# Callable Bond vs. Option-Free Bond

In Schweser, LOS 34.f, there is an example question

The value of an option-free bond today is stated to be \$102.99, while the value of a callable bond today is stated to be \$102.24, aka LESS than the option-free bond.

Why is this the case? I thought to investors, callable bonds were less attractive. If that’s the case, why do I get to pay less (102.24 < 102.99) to earn the same cash flow? What am I missing here?

Thanks uWu~

With a callable bond, there is a risk to the investor as the issuer can exercise the option to call back the bond when the current market value > exercise price. For example, if the exercise price (or call price) is \$100, then at \$102.24, the issuer can call back the bond and just pay \$100 to the investor. Investor loses \$2.24 and the \$100 has to be reinvested at a lower rate.

hi again fino

i get that, but my question is why on earth would the same bond be priced lower when it has an embedded option? shouldn’t it be priced higher than the option free bond?

Put yourself in the shoes of a bond investor who is about to choose between a callable bond and an option-free bond (both with the same coupon and tenor and par value).

When you get more benefits from the asset, you will pay more for it (value it higher). When you have disadvantages in holding the asset, you pay less for it (value it lower).

So in the case of the callable bond, the call option is a disadvantage to the investor, and with that uncertainty, means the investor will want a higher yield from the callable bond (relative to the option free bond). Higher yield translate to a lower price.

That’s why:

Value ~of ~callable ~bond = Value ~of ~option ~free~bond - Value ~of ~call ~option

But for a putable bond, the put option is a benefit to the investor, so the investor will pay a premium for it (hence value of putable bond > value of option free bond)

okay, with the relation of bond price/yield i get it now. i was just thinking before that the price of the bond equals the same cash flow, so all things held equal, the lower the price the better

thanks

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