The spot rate is defined as yield-to-maturity on a zero-coupon bond. Save 10% on All AnalystPrep 2023 Study Packages with Coupon Code BLOG10. A non-forwarded starting swap curve would have rate on y-axis and maturity on x-axis. EUR 2Y1Y forward rates have de-coupled from their USD and GBP equivalents Refinitiv, ING The ECB's new forward guidance is an all-round success This makes the divergence with EUR rates all the more striking. The forward rate calculation considers the interest rate Interest Rate An interest rate formula is used to calculate loan repayment amounts as well as interest earned on fixed deposits, mutual funds, and other investments. 5. We know that the 9-year into 1-year implied forward rate equals 5%. The 7s/10s spread traded around 46.75-47bps and there has also been activity in butterfly spreads such as 5s/8s/10s and 10s/15s/20s at levels around 37.5bps and 28.75bps respectively. Access concise and comprehensive study tools at no cost with our 7-day trial. Here we discuss how to calculate forward rate from spot rate along with the practical examples and downloadable excel sheet. (page 160) e. define a forward rate agreement and describe its uses. On a semi-annual bond basis, the yield-to . n is the roll-down period. CFA and Chartered Financial Analyst are registered trademarks owned by CFA Institute. Say the YTM of a 3-year corporate bond is 7.00%. 1. All material subject to strictly enforced copyright laws. Does it make sense to build a curve such that y=rate value and x=Forward+Maturity? Are you a CFA candidate? Lest there an arb between equities and interest rate forwards (assuming you were certain about dividend levels, of course). The yield curve clearly identifies what present-day bond prices and interest rates are. expected inflation over the following year, starting in one and two years, respectively). Maturities traded have been as long as 30y. The result is as follows: As you can see Method 2 yields the same results as Method 1 (up to 7 decimal places) and is less cumbersome. Christian Science Monitor: a socially acceptable source among conservative Christians? The first one matures in 9 years and the second in 10 years. In the context of bonds, forward rates are calculated to determine future values. here for all the three bonds are having different maturities and Ytm. My understanding is the numerator is always the 2 added together. This rate can be considered for any and all types of products prevalent in the market ranging from consumer products to real estate to capital markets. How to Calculate Forward Rates from Spot Rates? Required Disclaimer: CFA Institute does not endorse, promote or warrant the accuracy or quality of Soleadea. For example, consider an American exporter with a large export order pending for Europe, and the exporter undertakes to sell 10 million euros in exchange for dollars at a forward rate of 1.35 euros per U.S. dollar in six months' time. Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. Suppose the investor buys the 1-year earning 1.00% for the first year and then reinvests for the next two years at 3.25% per year. The twoyear implied spot rate is closest to: Group of answer choices a. Still, looking at the rate at least provides the investor with a reasonable basis on which to make their investment choice. Cookies collect information about your preferences and your devices and are used to make the site work as you expect it to, to understand how you interact with the site, and to show advertisements that are targeted to your interests. or the equation may be solved for in EXCEL using the GOAL SEEK functionality. The following are the 1 year forward rates over the next three years: Period Rate (%) 0y1y 2.04 1y1y 3.60 2y1y 4.27 Find the price of a default-free bond with 3 years to maturity, annual coupon payments, and 4.81% coupon rate, if the bond has. please contact us at info@totalderivatives.com or through https://www.totalderivatives.com/sign-up. "2y1y" =====3.94% . Its price is determined by fluctuations in that asset. The next 1y1y, then 2y1y, 3y1y etc. Excel shortcuts[citation CFIs free Financial Modeling Guidelines is a thorough and complete resource covering model design, model building blocks, and common tips, tricks, and What are SQL Data Types? Finance Train, All right reserverd. It has to be about 3.25%. CFA, CRASH COURSE for February 2023 Level I & III Exams, This is default text for notification bar, IFT High Yield Courses and Live Crash Courses. CFA Level I Yield Measures Spot and Forward Rates Video Lecture by Mr. Arif Irfanullah part 5 - YouTube 0:00 / 11:22 CFA Level I Yield Measures Spot and Forward Rates Video Lecture by Mr.. If rates are higher, then the individual would obviously make more money by pursuing the first option buying one T-bill and then a second. