Interest Rate Risk of a Bond

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!!

You’re welcome.