When we are ignoring volatility and simply looking at the change in interest rates, I wanted to know what the NET effect of the putable change is.
If we expect the yield curve to upward slope then rates are rising and bond prices are falling. Therefore, the Put becomes more valuable (increases in the formula above). However, the straight bond moves inversely and therefore decreases as rates rise.
What is the net effect, the putable increases or decreases? Is there a rule for this so that on exam day if something comes up like this, it should be easy marks.
The convexity of a putable bond tells you all of this really. As rates rise, yes, the value of the straight-bond falls and the value of the put option embedded rises. With that said, effective convexity for a putable bond is always positive. Meaning, if interest rates fall the value of the bond will increase by more than what effective duration predicts, and conversely, when interest rates rise the value of the bond will decrease by less than what effective duration predicts. The net effect of rising rates on a putable bond is that its value will fall but the put option embedded serves as a sort of “floor” on price and will only decline so much. Straight-bonds that don’t have the rising put option component in rising interest rate environments would fall more than an otherwise identical putable bond. Hope I’ve helped shed some light. I believe the curriculum has a good illustration of bond convexity for straight/callable/putables… might be worth checking out, those visual always helped me tremendously.
I am still a little unsure what your final answer is though. You said:
The net effect of rising rates on a putable bond is that its value will fall but the put option embedded serves as a sort of “floor” on price and will only decline so much.
So in a MCQ format Q: Rates rise, what happens to the puttable bond?
It’s easier to consider the straight bond value as being constant in the formula and looking at what happens to the option value as interest rates change.
Yes, technically the bond value does lose value as interest rates rise, but unless you’re given additional information about current market price, put premium, etc just keep in mind how the embedded option is affected.
Yes I agree.Interest rates rise: straight bond value decreases, put option increases, total value decreases (but less than callable/straight bond). Ignore my comment above.