Given the following maturities in an observed yield curve 2y

Given the following maturities in an observed yield curve: 2-year Yield = 2%, 10-Year Yield= 5%, 30-Year Yield=7%, the 2-10-30 year butterfly spread is

a. Butterfly Spread = -1%
b. Butterfly Spread = -4%
c. Butterfly Spread = 1%
d. Butterfly Spread = 4%

I know the answer is C but I do not know how this is calculated. Can anyone explain?

Solution

With a butterfly spread you will:

Buy 1 ITM Yield (2 Year Yield)

Sell 2 ATM Yield (10 Year Yield)

Buy 1 OTM Yield (30 Year Yield)

Therefore, Spread

-(1*2) + (2*5) - (1*7)= -2 + 10-7= 1