Why is YTC lower than YTM, isn't it supposed to have a higher Yield to compensate investors' risk of the call?

Jorge Fullen is evaluating a 7%, 10-year bond that is callable at par in 5 years. Coupon payments can be reinvested at an annual rate of 7%, and the current price of the bond is $106.50 per $1,000 of face value. The bond pays interest semiannually. Should Fullen consider the yield to first call (YTC) or the yield to maturity (YTM) in making his purchase decision?

A) YTM, since YTM is greater than YTC.
B) YTC, since YTC is less than YTM.
C) YTC, since YTC is greater than YTM.

The bond is trading at a premium, and if the bond is called at par that premium would be amortized over a shorter period, resulting in a lower return. The lower return is the more conservative number, so the YTC should be used. You could use your financial calculator to solve for YTC assuming 10 semiannual coupon payments of $35 (FV = 1,000; PMT = 35; PV = –1,065; N = 10; solve for i = 2.75; × 2 to get annual YTC = 5.5%). Calculation of YTM would use the same inputs except N = 20, to get YTM = 6.12%

So the answer here is whichever is lower. The yield we’re guaranteed to realize is the YTC.

However, there is something in this question that goes against my intuititions and understanding of FI. Why is YTC lower than YTM, aren’t investors supposed to require a higher yield when there is a call option embedded? Or maybe this bond is priced in a way that goes against that logic (premium)?

Why would you call a bond and pay your opponent (i.e., the bondholder) a higher yield?

Because the bondholder gave you the possibility to call the bond? The bonholder is exposed to reinvestment risk in case of lower interest rates in the future, so the bond issuer compensates that by providing a higher yield.

When a bond is sold with a put option (advantage to the bondholder), the yield required by the bond holder is lower. The opposite is true, when a bond is sold with a call option (advantage to the issuer), the bondholder requires higher yield.

So . . . if the car dealer gives you the option of buying this junker today only . . . at a higher price than normal . . . you’ll jump at it?

Let’s talk. I have some cars I need to unload.

s2000magician i’m confused.
Just to make things clear:
From a bondholder’s perspective (investor’s perspective), a bond with an embedded call option is riskier than a bond with no embedded call option. So Investors require a higher yield on bonds with embedded call options.

Ok. I just got it LOL. I should see YTC as just a bond with same characteristics but with lower maturity, so it makes sense that investors require a lower yield on it.

I mistakenly thought of this as YTC = Bond with embedded call option, and YTM = Bond with no embedded call option. Which is wrong. YTC = Yield if we’re sure that the bond will be redeemed (called) in 5 years, YTM = Yield if the bond is redeemed in 10 years.

Thanks S2000magician for clearing this up.

My pleasure.

Now . . . about them cars . . . .

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You are not wrong in your intuition that callable bonds are not in favor of the bond buyers. For that, the issuer usually gives a higher coupon. But the decision to call or not call depends on how the market interest rates evolve over time, after the issue.