Yield to Maturity Formula

[dtrynoski]

Does anyone know where in the CFA materials the Yield to Maturity Formula is? I’m looking for the actual formula to calculate it by hand (using trial and error) rather than the calculator method. Looked through all my L1 - L3 books and can’t find it. Could have sworn It was somewhere in the material…
Thanks in Advance

 

[bchad]

YTM is simply the IRR of bond cash flows, assuming everything gets paid in full on time as scheduled. So look for the IRR formula and substitute interest and principal payments for cash flows (remember that the current bond price is CF0)
calculating by hand sounds like a whole lot of fun.

 

[Would You Look]

It will likely be in your L1 quant materials under internal rate of return since that’s all it is.

 

[DoubleDip]

but if you have to have it….
PV of the bond = sum from i = 1 to n (where n is the total number of cashflows) of the period i cashflows (CF) discounted by (1+ytm)^i. You have to know PV and all i cash flows, then solve for the fixed ytm that equates the PV equal to the right hand side
see equation 1 here
https://www.fidelity.com/learning-center/fixed-income-bonds/yield-maturi...

 

[marco096]

why would you even want to calculate it by hand… such a waste of time

 

[bayofpigs]

I’m curious to know how you do this for a mortgage in terms of calculating its current price given that they are illiquid and don’t have secondary market to determine its current price. So my question is, how do you determine the current price of a commercial mortgage?
so if you are a lender and you lent $20 million for 5 years at a 25 year amort at a rate of 3.25%, and then decide to get to sell it, how do you determine it’s current value?

 

[bchad]

Well, I guess you’d choose a bunch of discount rates and compute the NPV of the mortgage payments, and then figure out what kind of spread over treasuries seems best to reflect the level of credit and prepayment and liquidity risk.
A more advanced method would be to calculate the spread over the yield curves at various maturities and discount each payment by the key rate plus spread.