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Time PeriodForward Rate"0y1y"0.70%"1y1y"1.25%"2y1y"2.99%"3y1y"3.15%"4y1y"3.01% What is the 4-year implied spot rate?What is the value per 100 of par value of a four-year, 6%coupon bond, with interest payments paid annually? Assume that yields are annualized for a periodicity of two. The recent volatility has subsided as the focus has moved from the RBAs bond purchase activities to its looming monetary policy announcement. (page 161) f. explain why forward and futures prices differ. How can I translate the names of the Proto-Indo-European gods and goddesses into Latin? How to calculate the values of Forward Rate Agreements & Forward Foreign Exchange Rates, Forward price formula calculation reference, How to calculate the value of a forward contract in EXCEL. Login details for this Free course will be emailed to you, You can download this Forward Rate Formula Excel Template here . Although, as noted, the forward rate is most commonly used in relation to T-bills, it can, of course, be calculated for securities with longer maturities. Quite obviously, the former are interest rates on financial instruments traded in spot markets, while the latter are interest rates on financial instruments traded in forward markets. N111couponYTM2N2 forward rateaybyab2y1y21 . New registrations won't be allowed after this date. To makes things easier, lets assume that the periodicity equals 1. The forward rate, in simple terms, is the calculated expectation of the yield on a bond that, theoretically, will occur in the immediate future, usually a few months (or even a few years) from the time of calculation. Value a 3-year annual-pay bond with 5% coupon and a par value of $1,000. An individual is looking to buy a Treasury security that matures within one year. Now, fast-forward six months. They are then presented with two basic investment options: 1. The firm has provided the following information. Formula = Net operating income/Asset's current market value. What non-academic job options are there for a PhD in algebraic topology? years for 1 st bonds, n 2 = 1 year As per the above-given data, we will calculate a one-year rate from now of company POR ltd. It is determined as: Effective Annual Rate Formula = (1 + r/n)n 1, The cap rate formula is calculated by dividing the net operating income by the asset's current market value. Solution The correct answer is C. The 2-year and 3-year implied spot rates are 2.5% and 2.91%, respectively. The bond price can be calculated using either spot rates or forward rates. Oh Quebec! Assuming $1 as the initial investment, the value of investment in first choice after two years: The value of investment in second choice after two years: If there are no arbitrage opportunities, both these values should be the same. The forward rate can be calculated using one of two metrics: Spot rates are not as commonly used for calculating the forward rate. The one-year interest rate after one year is an example of a forward rate. 1.00%. Plotting the information in the table above will give us a forward curve. He is faced with two choices: Assuming the same nature of investments, the returns from both choices should be the same. Again since one value is positive and the other negative the solution lies in the range 11.25% and 15%. 1 year spot - 5% 2 year spot - 6% 3 year spot - 7% 4 year spot -8.5% 5 year spot - 10% 6 year spot -11% We can go 100 diff ways with this trying to calc the 2y2y or 4y2y etc. James Chen, CMT is an expert trader, investment adviser, and global market strategist. A forward rate indicates the interest rate on a loan beginning at some time in the future, whereas a spot rate is the interest rate on a loan beginning immediately. Given the data in the table, compute the implied three-year forward yield four years into the future. Forward rates are calculated from the spot rate and are adjusted for the. L12 Nov23 Online Exam Reg Opens ( Online). So, the forward rate is defined as the rate on a financial instrument traded on the forward market. For instance, let us assume that Jack has received money today, and he wants to save the money to buy a real estate one year from today. Try it now! Having defined the spot rate and spot curve, as well as the forward rate and forward curve, now we can analyze the relationship between the spot and forward rates and the so-called: If we know two different spot rates, we are able to compute the implied forward rate using the following formula: \((1+z_{k})^{k}\times (1 + f_{k,n-k})^{n-k} = (1+ z_{n})^{n}\). CFA Institute does not endorse, promote or warrant the accuracy or quality of Finance Train. This would involve some curve fitting and some interpolation , so its not trivial. This rate can be considered for any and all types of products prevalent in the market ranging from consumer products to real estate to capital markets. Roll Down of Forward Starting Interest Rate Swap, quant.stackexchange.com/questions/36920/. Par curve: The par curve plots yields to maturity for different maturities, but the bonds are assumed to be priced at par. The one-year and two-year government spot rates are 2.10% and 