Assume that the effective $6-$month interest rate is $\frac{2}{\frac{?}{?}}\%,$ the $S$&$R6-$month forward price is $$1020,$ and use the premiums in the table below

for the S&R options with $6$ months to expiration.

Consider the ratio spread position on the S&R index consisting in buying four $1000-$strike call options and selling three $1020-$strike call

options.

a$)$ Find the payoff as a function of $S,$ the spot price of the $S$&$R$ index in $6$ months.

b$)$ Draw payoff and profit diagrams for this ratio spread position.

c$)$ For which values of the spot price $S$ at expiration will this position outperform a long $1000-$strike straddle?