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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:
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.
A Technical Note on the Smith-Wilson Method, The Financial Supervisory Authority of Norway, (1 July 2010) Lagerås, Andreas & Lindholm, Mathias.
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. For zero-coupon bonds selling at a discount, the ...
Consider a 30-year zero coupon bond with a face value of $100. If the bond is priced at a yield-to-maturity of 10%, it will cost $5.73 today (the present value of this cash flow). Over the coming 30 years, the price will advance to $100, and the annualized return will be 10%. This is incorrect.
To extract the forward rate, we need the zero-coupon yield curve.. We are trying to find the future interest rate , for time period (,), and expressed in years, given the rate for time period (,) and rate for time period (,).
Some zero coupon bonds are inflation indexed, and the amount of money that will be paid to the bond holder is calculated to have a set amount of purchasing power, rather than a set amount of money, but most zero coupon bonds pay a set amount of money known as the face value of the bond. Zero coupon bonds may be long or short-term investments ...
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.