YTM on a leveraged bond position, bond not trading at par
I have to build a tool for my clients so they can see the YTM for a bond taking into account the leverage we offer them. I will keep it simple for the purpose of this discussion.
Rate Charged on Loan= 0
Bond YTM 5% trading at par, dirty price=clean price=100
The YTM of the position in this case is simply 5*(200/100)=10%
The problem I am facing is when the bond is not trading at PAR, this simple calculation no longer holds, I confirm this by laying out the cash flows of the bond along with the leverage (double the coupons, at maturity make a loss/gain which gets magnified with leverage). While doing an IRR on the cashflows is the correct YTM of the position, I do not want to do this approach as it complicates the understanding for the clients. Is there a mathematical way i can arrive at the solution?
Bonus question, what is exactly causes this issue when bond is not trading at PAR, I know it is the nature of the IRR but I just cant put an explanation together…