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Even though the yield-to-maturity for the remaining life of the bond is just 7%, and the yield-to-maturity bargained for when the bond was purchased was only 10%, the annualized return earned over the first 10 years is 16.25%. This can be found by evaluating (1+i) from the equation (1+i) 10 = (25.84/5.73), giving 0.1625.
The yield will match the coupon rate when a bond is issued and sold at par value. However, if an investor pays less than the par value, their return would be more significant since the coupon ...
Analytic Example: Given: 0.5-year spot rate, Z1 = 4%, and 1-year spot rate, Z2 = 4.3% (we can get these rates from T-Bills which are zero-coupon); and the par rate on a 1.5-year semi-annual coupon bond, R3 = 4.5%. We then use these rates to calculate the 1.5 year spot rate. We solve the 1.5 year spot rate, Z3, by the formula below:
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).
The British pound yield curve on February 9, 2005. This curve is unusual (inverted) in that long-term rates are lower than short-term ones. 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 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 .
It is approximately equal to the percentage change in price for a given change in yield, and may be thought of as the elasticity of the bond's price with respect to discount rates. For example, for small interest rate changes, the duration is the approximate percentage by which the value of the bond will fall for a 1% per annum increase in ...
John Hull and Alan White, "One factor interest rate models and the valuation of interest rate derivative securities," Journal of Financial and Quantitative Analysis, Vol 28, No 2, (June 1993) pp. 235–254. John Hull and Alan White, "Pricing interest-rate derivative securities", The Review of Financial Studies, Vol 3, No. 4 (1990) pp. 573–592.