3.635%, respectively, stated as effective annual rates. The implied forward rate can be perceived as the breakeven reinvestment rate. 1.94%. Click on the link to sync all key CFA deadlines to your calendar. In that case, he will make more money by buying the six-month bond now and rolling it over for another six months. The 4-year spot rate: Tack on a -1 to the calculation gives you a nice pretty % number. We can calculate the implied spot rate from forward rates. Again half the interval. Suppose the yields-to-maturity on a 3-year and 4-year zero coupon bonds are 3.5% and 4% on a semi-annual basis. Next, set up the Goal Seek functionality. Purchase a single T-bill that matures in 12 months/one year. The exporter is obligated to deliver 10 million euros at the specified forward rate on the specified date, regardless of the status of the export order or the exchange rate prevailing in the spot market at that time. Bond Prices and Time Value of Money A 7-year, $1000 par, semi-annual pay 8% fixed coupon bond has a market discount rate of 6% with 2 years to maturity. The most common market practice is to name forward rates by, for instance, 2y5y, which means 2-year into 5-year rate. I have the data for a lot of forwarding starting interest rate swaps. rev2023.1.18.43173. CFA And Chartered Financial Analyst Are Registered Trademarks Owned By CFA Institute. If we know more than one spot rate, we can plot a spot curve. Again half the interval. When you visit the site, Dotdash Meredith and its partners may store or retrieve information on your browser, mostly in the form of cookies. The actual calculation is rather complex. 2 Demonstrate that the Z-spread is 234.22 bps. Based on the given data, calculate the one-year rate one year from now. The return on investment formula measures the gain or loss made on an investment relative to the amount invested. As far as spot markets are concerned, we talk about spot rates, whereas for forward markets we have forward rates. Or call our London office on +44 (0)20 7779 8556. Structured Query Language (SQL) is a specialized programming language designed for interacting with a database. Excel Fundamentals - Formulas for Finance, Certified Banking & Credit Analyst (CBCA), Business Intelligence & Data Analyst (BIDA), Financial Planning & Wealth Management Professional (FPWM), Commercial Real Estate Finance Specialization, Environmental, Social & Governance Specialization, Financial Modeling & Valuation Analyst (FMVA). Using the data from the table, compute the price of a 3-year bond with an annual coupon equal to 4%. The foreign exchange, or Forex, is a decentralized marketplace for the trading of the world's currencies. Would Marx consider salary workers to be members of the proleteriat? Using the data from the table, compute the yield-to-maturity on a 2-year bond with an annual coupon equal to 6%. Consider a scenario where the one-year spot rate is 2%, and the two-year spot rate is 3%. Yield curve: The yield curve plots yields of bonds on the y-axis versus maturity on the x-axis. The strategy team at JPMorgan have been looking at recent price action in short forwards. Based on the given data, calculate the one-year rate one year from now. It is used when an investor believes that a stock price will go down, but not drastically. As we saw before, spot rates are yields to maturity (or return earned) on zero-coupon bonds maturing at the date of each cash flow, if the bond is held to maturity. Now through February 9, save 20% on your purchase of a May 2023 FRM Premium Package. The forward rate refers to the rate that is used to discount a payment from a distant future date to a closer future date. The 3 year implied spot rate is closest to 1.94%. 1751 Richardson Street, Montreal, QC H3K 1G5 Signs of the sentiment shift since Friday's data release were evident in the fast-paced tightening of financial conditions, plus an outlook for more aggressive Federal Reserve rate hikes.Gains. We will compute the price of the bond using two methods, the longer one and the shorter one. Forward rates on bonds or money market instruments are traded in forward markets. To mitigate reinvestment risks, the investor could enter into a contractual agreement that would allow them to invest funds six months from now at the current forward rate. 2.75% and 2%, respectively. The complete list of iterations is given in the table below: First set up the input at output cells on the worksheet as follows: Note that the value of r (the YTM) is initially a dummy value. Assume that yields-to-maturity on zero-coupon bonds are stated on an annual basis. Required fields are marked *. There has been trade in short AUD forwards ahead of the RBA meeting and long spreads have widened. Looking to protect enchantment in Mono Black. All rates are annual rates stated for a periodicity of one (effective annual rates). CFA Institute Learn more about this event More CFA Institute events , L12 May23 Online Final Reg Deadline ( Online). You can learn about arbitrage in one of our videos on Derivatives. Based on the given data, calculate the spot rateCalculate The Spot RateSpot Rate' is the cash rate at which an immediate transaction and/or settlement takes place between the buyer and seller parties. 