# Bond yield to maturity vs current interest yield

How close is yield to maturity usually to current interest yield? Can I use yield to maturity to approximate current interest yield of a bond index?

I am trying to calculate bond index price returns and I only have yield to maturity and average coupon yield. Can I just divide average coupon yield by yield to maturity to get a "reasonable" approximation of bond index price, to get price returns with ~10% error?

Not really. For infinite maturity bonds we have $Price = coupon/yield$ so your approximation is actually correct. However for short dated bonds it is not a good approximation. For example , a 1 year annual pay bond gives $Price=(1+coupon)/(1+yield)$ which is very poorly approximated by $coupon/yield$.

• So would a better way to make the estimate be to use the "present value of an annuity formula"? I.e. Price = Coupon x ((1 - (1 / (1 + yield) ^ n)) / yield) + principal / (1 + yield) ^ n ? Where we assume an annual payment on the bond, and "n" is the number of years till maturity? – rinspy Jun 12 '17 at 13:42