Problem Set $2.($Stock Index Arbitrage$)$

An ETF investing in the S&P $500$ index pays a $1\%$ annual dividend yield $($continuously compounding$)$ and is

currently traded at $$1,300.$ The $3-$month futures contract on this S&P $500$ ETF is currently traded at $$1,310$

and each contract is for only one underlying ETF. The annual risk$-$free rate is $5\%($compounded continuously

for either depositing or borrowing$).$

a$)$ What is the theoretical price of this futures contract on the S&P $500$ ETF?

b$)$ The difference between this theoretical price and the actual price $($$$1,310)$ is the potential arbitrage profit.

Describe your arbitrage strategy if you can take a long or short position in ONE futures contract and another

position in ONE underlying ETF? $($Hints: do not forget the interest rate.$)$

c$)$ How much will you get $($net arbitrage profit$)$ on the expiration date of the futures contract $(3$ months later$)?$

$($Hints: interest rate is compounded continuously and do NOT forget to pay dividends to your broker.$)$