# Forward rates, Arbitrage

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?

https://brainmass.com/business/arbitrage-pricing-theory/forward-rates-arbitrage-14812

#### Solution Summary

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