6. One hedge fund named "Star Invest" is currently holding both equities and bonds in their portfolio. Bond portfolio has a modified duration of 5 years with the present value of $20 million. The March-2021 5-year T-bond Futures are available from CBT (with face value of 100,000). The equity portfolio has a beta of 1.20 with the value of $34 million. S&P500 index futures are traded on CME. Assuming both futures have the same the initial margin which is 15% of the contract value. The maintenance margin is fixed in dollar value by the two clearing houses at $650 per contract for 5-year T-bond Futures and $60,000 per contract for S&P500 index futures, respectively. The multiplier is 100 for each T-bond Futures contract and 250 for each S&P500 index futures contract. The current PVBP for 5-year T-bond Futures is at $125 and the current price of S&P500 Futures index is at 3400 given in the following table. [8 marks] a) If the interest rate is expected to increase by 25 basis points (i.e., 0.25%), how many T-bond futures contracts should Star Invest short? [2 marks] b) If the market is expected to decline by 1%, how many S&P500 index futures contract should Star Invest short? [2 marks] c) Given the following price change in next 3 days, fill in the margin account balances in both CBT and CME accounts respectively (including the variation margin if any). [4 marks] Day 5-year T-bond Futures Price (PVBP) 125 Margin Account Balance with CBT S&P500 Index Futures Price Margin Account Balance with CME 0 ? 3400 ? ? ? 1 120 3300 140 ? ? 3700 N 3 ? ? 135 3500 6. One hedge fund named "Star Invest" is currently holding both equities and bonds in their portfolio. Bond portfolio has a modified duration of 5 years with the present value of $20 million. The March-2021 5-year T-bond Futures are available from CBT (with face value of 100,000). The equity portfolio has a beta of 1.20 with the value of $34 million. S&P500 index futures are traded on CME. Assuming both futures have the same the initial margin which is 15% of the contract value. The maintenance margin is fixed in dollar value by the two clearing houses at $650 per contract for 5-year T-bond Futures and $60,000 per contract for S&P500 index futures, respectively. The multiplier is 100 for each T-bond Futures contract and 250 for each S&P500 index futures contract. The current PVBP for 5-year T-bond Futures is at $125 and the current price of S&P500 Futures index is at 3400 given in the following table. [8 marks] a) If the interest rate is expected to increase by 25 basis points (i.e., 0.25%), how many T-bond futures contracts should Star Invest short? [2 marks] b) If the market is expected to decline by 1%, how many S&P500 index futures contract should Star Invest short? [2 marks] c) Given the following price change in next 3 days, fill in the margin account balances in both CBT and CME accounts respectively (including the variation margin if any). [4 marks] Day 5-year T-bond Futures Price (PVBP) 125 Margin Account Balance with CBT S&P500 Index Futures Price Margin Account Balance with CME 0 ? 3400 ? ? ? 1 120 3300 140 ? ? 3700 N 3 ? ? 135 3500