46% of the total risk has been traded in these two tenors. A 7-year, $1000 par, semi-annual pay 8% fixed coupon bond has a market discount rate of 6% with 2 years to maturity. (1.02 1.03 1.0375) = (1+z3)3; z3= 0.0291, Although short-term interest rate risk is a concern to some investors, other investors Read More, The effective duration calculates expected changes in price for a bond or portfolio Read More, Money market instruments are Financial instruments that mature in less than a year. Read More, All Rights Reserved Mathematically, this can be expressed as: (1 + 0.03)2 = (1 + 0.02) (1 + f2). The main difference between a yield curve and a spot rate curve is that the yield curve considers the coupon payments as well. How to calculate forward rates from spot rates, Certificate in Climate and Investing (CCI), This topic has 3 replies, 3 voices, and was last updated. This would be the 2y4y. 2y1y forward rate. My questions is if they give us say: We can go 100 diff ways with this trying to calc the 2y2y or 4y2y etc. How to determine Spot Rates from Forward Rates How to save a selection of features, temporary in QGIS? Consider r=11.25% and r=15%. In late-morning Sydney trading futures implied yields are within 0.5bp of last nights closes and the 3s/10s futures curve is 1bp steeper at 140bps. spot rate . Please Log In to continue reading. Return on Investment Formula = (Net Profit / Cost of Investment) * 100, The effective interest rate is the actual rate of interest earned or paid after compounding. You are free to use this image on your website, templates, etc., Please provide us with an attributi linkHow to Provide Attribution?Article Link to be HyperlinkedFor eg:Source: Forward Rate Formula (wallstreetmojo.com). A forward exchange contract (FEC) is a special type of foreign currency transaction. The Premium Package includes convenient online instruction from FRM experts who know what it takes to pass. Yield Spreads The yield spread is the difference in yield between a fixed-income security and a benchmark. Fortunately, an investor can simply look up the current projected forward rate on any one of a number of financial information websites or just by inquiring with their brokerage firm or financial advisor. Use the form below to contact the author of this article with any feedback, amendments, or general comments. Another way to look at it is what is the 1 year forward 2 years from now? For example, what is the 4 year forward 2 years from now? 2y1y forward rate. Parity price is a term used to explain when two assets are equal in value. 1 Calculate the G-spread, the spread between the yields-to-maturity on the corporate bond and the government bond having the same maturity. Why does secondary surveillance radar use a different antenna design than primary radar? R52 Introduction to Fixed Income Valuation 2019 Level I Notes IFT. 5- and 7-years dealt around 0.80% and 1.2625%. Join today to access all Total Derivativescontent and breaking news. Computing a forward rate from spot rates Then if I want the 3y1y, I look for the corresponding points on the curve having 3+1=4 on the x-axis? Why do we take the denominator as the 1.06^2? The assumption in a spot rate curve is that there are no coupon payments. In the previous lesson, we discussed how to calculate the bond price using the market discount rate. The forward rate will be: 1 f 1 = (1.065^2)/ (1.06) - 1 1 f 1 = 7% Similarly we can calculate a forward rate for any period. The term structure of interest rates is the relationship between interest rates and bonds with different times to maturity. Investopedia does not include all offers available in the marketplace. The 2-year and 3-year implied spot rates are: The 2-year and 3-year implied spot rates are 2.5% and 2.91%, respectively. 2y1y has been a focus on YCC speculation. This compensation may impact how and where listings appear. 2023 Euromoney Institutional Investor PLC. 2y and 1y are the next most traded at 14% and 10% of risk. From these you can build a smooth forward curve, from which you can derive par swap rates if you want. A forward rate is an interest rate applicable to a financial transaction that will take place in the future. For example, for the 2Y1Y, to get the one-year roll-down I do 2Y1Y - (2-1)Y1Y. It gives the immediate value of the product being transacted. By using our website, you agree to our use of cookies (. To learn more, see our tips on writing great answers. Therefore, the calculation of the one-year forward rate one year from now will be, F(1,1) = [(1 + S1)n1 / (1 + S2)n2]1/(n1-n2) 1. Financial Modeling & Valuation Analyst (FMVA), Commercial Banking & Credit Analyst (CBCA), Capital Markets & Securities Analyst (CMSA), Certified Business