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Then continuing by trial and error, a bond gain of 5.53 divided by a bond price of 99.47 produces a yield to maturity of 5.56%. Also, the bond gain and the bond price add up to 105. Finally, a one-year zero-coupon bond of $105 and with a yield to maturity of 5.56%, calculates at a price of 105 / 1.0556^1 or 99.47.
There is a time dimension to the analysis of bond values. A 10-year bond at purchase becomes a 9-year bond a year later, and the year after it becomes an 8-year bond, etc. Each year the bond moves incrementally closer to maturity, resulting in lower volatility and shorter duration and demanding a lower interest rate when the yield curve is rising.
The average duration of the bonds in the portfolio is often reported. The duration of a portfolio equals the weighted average maturity of all of the cash flows in the portfolio. If each bond has the same yield to maturity, this equals the weighted average of the portfolio's bond's durations, with weights proportional to the bond prices. [1]
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:
YTM is thus the internal rate of return of an investment in the bond made at the observed price. Since YTM can be used to price a bond, bond prices are often quoted in terms of YTM. To achieve a return equal to YTM, i.e. where it is the required return on the bond, the bond owner must: buy the bond at price ,
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]
The current yield is the ratio of the annual interest (coupon) payment and the bond's market price. [4] [5] The yield to maturity is an estimate of the total rate of return anticipated to be earned by an investor who buys a bond at a given market price, holds it to maturity, and receives all interest payments and the payment of par value on ...
For instance, a bond paying a 10% annual coupon will always pay 10% of its face value to the owner each year, even if there is no change in market conditions. However, the effective yield on the bond may well be different, since the market price of the bond is usually different from the face value. Yield return is calculated from