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I am trying to synthesize everything I have learned about callable and putable bonds. Is the following information accurate?

  • A callable bond bought at a discount will have yield rate greater than coupon rate. For a fixed redemption value, it will be redeemed as late as possible. Compared to an equivalent bond without a call, it will be priced the same.
  • A callable bond bought at a premium will have yield rate lower than coupon rate. For a fixed redemption value, it will be redeemed as early as possible. Compared to an equivalent bond without a call, it will be priced lower.
  • A putable bond bought at a discount will have yield rate higher than coupon rate. For a fixed redemption value, it will be redeemed as early as possible. Compared to an equivalent bond without a put, it will be priced higher.
  • A putable bond bought at a premium will have yield rate lower than coupon rate. For a fixed redemption value, it will be redeemed as late as possible. Compared to an equivalent bond without a put, it will be priced the same.
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I see a few questionable things:

  • Compared to an equivalent bond without a call, it will be priced the same.

Adding a call option reduces the value of the bond since it provides optionality to the issuer (adds risk to the buyer). A callable bond would have to be sold at a deep discount (have very little chance of being called) to be priced the same as the equivalent non-callable version.

Similar for the putable bond - it adds optionality to the purchaser and thus increases the price.

  • it will be redeedmed as early/late as possible.

Not sure what this means. Options don't have to be exercised, but they could be exercised as soon as the strike of a put/call is above/below the market price.

Plus you can generalize one thing even further:

  • any bond bought at a discount will have a yield greater than the coupon rate (since you get the coupons plus the gain between the redemption value and the purchase price)
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  • For your first bullet point, my reasoning is that the coupon rate is lower than the yield rate, so it is in the seller's best interest to continue paying coupons as long as possible and not call the bond until the maturity date. If they do call the bond, then this will increase the yield rate of the bond, which is a detriment to the seller. I should have noted that I'm assuming a fixed interest rate.
    – kccu
    Feb 19, 2020 at 1:11
  • My study materials say "A callable bond bought at a discount is worth the same as an otherwise equivalent bond bought at a discount without a call. ... Since a bond issuer will want to pay the least amount possible in terms of PV, they will call the bond at maturity. ... This is effectively the same thing as a discount bond without a call, since the bond's redemption payment will always happen at the maturity date."
    – kccu
    Feb 19, 2020 at 1:13

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