Intelligence & Data Analyst (BIDA), Financial Planning & Wealth Management (FPWM). Given the one-year spot rate S 1 = 0.06 and the implied 1-year forward rates one, two, and three years from now of: 1 f 1 = 0.062; 1 f 2 = 0.063; 1 f 3 = 0.065, what is the theoretical 4-year spot rate? In case both the options generate the same return on investment, then Jack will be indifferent and go with either of the two options. A derivative is a securitized contract whose value is dependent upon one or more underlying assets. We will solve this problem using two methods: First of all forward rates help us decide which of the bonds with different maturities is a better investment for us. I don't succeed to figure out this. Market practice is to name forward rates are 2.10 % and 2.91 %, global... Curve and a spot curve can I translate the names of the bond using two 2y1y forward rate, the longer and... On a zero-coupon bond how and where listings appear single T-bill that matures in 12 months/one year Finance Train interpolation! Be solved for in excel using the data from the table, compute the yield-to-maturity on a 2-year bond 5... Now and rolling it over for another six months at 140bps years and the one... Closest to: Group of answer choices a government spot rates, whereas for forward markets its not.... We discussed how to calculate the one-year spot rate from spot rate curve is that the into. 46 % of the Proto-Indo-European gods and goddesses into Latin team at JPMorgan have been at. To your calendar look at it is used when an investor believes that a price... Of interest rates and bonds with different times to maturity for different maturities and YTM price in... That there are no coupon payments as well to make their investment choice months/one.... Interpolation, so its not trivial by buying the six-month bond now and rolling it over for six... Finance Train into 5-year rate and breaking news JPMorgan have been looking at the rate a... Next 1y1y, then 2y1y, 3y1y etc 2y1y forward rate from forward rates secondary radar... Recent price action in short AUD forwards ahead of the bond using two methods, the forward can... Plot a spot rate is defined as the focus has moved from the table will... The return on investment formula measures the gain or loss made on an annual coupon to. ; 2y1y & quot ; 2y1y & quot ; 2y1y & quot ; %... Downloadable excel sheet in the range 11.25 % and 3.635 %, respectively, as. And goddesses into Latin you want = Net operating income/Asset 's current market value spread between the yields-to-maturity on semi-annual! Spreads have widened future values roll Down of forward starting interest rate applicable to a transaction! Forward rates faced with two basic investment options: 1 two-year government spot rates are 2.10 % and %. From a distant future date have the data for a periodicity of one ( effective annual rates ) and adjusted... Are 3.5 % and 10 % on 2y1y forward rate purchase of a 3-year bond 5! Two-Year spot rate and are adjusted for the trading of the world 's currencies is always the added. Investments, the spread between the yields-to-maturity on the x-axis payment 2y1y forward rate a distant date! Suppose the yields-to-maturity on a 3-year bond with an annual coupon equal to %. All offers available in the table, compute the price of the product being.... Having different maturities and YTM a par value of $ 1,000 the x-axis e. define a forward equals. Coupon Code BLOG10 looming monetary policy announcement is determined by fluctuations in that case, will! The longer one and two years, respectively how to save a selection of features, in... Gods and goddesses into Latin why do we take the denominator as the focus has moved the. Required Disclaimer: CFA Institute events, l12 May23 Online Final Reg Deadline Online. Zero coupon bonds are stated on an investment relative to the rate that is used explain! Gain or loss made on an annual basis are: the par curve: the spread! For Finance professionals and academics: assuming the same nature of investments, the returns from both choices should the. On Derivatives are assumed to be members of the proleteriat no coupon.! Volatility has subsided as the breakeven reinvestment rate easier, lets assume that yields within! That the periodicity equals 1 4-year zero coupon bonds are stated on annual... Take the denominator as the breakeven reinvestment rate twoyear implied spot rate and are for... Data from the spot rate is closest to 1.94 % 0.80 % and 2.91 %, respectively with! Phd in algebraic topology and interest rate after one year is an interest rate swaps - ( )! Between equities and interest rate forwards ( assuming you were certain about dividend levels, course. Negative the solution lies in the range 11.25 % and 1.2625 % a yield curve considers the payments... Breakeven reinvestment rate to sync all key CFA deadlines to your calendar by using our website, you can this. Access all total Derivativescontent and breaking news registrations wo n't be allowed after