Question

An interest rate collar has a cap strike rate of 10.00% and a floor strike rate of 9.50%. If the reference interest rate moves from 9.50% to 9.75%, what is the effective rate of the collar? a. 9.50% b. 9.625% c. 9.75% d. 9.875%

Answer 1

Answer is C 9.75%

In the given problem the collar has a Cap rate with strike rate of  10% and a floor strike rate of 9.5%
Implication of Cap Rate. If the Reference Rate Moves higher than the Strike price of 10%, the interest payment would be capped at 10%. the Effective interest rate would be 10 % if reference rate moves beyond 10 %

Implication of Floor Rate, if the reference rate drops below strike rate of 9.5% , the interest payments would be restricted to 9.5 %. SO if the rates go below 9.5 %. The effective interest rate would be 9.5 %


However, in the given case reference rate is 9.75%, if the rate was more than 10 % effective rate would be 10% and if it were less than 9.5% it would be 9.5%. However when reference rate lies between the cap strike rate and floor strike rate, the effective rate of collar is reference rate itself which is 9.75 %



Suppose, a investor has a floating interest loan, to hedge it self it constructs a collar,
so the cash flows would be :
For the loan = Reference Rate
The pay off of cap is Max[(Reference- Strike),0]
The pay off on floor is Max[(Strike - Reference),0]
Cap + floor- Reference = Max[(9.75%-10),0] + Max[(9.5%-9.75),0]- 9.75%
= max[(-0.25%),0] + Max [-0.25%,0]- 9.75%
= -9.75%