Calculate forward rate zero coupon bond
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We now return to the question we posed earlier, namely: Is the yield to maturity what you will actually earn? Assume the spot and forward rates given in the example 1 above.
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To earn the yield to maturity over the life of the investment requires that investors reinvest their coupon payments at the yield to maturity. The problem, however, is that no such interest rate is available in the market.
Instead, only spot interest rates are available. These spot rates, however, imply a set of forward rates over the periods of time that the coupon payments need to be reinvested.
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As a result, we can compare two courses of action:. Reinvest coupon payments at the forward interest rates implied from the spot rates.
Timing of Cash Flow: This is because the upward sloping yield curve in the example means that the implied forward rates for Years 2 and 3 must be higher than in Year 1. Therefore, compounding at these rates results in more interest than does compounding at some weighted geometric average of all spot rates. We can now return to the question we posed earlier: What are the interest rates at which coupons can be reinvested?
Exactly how you interpret this information is the subject matter of Topic 3. For example, under the unbiased expectations theory, the forward interest rate gives you an unbiased estimate of the rate at which you expect to be able to reinvest your coupons.
We can make two observations about these forward rates. First, these rates are not guaranteed, because the yield curve itself may change. You will see later, however, that if you can trade forward contracts, you can guarantee or "lock in" these rates in the future. Second, even if the yield curve does not change over time, the yield to maturity is only applicable as an assumed reinvestment rate when the yield curve is horizontal.
The yield to maturity has the advantage of simplicity for ranking returns from fixed-income securities.
Forward rate
However, the yield to maturity is a hypothetical construct that, even with interest rate certainty, you cannot obtain in the marketplace for any security other than a zero-coupon bond. Exercises Interactive FTS. The simple timeline in Figure 3.
Now, compare two strategies: It is denoted as follows: It is computed by solving the equation: In general, the implied forward interest rate between-period t and Period T , calculated today, solves the equation: Example 1 Assume the following 3 year term structure of spot interest rates: This yields: Or, by taking the square root of each side: Similarly, the three year spot rate is the geometric average of the one-, two-, and three year spot and forward rates: For the present example, this results in: The yield curve window displays the new yield curve as follows: For the current problem these are: Clicking on the Numeric button on the Forward Rate window displays the forward rates numerically: This means find F 4,2.
So, if I understand this correctly, when the forward expires in 4 years, you can buy or sell a 2-year zero at In any case, you need to calculate the 2-year forward rate starting 4 years from today implied by the current spot rates and compare that to the 2-year rate implied by the price on the zero. Skip to main content. Be prepared with Kaplan Schweser. Twitter Facebook LinkedIn. Search form.
6 days ago For simplicity, consider how to calculate the forward rates for zero-coupon bonds. A basic formula for calculating forward rates looks like this. The forward rate is the future yield on a bond. It is calculated using the yield curve . For example Forward rate calculation[edit]. To extract the forward rate, we need the zero-coupon yield curve. We are trying to find the future interest rate r 1, 2.
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Spot Rates, Forward Rates, and Bootstrapping
Compare Packages. Smagician Apr 16th, 1: This makes no sense: Please recheck your numbers. Simplify the complicated side; don't complify the simplicated side.