1. Cross Hedge and Minimum Variance Hedge Ratio A cryptocurrency trader owns 1 unit of Ethereum and decides to hedge the value of the position with futures contracts on Bitcoin. In the "Q1 sheet of the Excel file, you can find the data for the spot price of Ethereum and futures price of Bitcoin from 23 September 2020 to 23 September 2021. (a) Let AS denote the daily change in Ethereum spot price. In addition, let AF denote the daily change in Bitcoin futures price. In the data, what is Cov (AS, AF)? What is Var (AF)? (b) What is the minimum variance hedge ratio? (c) Suppose that, in addition to Ethereum, the trader takes a short position in futures contract for delivery of h unit of Bitcoins. Then, the variance of change in portfolio value is Var (AS-hAF). What is the variance if we use the minimum variance hedge ratio found in (b)? (d) Let's try different hedge ratios that range from 0.01 to 0.09. What is the resulting variance for each choice of hedge ratio? To answer this, fill the following table. Hedge ratio Var (AS hAF) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 (e) Compare the variances in (c) and (d). Which hedge ratio results in the minimum variance?