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The yield to maturity (YTM), book yield or redemption yield of a fixed-interest security is an estimate of the total rate of return anticipated to be earned by an investor who buys it at a given market price, holds it to maturity, and receives all interest payments and the capital redemption on schedule. [1] [2]
Yield curves are usually upward sloping asymptotically: the longer the maturity, the higher the yield, with diminishing marginal increases (that is, as one moves to the right, the curve flattens out). The slope of the yield curve can be measured by the difference, or term spread, between the yields on two-year and ten-year U.S. Treasury Notes. [7]
The yield to maturity (YTM) is the discount rate which returns the market price of a bond without embedded optionality; it is identical to (required return) in the above equation. YTM is thus the internal rate of return of an investment in the bond made at the observed price.
Holding that bond for one year (to maturity) would result in a yield of 5%. That would be its coupon yield or nominal yield. Current Yield – But now consider how yield changes if the price of ...
Expression (3) which uses the bond's yield to maturity to calculate discount factors. The key difference between the two durations is that the Fisher–Weil duration allows for the possibility of a sloping yield curve, whereas the second form is based on a constant value of the yield , not varying by term to payment. [10]
Par yield is based on the assumption that the security in question has a price equal to par value. [5] When the price is assumed to be par value ($100 in the equation below) and the coupon stream and maturity date are already known, the equation below can be solved for par yield.
The forward rate is the future yield on a bond. It is calculated using the yield curve . For example, the yield on a three-month Treasury bill six months from now is a forward rate .
Of course, the yield curve is most unlikely to behave in this way. The idea is that the actual change in the yield curve can be modeled in terms of a sum of such saw-tooth functions. At each key-rate duration, we know the change in the curve's yield, and can combine this change with the KRD to calculate the overall change in value of the portfolio.