# Callable and putable bonds

In rising rates environment, callable and putable outperform the non-callable?

I’m confused by this statement.

when rates rise -

a callable bond falls less than a non-callable bond in value due to the negative convexity. (which is introduced by the presence of the call option - ceiling to which price may otherwise have risen).

putable bond is put back to the bond issuer. so it will outperform the non-option bond.

Suppose that you have three bonds:

• C is a 10-year, 6% coupon, semiannual pay, \$1,000 par bond, callable at 104
• O is a 10-year, 6% coupon, semiannual pay, \$1,000 par, option-free bond
• P is a 10-year, 6% coupon, semiannual pay, \$1,000 par bond, putable at 96

At a 4% yield,

• Bond C trades at less than \$1,040
• Bond O trades at \$1,164
• Bond P trades at \$1,164

At an 8% yield,

• Bond C trades at \$864
• Bond O trades at \$864
• Bond P trades at more than \$960

Thus, if yields increase from 4% to 8%,

• Bond C’s price drop is less than \$176, or less than about 17%
• Bond O’s price drop is \$300, or about 26%
• Bond P’s price drop is less than \$204, or less than about 18%

So the callable bond and the putable bond outperform (i.e., have a smaller loss than) the option-free bond.

Both good answers but my way of remembering is that options have either positive or negative value to the issuer and holder. These options change in value with interest rates as well. So in a rising environment the put option will increase in value counteracting the decline in bond price. The callable bond will have the effect of a decrease in the call option value which is held by the issuer, which is a positive for the holder. The option free bond will not have these counter effects therefore will see their price decline due to the interest rate change. The holder should also pay this premium up front for the putable and get a discount for the callable.