1. Operation of Margin Accounts Suppose that we take a long position of one futures contract on Bitcoin on 26 August 2020. Daily futures prices until 15 September 2020 are given in the Q1 sheet of the Excel file. One contract is for delivery of 5 Bitcoins. The initial margin is $20,000 and the maintenance margin is $15,000. What is gain/loss from the settlement for each day? What is the balance in the margin account? Do we receive a margin call? To answer these, fill the following table. Date Futures price Daily gain Margin account Margin calls ($ per coin) balance 11,675 20,000 26 Aug 27 Aug 28 Aug 30 Aug 31 Aug 1 Sep 2 Sep 3 Sep 4 Sep 8 Sep 9 Sep 10 Sep 11 Sep 14 Sep 15 Sep 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)? (b) 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). 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. Hedge ratio Var(AS hAF) 0.010 0.012 0.014 0.016 0.018 0.020 (c) Among considered choices of hedge ratio in (b), which ratio results in the smallest variance? (Note: In lecture 4, we will discuss on how to solve for the exact value of the minimum-variance hedge ratio. In this problem set, however, let's find one among hedge ratios considered in (6).) Date Bitcoin Futures Price 11675 11410 11705 11950 11940 12180 11560 10795 10705 10090 10400 10405 10420 10780 10890