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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 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. Since YTM can be used to price a bond, bond prices are often quoted ...
The concept of current yield is closely related to other bond concepts, including yield to maturity (YTM), and coupon yield. When a coupon-bearing bond sells at; a discount: YTM > current yield > coupon yield; a premium: coupon yield > current yield > YTM; par: YTM = current yield = coupon yield.
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 ...
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]
The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, ... The discount factor formula for period (0, t) ...
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.
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: