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|Subject: YTM vs. CAGR||Date: 12/2/2009 2:26 PM|
|Author: junkman02||Number: 29281 of 35803|
How to interpret reported bond returns has been on my mind for a while, especially the difference between the YTMs for zeros versus those for couponed bonds. So I queried Investopedia to see what they might have to say.
What Does Yield To Maturity - YTM Mean?
The rate of return anticipated on a bond if it is held until the maturity date. YTM is considered a long-term bond yield expressed as an annual rate. The calculation of YTM takes into account the current market price, par value, coupon interest rate and time to maturity. It is also assumed that all coupons are reinvested at the same rate. Sometimes this is simply referred to as "yield" for short.
What Does Compound Annual Growth Rate - CAGR Mean?
The year-over-year growth rate of an investment over a specified period of time. The compound annual growth rate is calculated by taking the nth root of the total percentage growth rate, where n is the number of years in the period being considered. CAGR isn't the actual return in reality. It's an imaginary number that describes the rate at which an investment would have grown if it grew at a steady rate. You can think of CAGR as a way to smooth out the returns.
For now, set aside the fact that brokers might report YTMs using a 360-day year (instead of a more reasonable “Actual/actual”, which would include leap days). Also, set aside the possibility that coupons are being reinvested at the coupon rate (which is a near impossibility if the coupon-rate is higher than the prevailing, benchmark interest-rate.)
In my experience, if a couponed bond is priced near par, the YTM a broker will report, and the YTM I will calculate using Excel, will be very close. But when the bond is priced at a steep premium or discount, then my results differ significantly from theirs. I trust my own numbers, not theirs, so the fact of a difference is simply an annoyance, and I make the following mental adjustments: If I’m buying at discount, my yield will be higher than they report. If I’m buying at a premium, my yield will be lower than they report.
So far, so good. But here’s the problem and the reason for this post. If the bond is a zero, then brokers report a YTM that is actually a CAGR. Don’t trust my word on this. Run the numbers yourself. But here is a concrete example.
This morning, a lot of 25 of Toyota’s 0’s of 25 came onto