A cryptocurrency trader owns 10,000 unit of Ethereum and decides to hedge the value of the position with futures contracts on Bitcoin. One futures contract is for delivery of 5 Bitcoins. In answering the following questions, please use the statistics that you obtained in Assignment 2 Question 2 regarding Cov(S,F) and Var (F ).
(a) What is the minimum variance hedge ratio?
(b) To minimize the variance of portfolio value, how many contracts does the trader need? Does the trader need to long or short?
You may use Excel for calculation but final answer should be in text format
Assignment 2 Question 2:
2. Cross Hedge and 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 "Q2" sheet of the Excel file, you can find the data for the spot price of Ethereum and futures price of Bitcoin from 16 September 2019 to 31 December 2019. (a) Let AS denote the change in Ethereum spot price per day. In addition, let AF denote the change in Bitcoin futures price per day. In the data, what is Cov (AS, AF)? What is Var (AF)? Solution: Using the sample variance and covariance in Excel, we find Cov (AS, AF) = 1,487.74, Var (AF) = 115,724.7. Alternatively, if population variance and covariance are used, then Cov (AS, AF) = 1, 468.16, Var (AF) = 114, 202. contract delivery (b) Suppose that, addition Ethereum, the trader takes a short position in futur of h unit of Bitcoins. Then, the variance of change in portfolio value is Var (AS - HAF) For this hedging, the trader considers different hedge ratios that range from 0.01 to 0.02. What is the resulting variance for each choice of hedge ratio? To answer this, fill the following table. Solution: The variance of change in portfolio value is Var (AS) +h? Var (AF) 2h Cov (AS, AF) =48.32 =115724.7 =1487.74 For considered values of h, the resulting variance is as follows: 2. Cross Hedge and 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 "Q2" sheet of the Excel file, you can find the data for the spot price of Ethereum and futures price of Bitcoin from 16 September 2019 to 31 December 2019. (a) Let AS denote the change in Ethereum spot price per day. In addition, let AF denote the change in Bitcoin futures price per day. In the data, what is Cov (AS, AF)? What is Var (AF)? Solution: Using the sample variance and covariance in Excel, we find Cov (AS, AF) = 1,487.74, Var (AF) = 115,724.7. Alternatively, if population variance and covariance are used, then Cov (AS, AF) = 1, 468.16, Var (AF) = 114, 202. contract delivery (b) Suppose that, addition Ethereum, the trader takes a short position in futur of h unit of Bitcoins. Then, the variance of change in portfolio value is Var (AS - HAF) For this hedging, the trader considers different hedge ratios that range from 0.01 to 0.02. What is the resulting variance for each choice of hedge ratio? To answer this, fill the following table. Solution: The variance of change in portfolio value is Var (AS) +h? Var (AF) 2h Cov (AS, AF) =48.32 =115724.7 =1487.74 For considered values of h, the resulting variance is as follows
