Background Information This assignment is concerned with a total return swap (TRS) on an interest rate index constructed as follows: A. At inception of the index, $1,000 is deposited for 4 weeks at the prevailing BBSW1M rate. B. For each of the next 3 weeks, additional $1,000 deposits are made, each for 4 weeks and at the prevailing BBSW1M rate at the time. This results in 4 separate deposits, each with initial amount $1,000 and maturity of 4 weeks, but with maturities offset by 1 week. C. As each deposit matures, the total amount including the interest is rolled over into another 4 week deposit at the prevailing BBSW1M rate. D. On any given date t, the value of the portfolio of deposits is computed as follows Vt = X4 i=1 Ai(1 + Ri 28/365) 1 + Ri di/365 , where Ai are the current deposit amounts, Ri are the BBSW1M rates at which the i-th deposit was made, and di is the remaining number of days to maturity for the i-th deposit. E. The index value at inception is set to I0 = 1, 000, and updated each day according to the rule It+1 = It Vt+1/Vt. F. For simplicity, assume that the second to fourth $1,000 amounts do not earn any interest until they are deposited, so that Ri = 0 for these amounts in the above expression for Vt over the initial 4 week period. You may assume that the index is maintained and published daily by a well-known financial data vendor, and has been in existence for well over 10 years. Suppose you work on an interest rate desk in a bank, and a client, who is a fixed income fund manager, wishes to enter into a TRS where they receive the return on the above index every 4 weeks on the notional of $100,000,000. The client will give the bank $100,000,000 at the start of the TRS, and the bank must return the $100,000,000 to the client at the end of the TRS. You have been given the task of analysing the risks associated with the TRS and to propose a method for managing the risks. After some investigation, you discover that the banks treasury department will pay BBSW1M plus 5 basis points on any cash you leave with them for 4 weeks, and will pay the official cash rate of 1.5% for overnight deposits. You realize that you can mimic the 4 deposits underlying the index with the treasury, and hence potentially make the 5 basis point margin the treasury pays above the BBSW1M rate. 2 You have collected the BBSW1M rate each week for the past 4 years, and have decided to test your idea with this data. Please download the file BBSW1M.xlsx from Canvas that contains (fictitious) BBSW1M and official cash rates to use for the assignment. You may assume that the value of the index 4 years ago was I = 1, 386.82, and the notional amounts, the times to maturity, and the BBSW1M rates for the 4 deposits underlying the index at that time were as follows: Deposit number Notional Weeks to maturity BBSW1M 1 1,324.24 4 1.5134% 2 1,316.15 3 1.5128% 3 1,346.82 2 1.5126% 4 1,362.90 1 1.5201% Note that Week 0 in the file BBSW1M.xlsx corresponds to the time at which Deposit number 1 in the above table has exactly 28 days to maturity. For overnight deposits with treasury, you may assume for simplicity that the interest earned over n weeks is given by the expression Interest = A 1 + R 7 365 n A, where A is the deposit amount and R is the official cash rate, so that it is weekly compounded.1 You realize that there are 3 distinct stages, with different risk characteristics, that make up your strategy, viz. entry stage, continuation stage, and exit stage. You may assume that the value of the deposits you have with the treasury can be valued similarly to the way the portfolio in the index is valued so that Vt = X4 i=1 Ai(1 + (Ri + m) 28/365) 1 + Ri di/365 , (1) where m is the margin above BBSW1M paid by the treasury. If a question asks you compute numerical values, then you must provide a brief explanation of how you computed these values to earn full marks. If you do not provide any explanation and your values are incorrect, then you will not be awarded any marks. Questions 1. Using the data in the file BBSW1M.xlsx and the index data in the table above, compute the values of the portfolio underlying index and hence the index values for each week given in the file. Fill in the table below with the values you computed: Week 0 4 195 199 Vt It Round the portfolio values to 4 decimal places, and the index values to 2 decimal places in the table.