What should be the logical steps to solve the question below? Thanks!

Q) All else equal, which of the following is *least likely* to increase the interest rate risk of a bond?

a- a longer maturity

*b- inclusion of a call feature*

c- a decrease in the YTM

A) my attempt:

a - a longer maturity: with longer maturity, a bond is susceptible to **higher** interest rate risk. It also increases the duration of a bond given that it takes longer to get the cash flow back.

b- with a call feature, the *yield* should be higher? So given the higher yield, the interest rate risk of a bond is lower?

c - not quite sure about this one. if YTM decreases, yield is lower, so higher interest rate risk?

At high interest rates, callable bonds behave almost identically to option-free bonds. At low interest rates, the call feature puts a cap on the bond price. Because the price cannot rise as much as it can for an option-free bond, the interest rate risk is lower.

As the YTM decreases (for an option-free bond, the duration increases, so the interest rate risk increases. The easiest way to see this is to draw the price-vs-YTM curve: the price decline is greater for lower interest rates than it is for higher interest rates. (Yes: I know that the effective duration isn’t the slope of the price-vs-YTM curve, but the curve gives a nice visual reminder of the effect. If you want to be picky about it, effective duration is the slope of the ln(price)-vs-YTM curve. Oh . . . I see you no longer want to be picky about it.)

Perfect, got it. Thanks so much!!