Consider these data for the S&P $500$ future's contract maturing in$,$ exactly one year. The S&P $500$ index is at $4,290,$ and the contract price is F$0=4,292.$

Required:

If the current interest rate is $2\mathrm{.}5\%,$ and the average dividend rate of the stocks in the index is $1\mathrm{.}9\%,$ what fraction of the proceeds of stock short sales would need to be available to you to earn arbitrage profits?

Note: Enter your answer in numbers and not in percentage. E$.$g$.,$ enter $0\mathrm{.}12$ and not $12\%.$ Do not round intermediate calculations. Round your answer to $4$ decimal places.

Suppose now that you in fact have access to $90\%$ of the proceeds from a short sale. What is the lower bound on the futures price that rules out arbitrage opportunities?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

By how much does the actual futures price fall below the no$-$arbitrage bound?

Note: Round your intermediate calculations and final answer to $2$ decimal places.

a$.$ Fraction

b$.$ Lower bound on the futures price

c$.$ Futures price falls by points