Question 1

Today is October 12, 2020. You want to check if there are any arbitrage opportunities available to arbitrage away mispricing between S&P 500 index e-mini futures expiring in December (ES=F) and the underlying asset, S&P 500 index (SPX). For this arbitrage strategy, you would like to use one of the ETFs that track the index: SPY, IVV, or VOO. All of these ETFs are pretty liquid, so you can easily use any of them for your strategy. Arbitrage opportunities in S&P 500 index rarely arise and usually don’t last for more than 50 milliseconds. The order protection rule in the U.S. requires all market orders to be routed to the exchange (trading venue) that posts the national best bid and offer (NBBO) quotes across all exchanges. Trading venues charge fees for each share traded on their venues. However, these fees differ depending on whether you demand liquidity, i.e., consume quotes available at the venue (take fee), or provide liquidity, i.e., post additional limit order quotes to the venue (make fee). Positive fees in the table below indicate that you need to pay this amount of money per each share/contract executed, while negative fees mean that you will receive a rebate per each share/contract executed.

a) How much net arbitrage profits can you earn (in present value terms) with each of these ETF contracts (assume that you transact in 1 futures contract)?

b) Which ETF contract will bring you the highest profit net of all costs?

• Note: enter 1 for SPY, 2 for IVV, or 3 for VOO

Now let’s look at the similar S&P 500 e-mini futures that expire in March 2021.

c) Which ETF contract will bring you the highest profit net of all costs?

• Note: enter 1 for SPY, 2 for IVV, or 3 for VOO

d) How much net arbitrage profits can you earn (in present value terms) with this ETF contract (assume that you transact in 1 futures contract)?

For simplicity, assume that there are no margin requirements. Ignore all other costs that are not mentioned in this question. On October 12, 2020, 3-month and 6-month USD LIBORs are equal to 0.22025% and 0.23025%, respectively. In your calculations, account for the fact that you can only buy an even number of ETF shares and futures contracts.