Yield curve . Consider only bonds with semiannual coupons (two coupons per year)

Question

Yield curve . Consider only bonds with semiannual coupons (two coupons per year). ·The bonds all have face F = 100. 1.4 Let us have three newly issued par bonds, with maturities of 0.5, 1.0, 1.5 years. » You are given the following values for the yields: 30.5 = 4.0 % , no = 4.2%, y1.5 = 4.1%. . Use the formulas in the lectures to compute the values of the discount factors do.5, d1.0 and d.5. State your answers to four decimal places. » Also calculate the continuously compounded spot rates ro.5, r1.0 and r1.s. State your answers as percentages, to two decimal places. This is an example of a humped yield curve. The yields go up, then down. A humped yield curve is rare, but can exist.

Explanation / Answer

discount rate = 1/(1 + r/n)^(n*m)

d.5 = 1/(1+ .04/2) = .9804

d1 = 1/(1+ .042/2)^2 = .9593

d1.5 = 1/(1 + .041/2)^3 = .9409

continuous compounded spot rate can be find using following formula

r =n * ln(1 + r/n)

r.5 = 2 * ln(1.02) = 3.96%

r1 = 2 *ln(1.021) = 4.16%

r1.5 = 2 * ln(1.0205) = 4.06%

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