Since i got some strange results, i wanna check if i'm prolly false .Yield:When i got bond with let's say 6% coupon and a principle of 100, and a marketvalue of 95, current yieldwould be 6.316 ( 6*100/95 ). Yield to maturity would be more complicated, solving for a a rate, for whichall future cash flows give the current market price, here 95. Hereby maturity is important. For our example,the YTM would be 6.702.Spread:Spread is the difference between the yield? and the current risk free interest rate (or what i think it is )?Yield or YTM?If i wanna calculate a virtually risk free bond, a formula could be c/r + exp(-rT)*(p-c/r) , right?Since this is not the result from yield solved for price, i guess i have to use ytm for spreads?Thx for your answers, Flex

First of all, forget current yield. It's not useful for anything.Any difference of interest rates is called a spread. The credit spread is the difference between the Yield to Maturity and a risk-free bond with the same cash flows. The maturity spread is the difference between the Yield to Maturity and short-term obligations by the same borrower (actually, this is usually defined in a slightly more complicated model-dependent way, but that's the general idea). You can compute lots of spreads. In most cases, Yield to Maturity is one of the interest rates, never current yield. But you can also compute spreads with Yield to Worst Call or other things.Your formula is nonstandard. Usually with bonds you use interest rates compounded at the coupon interval. In that case you don't have exp(-r*t) but (1+r)^(-t), with t measured in coupon periods and r the simple interest rate per coupon interval. If your bond were semi-annual, for example, you would have Price = 3%/r + (1 - 3%/r)*(1+r)^(-n), where Price is per $1 face and r is a six-month rate. To annualize to a bond-equivalent rate you would use (1+r)^2 - 1.If you are not valuing on a coupon date you can either use the formula above with a fractional r, but that will not mesh with market convention. The convention is to figure the price as of the last coupon date and add linear accrued interest.

Thx for your answer, aaron, i to thought that current yield was of limited use. So if i havea bond and a risk free interest rate, i have to calculate ytm to gainspreads. So 1) What is the easiest way to calculate this? Generally said, it is to solve the equationall cash flows discounted at yield to maturity equals the current price for ytm. I can solvethis, but what is the simpliest way ? I only consider yearly payments.2) How do you do time-adjustments when you calculate daily ytm? e.g. after 50 dayspassed, you use t= 9 + (365-50)/365 instead of t=10 (and resp. for every point of cash flow)?Your point about the risk free bond is ofcos true Thx, Flex

There is no closed form solution for yield to maturity in the general case, you need an interative algorithm. The simplest one is Newtonian iteration or a variant. If you're writing a general routine, watch out for cash flows with multiple solutions. You can get one solution each time the cash flows change sign. Normally that's once, you pay money to buy a bond and receive cash flows thereafter.You can use factional periods as you suggest. However, the answer will not be exactly correct. You could go to a daily interest rate and compute all times in days. That will be exact, but will not match market convention. And if you do it, you might as well go all the way to continuously compounded so you don't have to worry about intervals any more. Market convention requires a computation of accrued interest in between coupon dates.