Suppose you manage a mutual fund that specializes in investing in technology stocks. You generally pick a portfolio of technology stocks and hedge out some risks using futures contracts on some market index. The total value of your current portfolio is 100 million dollars. Please find in the EXCEL sheet CrossHedging.xlsx the monthly data of the futures on the S-index, N-index, and the return on your fund portfolio. You can use either the S-index futures contract or the N-index futures contract to hedge the risk. Note that the S-index futures contract has a contract unit of 50, or one S-index futures contract has a notional value of 50S-Index. The N-index futures contract has a contract unit of 20, or one N-index futures contract has a notional value of 20N-100 Index. The futures price data in the Excel spreadsheet are for indices and do not take the multipliers of 20 and 50 into account. Assume you can take fractions of a futures contract

When answering the following questions a), b), and c), assume today is the end of July 2019, and use the values given by cells B8 and C8 in the sheet Data for Q1 when you calculate the number of contracts. a) Suppose you decide to use the S-index futures to hedge the risk. Should you take long or short positions in the S-index futures contracts? How many S-index futures contracts do you need to go long (or short) in order to minimize the variance of the hedged portfolio? b) Suppose you decide to use the N-index futures to hedge the risk. Should you take long or short positions in the N-index futures contracts? How many N-index futures contracts do you need to go long (or short) in order to minimize the variance of the hedged portfolio? c) Which is a better hedge? The S-index futures or the N-index futures? Explain why.

\begin{tabular}{|c|c|c|} \hline 40 & 20/9/2019 & 2992 \\ \hline 41 & 23/9/2019 & 2999.25 \\ \hline 42 & 24/9/2019 & 2972.25 \\ \hline 43 & 25/9/2019 & 2988.5 \\ \hline 44 & 26/9/2019 & 2982.75 \\ \hline 45 & 27/9/2019 & 2965.75 \\ \hline 46 & 30/9/2019 & 2980.5 \\ \hline 47 & 1/10/2019 & 2939 \\ \hline 48 & 2/10/2019 & 2881.5 \\ \hline 49 & 3/10/2019 & 2912 \\ \hline 50 & 4/10/2019 & 2951.75 \\ \hline 51 & 7/10/2019 & 2938.25 \\ \hline 52 & 8/10/2019 & 2892.75 \\ \hline 53 & 9/10/2019 & 2919.25 \\ \hline 54 & 10/10/2019 & 2941.75 \\ \hline 55 & 11/10/2019 & 2972 \\ \hline 56 & 14/10/2019 & 2966.5 \\ \hline 57 & 15/10/2019 & 2999 \\ \hline 58 & 16/10/2019 & 2993 \\ \hline 59 & 17/10/2019 & 2999.5 \\ \hline 60 & 18/10/2019 & 2989.5 \\ \hline 61 & 21/10/2019 & 3008 \\ 62 & 22/10/2019 & 2996 \\ \hline 63 & 23/10/2019 & 3007.25 \\ 64 & 24/10/2019 & 3005.75 \\ \hline 65 & 25/10/2019 & 3022 \\ 66 & 28/10/2019 & 3038.25 \\ \hline 67 & 29/10/2019 & 3037.5 \\ \hline 68 & 30/10/2019 & 3049.75 \\ \hline 6 & 31/10/2019 & 3049.25 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|} \hline & A & B \\ \hline 31 & 9/9/2019 & 7866.75 \\ \hline 32 & 10/9/2019 & 7851.25 \\ \hline 33 & 11/9/2019 & 7929.75 \\ \hline 34 & 12/9/2019 & 7960 \\ \hline 35 & 13/9/2019 & 7925.25 \\ \hline 36 & 16/9/2019 & 7893.75 \\ \hline 37 & 17/9/2019 & 7937 \\ \hline 38 & 18/9/2019 & 7939 \\ \hline 39 & 19/9/2019 & 7938.25 \\ \hline 40 & 20/9/2019 & 7853 \\ \hline 41 & 23/9/2019 & 7873.25 \\ \hline 42 & 24/9/2019 & 7758.25 \\ \hline 43 & 25/9/2019 & 7843.75 \\ \hline 