The Zuber Hedge Fund has formed a proxy portfolio that it is using to identify arbitrage opportunities using index arbitrage strategies. The proxy portfolio is worth \(\$ 100\) million, has a beta of one, and dividends estimated to be worth \(\$ 5\) million one year later. The current S\&P 500 spot index is at 1,250 and the annual risk-free rate is \(5 \%\).

a. Define the Zuber Hedge Fund's portfolio as an investment in hypothetical shares in the S\&P500. What is the dividend per index share to be paid in one year?

b. Determine the equilibrium price of an S\&P 500 futures contract expiring in one year using Zuber's proxy portfolio.

c. Describe the index arbitrage strategy Zuber could employ if the S\&P 500 futures were trading at 1,260. (Note: The S\&P 500 futures multiplier is \(\$ 250\).)

d. Evaluate the index arbitrage from \(\mathrm{c}\) at the futures' expiration by assuming the market increases by \(10 \%\) and decreases by \(10 \%\). Assume the portfolio is perfectly correlated with the index.

e. Describe program trading.

f. What is the triple witching hour?