Let's assume that you were hired on March 19 th , 2021 to manage a $100 million

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Question:

Let's assume that you were hired on March 19^th, 2021 to manage a $100 million S&P 500 index fund for a U.S. pension fund for 365 days.* Also assume market conditions are similar then to what exists in Tables 1 and 2.**

Table 1

ETF Price = 391.6

ETF Management Fee = 5 bps/yr

ETF Commission = 1.0 bps

ETF Estimated Execution Shortfall = 10 bps

Futures Commissions = 0.4 bps per quarter

Futures Execution Shortfall at Initiation = 5 bps

Execution Shortfall on Calendar Spreads = 0

Table 2

S&P 500 Index = 3,916

June 2021 S&P 500 Futures Price = 3,905

September 2021 S&P 500 Futures Price = 3,895

Days until June expiry = 91

Days until September expiry = 182

Dividend Yield thru June = 1.5% per annum

Dividend Yield thru September = 1.5% per annum

LIBOR thru June = 0.18% per annum

LIBOR thru September = 0.18% per annum

*To be more precise, assume your assignment ends at the expiration of the March

2022 S&P 500 Futures contract, and you are holding the position for 365 days.

**Since you may hold the position for more than 365 days, you can ignore

transaction costs to unwind the position.

a)What are the Fair Values of the June and September 2021 S&P 500 futures contracts?

b)If you are able to invest cash at LIBOR + 25 bps per annum, would you prefer futures or ETFs as your way to obtain S&P 500 index exposures?Why?Please assume that the calendar spread mispricing between September and December 2021 and December 2021 and March 2022 will be the same as the calendar spread mispricing between June and September 2021.

c)At what cash reinvestment rate would the ETF strategy provide a higher expected return than the futures strategy?

d)Using an S&P 500 Index Swap, you can contract to receive the total return of the S&P 500 for a spread of LIBOR plus 40 basis points.Please assume that you can invest cash at LIBOR + 25 bps.Please compare the expected returns of the S&P 500 futures strategy with a comparable strategy using S&P 500 swaps.Which strategy would you prefer?

e)How much does the calendar spread mispricing in the September and December 2021 and December 2021 and March 2022 S&P 500 futures contracts have to change for your recommendation in 1(d) to change?