coupon, the put price sets a floor under the price.

A poison put is a put that investors can use if the issuer is taken over. It makes the takeover costlier because it creates an immediate claim on cash.

How do convertible bonds work?

A convertible bond gives the investor the right to exchange the bond for a set number of the issuer’s shares. The share price at which the exchange happens is the conversion price . If exercised, the option replaces debt with equity, rather than retiring debt as a call or put does.

$$\text{CR} = \frac{\text{Par}}{\text{Conversion price}}$$

$$\text{CV} = \text{CR} \times \text{Share price}$$

The conversion ratio is the number of shares one bond converts into. The conversion value is what those shares are worth now. The conversion premium measures how far the conversion price is above today’s share price.

$$\text{Prem} = \frac{\text{Conversion price} - \text{Share price}}{\text{Share price}}$$

When the share price is well below the conversion price, a convertible behaves like straight debt. When it is far above, it behaves like the shares. Growth companies use convertibles to pay a low cash coupon, and many convertibles are also callable so the issuer can force conversion once the shares have risen.

A warrant is an option to buy shares that is attached to a bond but trades separately. It is not embedded, and is used to enhance the yield investors get.

Contingent convertible bonds (CoCos) are bank bonds that convert into equity, or are written down, automatically when a regulatory capital ratio falls below a set minimum. Standard convertibles convert on the upside at the investor’s choice; CoCos convert on the downside, so they pay a higher yield. The trigger is a capital breach, not a share price level.

Go deeper Why a call is worth most when yields are far below the coupon

A call is a right to refinance. It only pays when the issuer can borrow at a clearly lower rate than the coupon, which is when yields have fallen well below it. That is why investors in callable bonds look at the yield to worst, the lowest yield across the maturity and every call date, covered in the yield lessons.

Go deeper Embedded options and duration

A callable bond’s price is capped as yields fall, so its price becomes less sensitive to yield changes than its maturity suggests. A putable bond’s price is floored as yields rise, with the same effect on the other side. The curve-based risk measures module handles this with effective duration.

Go deeper Options are rights, not obligations

The holder of an option chooses whether to use it; the other side must go along. In a callable bond the issuer holds a call on the bond. In a putable bond the investor holds a put. The derivatives topic develops the pricing of options in general.