44 & 26/9/2019 & 7810.25 \\ \hline 45 & 27/9/2019 & 7723 \\ \hline 46 & 30/9/2019 & 7792.25 \\ \hline 47 & 1/10/2019 & 7715.75 \\ \hline 48 & 2/10/2019 & 7564.5 \\ \hline 49 & 3/10/2019 & 7675.75 \\ \hline 50 & 4/10/2019 & 7785.25 \\ \hline 51 & 7/10/2019 & 7758.25 \\ \hline 52 & 8/10/2019 & 7639.25 \\ \hline 53 & 9/10/2019 & 7717.5 \\ \hline 54 & 10/10/2019 & 7779 \\ \hline 55 & 11/10/2019 & 7879.25 \\ \hline 56 & 14/10/2019 & 7876.5 \\ \hline 57 & 15/10/2019 & 7979.5 \\ \hline 58 & 16/10/2019 & 7968.5 \\ \hline 59 & 17/10/2019 & 7973 \\ \hline 6 & 18/10/2019 & 7900 \\ 61 & 21/10/2019 & 7967.75 \\ \hline 2 & 22/10/2019 & 7878 \\ \hline 63 & 23/10/2019 & 7920.75 \\ \hline 64 & 24/10/2019 & 7947.75 \\ 65 & 25/10/2019 & 8056 \\ 66 & 28/10/2019 & 8116 \\ \hline 67 & 29/10/2019 & 8076.25 \\ \hline 68 & 30/10/2019 & 8132.25 \\ \hline 69 & 31/10/2019 & 8139.5 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|} \hline 40 & 20/9/2019 & 2992 \\ \hline 41 & 23/9/2019 & 2999.25 \\ \hline 42 & 24/9/2019 & 2972.25 \\ \hline 43 & 25/9/2019 & 2988.5 \\ \hline 44 & 26/9/2019 & 2982.75 \\ \hline 45 & 27/9/2019 & 2965.75 \\ \hline 46 & 30/9/2019 & 2980.5 \\ \hline 47 & 1/10/2019 & 2939 \\ \hline 48 & 2/10/2019 & 2881.5 \\ \hline 49 & 3/10/2019 & 2912 \\ \hline 50 & 4/10/2019 & 2951.75 \\ \hline 51 & 7/10/2019 & 2938.25 \\ \hline 52 & 8/10/2019 & 2892.75 \\ \hline 53 & 9/10/2019 & 2919.25 \\ \hline 54 & 10/10/2019 & 2941.75 \\ \hline 55 & 11/10/2019 & 2972 \\ \hline 56 & 14/10/2019 & 2966.5 \\ \hline 57 & 15/10/2019 & 2999 \\ \hline 58 & 16/10/2019 & 2993 \\ \hline 59 & 17/10/2019 & 2999.5 \\ \hline 60 & 18/10/2019 & 2989.5 \\ \hline 61 & 21/10/2019 & 3008 \\ 62 & 22/10/2019 & 2996 \\ \hline 63 & 23/10/2019 & 3007.25 \\ 64 & 24/10/2019 & 3005.75 \\ \hline 65 & 25/10/2019 & 3022 \\ 66 & 28/10/2019 & 3038.25 \\ \hline 67 & 29/10/2019 & 3037.5 \\ \hline 68 & 30/10/2019 & 3049.75 \\ \hline 6 & 31/10/2019 & 3049.25 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|} \hline & A & B \\ \hline 31 & 9/9/2019 & 7866.75 \\ \hline 32 & 10/9/2019 & 7851.25 \\ \hline 33 & 11/9/2019 & 7929.75 \\ \hline 34 & 12/9/2019 & 7960 \\ \hline 35 & 13/9/2019 & 7925.25 \\ \hline 36 & 16/9/2019 & 7893.75 \\ \hline 37 & 17/9/2019 & 7937 \\ \hline 38 & 18/9/2019 & 7939 \\ \hline 39 & 19/9/2019 & 7938.25 \\ \hline 40 & 20/9/2019 & 7853 \\ \hline 41 & 23/9/2019 & 7873.25 \\ \hline 42 & 24/9/2019 & 7758.25 \\ \hline 43 & 25/9/2019 & 7843.75 \\ \hline 44 & 26/9/2019 & 7810.25 \\ \hline 45 & 27/9/2019 & 7723 \\ \hline 46 & 30/9/2019 & 7792.25 \\ \hline 47 & 1/10/2019 & 7715.75 \\ \hline 48 & 2/10/2019 & 7564.5 \\ \hline 49 & 3/10/2019 & 7675.75 \\ \hline 50 & 4/10/2019 & 7785.25 \\ \hline 51 & 7/10/2019 & 7758.25 \\ \hline 52 & 8/10/2019 & 7639.25 \\ \hline 53 & 9/10/2019 & 7717.5 \\ \hline 54 & 10/10/2019 & 7779 \\ \hline 55 & 11/10/2019 & 7879.25 \\ \hline 56 & 14/10/2019 & 7876.5 \\ \hline 57 & 15/10/2019 & 7979.5 \\ \hline 58 & 16/10/2019 & 7968.5 \\ \hline 59 & 17/10/2019 & 7973 \\ \hline 6 & 18/10/2019 & 7900 \\ 61 & 21/10/2019 & 7967.75 \\ \hline 2 & 22/10/2019 & 7878 \\ \hline 63 & 23/10/2019 & 7920.75 \\ \hline 64 & 24/10/2019 & 7947.75 \\ 65 & 25/10/2019 & 8056 \\ 66 & 28/10/2019 & 8116 \\ \hline 67 & 29/10/2019 & 8076.25 \\ \hline 68 & 30/10/2019 & 8132.25 \\ \hline 69 & 31/10/2019 & 8139.5 \\ \hline \end{tabular}