Calculating YTM for a PTC with Monthly Payouts:
The YTM for a PTC is essentially its *current yield* adjusted for the reinvestment of the monthly payouts. We can find this through an iterative process, often solved using numerical methods such as the Newton-Raphson method, rather than a direct formula. Here's the basic concept:
* Present Value (PV): This is the current market price of the PTC.
* Periodic Payment (PMT): This is the monthly cash payout.
* YTM (r): This is the unknown we are solving for. It represents the periodic yield (monthly in this case). The annual YTM would then be 12*r.
The equation to solve is:
PV = PMT / r
This is a simplified model, however, assuming the monthly cash payout remains constant and is the only cashflow of the PTC. In reality, PTC's distributions vary over time. Therefore, in order to derive a more accurate YTM a more sophisticated model must be implemented:
PV = Σ PMTᵢ / (1+r)ⁱ for i=1 to ∞
Where:
* PV is the current market price of the PTC
* PMTᵢ is the expected cash flow at time i
* r is the periodic YTM (monthly)
* ∞ Represents the infinite life of the PTC.
Given the infinite sum, this requires a numerical method like the Newton-Raphson method to solve for 'r'. Financial calculators and software packages easily handle this calculation.
Modified Duration:
Modified duration is also not directly applicable to a PTC in the same way it is for a finite-maturity bond. Modified duration measures the percentage change in price for a 1% change in yield. Since a PTC has no maturity, its price sensitivity to interest rate changes is different.
Instead of modified duration, we might consider using a measure of *effective duration*. Effective duration uses a numerical approach to approximate the price sensitivity to interest rate changes. This involves calculating the price of the PTC at slightly higher and lower interest rates and then using the change in price to approximate the duration.
In Summary:
For a PTC with monthly payouts:
* YTM: Cannot be calculated with the standard YTM formula; requires an iterative numerical solution considering the present value, ongoing monthly payouts, and the assumption of constant payouts, or a more realistic method involving expected future cash flows.
* Modified Duration: Not directly applicable; use effective duration as a more suitable measure of interest rate sensitivity. This requires a numerical approach. Software or financial calculators are typically needed to perform these calculations accurately.