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Eurodollars, and Swap Maturities Lasting Less Than a Year

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Eurodollars, and Swap Maturities Lasting Less Than a Year Word Capital Open Source Asset Management 408 West 14th Street, 2F New York, NY 10014 www.word.am www.wordcapital.com US Yield Curve Tutorial Jake Roth | Caroline Davidson Tools Needed 1 Microsoft Excel 2 Access to a Bloomberg Terminal Contents 1 Getting Started: Defines terms that are important to know for building a yield curve. 2 Components and Formulas: Explains several concepts used for relating components of the yield curve. 3 Step-by-Step Guide: Gives instructions for extracting and using data to create a curve. Downloaded from www.hvst.com by IP address 192.168.160.10 on 09/24/2021 The yield to maturity refers to the rate of Getting Started return on a bond at the end of its maturity. It is essentially an average of the yields for the different time periods on payments throughout its maturity. We take the yield to maturity into The yield refers to the return on an account when using swap rates to investment. A yield curve plots the compute the yield for the 2-year to 30- interest rates for investments that year portion of the curve. mature at different points in time. It shows what rate should be used for Simple interest rates are most lending at various maturities. We will use commonly used when dealing with deposit rates, Eurodollars, and swap maturities lasting less than a year. We rates to build our US yield curve. The US use simple interest rates when dealing Dollar yield curve is the most relevant with the deposit rates and Eurodollars. application to all global markets participants.“Vivamus porta Compounding interest rates are rates where interest is added to the notional Deposit ratesest are sed the est. interest” rates that so that, from that moment on, the banks charge for lending and pay for interest that has been added also earns borrowing at different maturities. interest. We deal with compounding interest rates when we start using swap Eurodollar futures contracts are deposits rates to determine points on the yield of US dollars in foreign banks that have curve. The swap rates we deal with are a 3-month maturity with contracts compounded annually. starting every month. The price of the futures contracts is related to the Day-count conventions are used to interest rate offered. We will use calculate the interest rates between contracts starting in March, June, two dates. In building a yield curve, we September, and December. The often need to compute the interest rate deposits are made outside of the United for periods between payments or States, so they are not subject to another period, which requires using a Federal Reserve regulation. reference period for which we already know the rate. We use the equation: The swap rate is the rate at which the fixed-rate payment in an interest rate swap is traded. An interest rate swap is the exchange of a fixed-rate payment for a floating-rate payment on a standardized notional. Downloaded from www.hvst.com by IP address 192.168.160.10 on 09/24/2021 1 Components and Formulas Today—3 months Deposit rates Deposit rates are short term, so we use them to determine the portion of the curve from the current date to the start of the first available Eurodollar contract. We use the spot-next deposit rate (which we will refer to as the 1-day rate), 1-week, 2-week, 3-week, 1-month, 2-month, and 3- month rates. In order to get the rates for days in between these tenors, we use linear interpolation and the theory of similar triangles. Here, we know iupper, ilower, upper, and lower: Using the endpoints of the triangle, we can create a new, smaller triangle within the larger one. We know that the ratios between these right triangles are equivalent, so we can solve for ix using the equation below and plugging in the information we know. This formula can be expressed in a way to solve for any interest rate between two known data points: Downloaded from www.hvst.com by IP address 192.168.160.10 on 09/24/2021 2 3 months—2 years Eurodollars Eurodollar contracts last for 90 days (3 months), and we use the contracts that start in March, June, September, and December (or in market terminology: EDH, EDM, EDU, EDZ). They extend to 10 years; however, we use them only to calculate the 3-month to 2-year portion of the yield curve. Because the rates represent only a 90 day time period that starts and ends at different points in time, it is important to account for the interest rate relative to the portion of time before that rate is put into effect. Using the rate for the previous term (i1) and the rate for the 3-month contract (i2), we can solve for itotal using the equation: To solve for the interest rate for the total period of time, we manipulate the equation: To calculate the interest rate for the next Eurodollar contract, i1 becomes the previous itotal. This equation always breaks the total time period into two segments: the time period that we have already dealt with and the newest piece of time that we are adding on. Bloomberg gives data in percent form, but the equation requires that the interest rates be in decimal form. Yet we want to use interest rates in percentage form for the yield curve, so it is important to make the conversions when necessary, i.e. multiplying or dividing by 100 when appropriate. Downloaded from www.hvst.com by IP address 192.168.160.10 on 09/24/2021 2 years—30 years Swap rates We use swap rates to determine the 2-year to 30-year portion of the yield curve. However, the data for swap rates gives the yield to maturity, and we must calculate the yield for the final portion of the time to maturity while incorporating interest rates for the previous periods of time. Now we know i1 and itotal, and we are solving for i2. We use the equation: To calculate the yield, solve for in in the equation above and manipulate it to become: Again, coupons (C) are given in percent form, so the appropriate conversion to decimal form is required. When calculating rates, we assume the bonds are priced at par. A bond priced at par means that its future cash flows, when brought to present day terms, are equal to the given price. Downloaded from www.hvst.com by IP address 192.168.160.10 on 09/24/2021 day. The first column is the lower V-Lookup Table bound day, and the following Step-by-Step columns are the lower bound day’s rate, the upper bound 1. Create a V-Lookup table of 4 day, the upper bound day’s columns. This table will be used Guide rate, and then the formula to get the upper and lower calculating ix in the final bounds needed for linear column. After the deposit rate is interpolation. The first two calculated the other yield rates columns are maturity lengths will be added to this table as and the corresponding rate. The well. next two columns should be 3. Be sure to lock the V-Lookup identical to the first two, but table in place before dragging shifted up one row. (See V- down. Otherwise, the Data Lookup Table Excel Example) VLOOKUP() will search through 2. To begin with, only fill this table a table filled with incorrect with deposit rates (1-90 day 1. Use the Bloomberg Terminal to information. extract data for deposit rates rates). Rates on longer maturities will be calculated up to 3 months using the BLP() function. You can find data on and added to the table later. Eurodollars the deposit rates by typing “BBC For example, the overnight 33”, <GO>. information on the left side 2. Extract data for Eurodollars up should be in line with the 1- 1. When the first Eurodollar to 2 years. Use the formula 100- week information on the right contract goes into effect, the BLP() to determine the rate. side. formula must be changed: Also, extract data for the expiration date of each contract by using the BLP() Linear Interpolation function with 2. Use the rate for the previous LAST_TRADEABLE_DT as the time period (i1) and the rate for second input. Data on 1. Use the VLOOKUP() function to the next 3-month Eurodollar Eurodollar rates can be found get the upper and lower contract (i2) to solve for itotal in by typing “EDSF”, <GO>. bounds for any given day and the equation above. Both 3. Extract data for swap rates up create a table using the Date pieces of information must be to 30 years. Use the BLP() and Day Count columns. (See used to compute the rate for formula to retrieve rate data. Linear Interpolation Excel the total period of time each Swap rates can be found by Example). time a new Eurodollar futures typing “IRSB 42”, <GO>. Insert 2. Set your VLOOKUP() formula so contract comes into effect. rows between 10, 15, 20, 25, that the final input is TRUE, which 3. Plug this data into the V-Lookup and 30 years to account for all tells the function to find the first table. Using the same logic from years in between. closest match. It will always find the deposit rates, get the lower a hit on the lower bound of a and upper bounds and use number. linear interpolation to calculate 3. Use the VLOOKUP() with the first the rates for the days in Dates and Day input being the specific day.
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