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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 market interest rate. So the market price of a 17-year bond with a duration of 7 would fall about 7% if the market interest rate (or more precisely the corresponding force of interest ...
Consider a bond with a $1000 face value, 5% coupon rate and 6.5% annual yield, with maturity in 5 years. [26] The steps to compute duration are the following: 1. Estimate the bond value The coupons will be $50 in years 1, 2, 3 and 4. Then, on year 5, the bond will pay coupon and principal, for a total of $1050.
The bonds are purchased from the market at $985.50. Given that $2.00 pays the accrued interest, the remainder ($983.50) represents the underlying value of the bonds. The following table illustrates the values of these terms. The market convention for corporate bond prices assigns a quoted (clean price) of $983.50.
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The Z-spread of a bond is the number of basis points (bp, or 0.01%) that one needs to add to the Treasury yield curve (or technically to Treasury forward rates) so that the Net present value of the bond cash flows (using the adjusted yield curve) equals the market price of the bond (including accrued interest). The spread is calculated iteratively.
The net return on bonds is the sum of the interest payments and the capital gains (or losses) from their varying market value. A rise in interest rates causes aftermarket bond prices to fall, and that implies a capital loss from holding bonds. Accordingly, the return on bonds can be negative. Thus, people may hold money to avoid the loss from ...
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:
The more curved the price function of the bond is, the more inaccurate duration is as a measure of the interest rate sensitivity. [2] Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest rate, i.e. how the duration of a bond changes as the interest rate changes. [3]