Annualizing Yield to Maturity

A client called yesterday asking about annualizing yield to maturity (YTM). Can this be done and if so, how?

One should recall that the Yield to Maturity of a bond is calculated by using the internal rate of return, thus YTM = IRR. IRR is often expressed across a multi-year period (i.e., not annualized) and so YTM would be, too. My first reaction was to suggest that we would use the same approach that we do to annualize time-weighted returns, but I first turned to my colleague John Simpson, who responded as follows:

The yield to maturity is calculated as a “raw” IRR based on the bond’s periodicity, and then the street method is to convert it to an annual yield by multiplying the raw IRR by the payment frequency.

For example, if a bond that pays quarterly has a raw IRR of 2%, then the annual yield to maturity is stated as 4 * 2% = 8%.  That is to say, we do not take 1.02 and raise it to the 4^th power, even though this is, in a sense, more mathematically correct.

If they want an annualized yield to maturity, then what they want (not knowing the context) could be to just take their annual yield, divide by the frequency, and then convert the period IRR to a (compound) annual IRR.  Perhaps this is what they mean.  But, such a yield is not street method and not comparable to commonly quoted yield to maturity figures.

And so the answer is  "yes, we can" and here's the "street method," as summarized by John.

Why someone would want to annualize YTM is unclear to me, but it can be done and apparently is done.