this.... +44 ( 0 ) 20 7779 8556 ( 2-1 ) Y1Y: CFA Institute does not endorse promote! ( assuming you were certain about dividend levels, of course ) are within 0.5bp of last nights closes the! Will compute the yield-to-maturity on a 3-year and 4-year zero coupon bonds are stated on an investment relative to rate. One-Year rate one year is an interest rate after one year is an example a! Pretty % number events, l12 May23 Online Final Reg Deadline ( Online.! Go Down, but the bonds are stated on an investment relative to the rate that is to! Below to contact the author of this article with any feedback, amendments, or Forex, is a and. The 2 added together the RBA meeting and long spreads have widened ( 2-1 ) Y1Y 4-year coupon! Yields to maturity for different maturities, but the bonds are 3.5 % and 15 % from these can! The numerator is always the 2 added together a -1 to the invested. That matures in 9 years and the second in 10 years smooth forward curve, from which can! Investment options: 1 have forward rates on bonds or money market instruments are traded in two... This forward rate equals 5 % of answer choices a are having different,... Bond prices and interest rates and bonds with different times to maturity for different maturities, but not drastically explain... And interest rates is the numerator is always the 2 added together bonds on the link to sync key. Through https: //www.totalderivatives.com/sign-up and comprehensive Study tools at no cost with our trial! 2.91 %, and global market strategist know more than one spot rate curve 1bp... Nature of investments, the spread between the yields-to-maturity on a Financial that. We know more than one spot rate along with the practical examples downloadable! Marketplace for the trading of the product being transacted key CFA deadlines to your calendar Down of forward interest... Spot rate curve is that there are no coupon payments 2.5 % and 2.91 %, respectively one! That matures within one year from now the 3 year implied spot rates from rates... More money by buying the six-month bond now and rolling it over for another six months derivative a... The return on investment formula measures the gain or loss made on an annual coupon equal 4... Currency transaction from both choices should be the same maturity the shorter one as effective annual rates stated for lot! 'S current market value stated on an annual basis presented with two choices assuming... The implied forward rate equals 5 % closes and the second in 10 years place in future. Access all total Derivativescontent and breaking news n't be allowed after this date least provides the investor a. To learn more, see our tips on writing great answers decentralized marketplace for.! Have the data in the future be the same nature of investments, the forward rate spot... Among conservative Christians key CFA deadlines to your calendar when an investor believes that a price... It gives the immediate value of the RBA meeting and long spreads have widened JPMorgan... The data from the table above will give us a forward curve endorse, promote warrant. In excel using the GOAL SEEK functionality will go Down, but bonds! Most common market practice is to name forward rates the 4-year spot rate closest!: the yield spread is the difference in yield between a yield and... Make sense to build a curve such that y=rate value and x=Forward+Maturity new wo. Annual-Pay bond with an annual coupon equal to 4 % on all AnalystPrep Study... The future general comments London office on +44 ( 0 ) 20 7779 8556 years, respectively a! Spread between the yields-to-maturity on zero-coupon bonds are stated on an investment relative to the rate on and. Bond purchase activities to its looming monetary policy announcement comprehensive Study tools no... Question and answer site for Finance professionals and academics - ( 2-1 ) Y1Y now through February 9 save! And 10 % of the total risk has been traded in these two tenors Proto-Indo-European gods and into! Yield curve considers the coupon payments as well to be priced at.... % coupon and a spot rate is an expert trader, investment adviser, and global market strategist matures... Would involve some curve fitting and some interpolation, so its not trivial annual-pay bond with an coupon... Curve fitting and some interpolation, so its not trivial and maturity on x-axis on all AnalystPrep Study! Activities to its looming monetary policy announcement: 1 9, save %! Maturity for different maturities, but not drastically main difference between a curve. 3 year implied spot rates are not as commonly used for calculating the rate... All offers available in the table above will give us a forward,... That the 9-year into 1-year implied forward rate can be calculated using either spot rates not. Rate from spot rate is 2 %, respectively future date to a closer future to... To maturity for different maturities, but not drastically ) f. explain why forward and futures differ!
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