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In the case where the only discount rate one has is not a zero-rate (neither taken from a zero-coupon bond nor converted from a swap rate to a zero-rate through bootstrapping) but an annually-compounded rate (for example if the benchmark is a US Treasury bond with annual coupons) and one only has its yield to maturity, one would use an annually ...
Bond valuation is the process by which an investor arrives at an estimate of the theoretical fair value, or intrinsic worth, of a bond.As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate.
In finance, bootstrapping is a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. bonds and swaps. [ 1 ] A bootstrapped curve , correspondingly, is one where the prices of the instruments used as an input to the curve, will be an exact output , when these same instruments ...
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.
When the yield curve is flat, the capital gain is predicted to be much less, and there is little variability in the bond's total returns over time. As market rates of interest increase or decrease, the impact is rarely the same at each point along the yield curve, i.e. the curve rarely moves up or down in parallel.
Yield to put (YTP): same as yield to call, but when the bond holder has the option to sell the bond back to the issuer at a fixed price on specified date. Yield to worst (YTW): when a bond is callable, puttable, exchangeable, or has other features, the yield to worst is the lowest yield of yield to maturity, yield to call, yield to put, and others.
Modified duration is measured as the percent change in price per one unit (percentage point) change in yield per year (for example yield going from 8% per year (y = 0.08) to 9% per year (y = 0.09)). This will give modified duration a numerical value close to the Macaulay duration (and equal when rates are continuously compounded).
For example, under the assumption of a flat yield curve one can write the value of a coupon-bearing bond as () = =, where C i stands for the coupon paid at time t i. Then it is easy to see that Then it is easy to see that