By William Feller

***** overseas variation *****

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**Extra resources for An Introduction to Probability Theory and its Applications**

**Example text**

15, the bond is a discount one. The dependence of the price of the bond on time to maturity is graphically illustrated in Figure 8. 05, etc. 2 Exercise. , with frequency 2, which is perhaps the most frequent case. I. 3 51 Remark (Construction of the Yield Curve of Coupon Bonds) The silllplest way is to take a set of similar coupon bonds with different maturities and their calculated yields to maturity. Then some method of fitting discussed above may be applied. An alternative approach is known as bootstrapping.

The crossover rate IAB is defined as a solution to the equation Obviously, there may be more than one solution so that we must select that one with a reasonable economic interpretation. Since the present value is a linear function on the space of cash flows, we see that the crossover rate iABis in fact the internal rate of return determined by the difference between the two projects, I R R A - ~ : In the neighborhood of the crossover rate the investor should take care and carefully study also the sensitivity of the present value profiles with respect to the interest rate.

A crossover* rate of two projects is such an interest rate for which the present values of the two projects are equal. Formally, let us consider two projects CFA and CFB. The crossover rate IAB is defined as a solution to the equation Obviously, there may be more than one solution so that we must select that one with a reasonable economic interpretation. Since the present value is a linear function on the space of cash flows, we see that the crossover rate iABis in fact the internal rate of return determined by the difference between the two projects, I R R A - ~ : In the neighborhood of the crossover rate the investor should take care and carefully study also the sensitivity of the present value profiles with respect to the interest rate.