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Forward rates, Arbitrage

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Please see attachment for tables and pre-question information.

Questions:

Data:
Suppose the following coupon info

Maturity (year) Coupon Rate price
1 0% 97
2 3.00% 99
2 0% 91
3 4.00% 98
3 0% 87
Please note there are arbitrage opportunities (shown below).

The 1-yr rate implied by the 1-yr zero coupon bound is
= 100/97 - 1 = 3.09%
The 2-yr rate implied by the 2-yr zero coupon bound is
91 = 100/ = - 1 = 4.828%
The 2-yr rate implied by the 2-yr coupon bound is
99 = = 3.5%
The 3-yr rate implied by the 3-yr zero coupon bound is
87 = 100/ = - 1 = 4.75%
The 3-yr rate implied by the 3-yr coupon bound is
98 = = 4.75%

The 2-year rates implied by coupon bond is different to those implied by zero coupon bonds. Hence there is arbitrage opportunity for this segment of term structure.

Questions:

1. Is there any other arbitrage opportunity?
2. Given above bonds, what are the implied forward rates?
3. If one was to invest $1,000 two years from now for one year. Which would be the best strategy (what forward rate to use)? What is the return?

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Solution Summary

The solution identifies arbitrage opportunities and calculates the implied forward rates.

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