1. Cross Hedging and Minimum Variance Hedge Ratio 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 (AS, AF) and Var (AF). (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? 2. Arbitrage Using a Forward A stock currently sells for $80, and it will pay no dividends in the future. Consider a 2-year forward contract on this stock. The forward price is $90. The risk-free rate is 3% per annum. Is there an arbitrage? If so, show the arbitrage strategy using a table listing asset positions and cash flows. 3. No Arbitrage Argument Suppose that we have asset A, B, and C that will deliver cash flows one year later. The cash flows will depend on the state of economy as follows: Asset Boom Recession 25 20 A B 10 10 20 25 (a) Suppose that we want to replicate the cash flows of asset C using asset A and asset B. In other words, we want to construct a portfolio consisting of asset A and asset B such that the portfolio will have the same cash flows as asset C one year later in both boom and recession. How many asset A and asset B do we need in the portfolio? (Hint. Let denote the number of asset A and y denote the number of asset B. Solve for r and y.) (b) The current price of asset A is $19 and the current price of asset B is $9. If there is no arbitrage, what is the price of asset C? 1. Cross Hedging and Minimum Variance Hedge Ratio 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 (AS, AF) and Var (AF). (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? 2. Arbitrage Using a Forward A stock currently sells for $80, and it will pay no dividends in the future. Consider a 2-year forward contract on this stock. The forward price is $90. The risk-free rate is 3% per annum. Is there an arbitrage? If so, show the arbitrage strategy using a table listing asset positions and cash flows. 3. No Arbitrage Argument Suppose that we have asset A, B, and C that will deliver cash flows one year later. The cash flows will depend on the state of economy as follows: Asset Boom Recession 25 20 A B 10 10 20 25 (a) Suppose that we want to replicate the cash flows of asset C using asset A and asset B. In other words, we want to construct a portfolio consisting of asset A and asset B such that the portfolio will have the same cash flows as asset C one year later in both boom and recession. How many asset A and asset B do we need in the portfolio? (Hint. Let denote the number of asset A and y denote the number of asset B. Solve for r and y.) (b) The current price of asset A is $19 and the current price of asset B is $9. If there is no arbitrage, what is the price of asset C