Question

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Show your answers along with the formula and steps you used for each question Table 1.en January 1,2019 LIBOR so Im days) Problem 3: On January 1, 2019,a US-based lender wishes to hedge against decrease n future interest rates. The lender proposes to hedge against this risk by entering into an FRA with the notional amount of S10 million Use 30/360 day ceent coav ention ลnd simple interest rate 540% 530% s 20% 510% A) An 360 Table I has spot LIBOR rates for maturities ranging freem 30 days to 360 days announced by the British Bankers Asseciation (BBA) en January 1,2019 Table 2. on February 15,2019 A) Indicate whether the manager should take a long or short FRA in seder to fully hedge interest rate risk and why? (2 points) 1) Cakine the price of this 3X12 FRA today. (2 Psints) C) Caelale the price of this 3X6 FRA oday 2 poins) 135 315 ) Ans: Suppose 45 days later on February 15, 2019, interest rates have decreased Table 2 has spot LIBOR ales for maturities ranging froem 45 days to 315 days announced by the British Banker's Association (BBA) on February 15, 2019 D) Suppose the manager enicred into 3X12 FRA at the price computed in (B). Calculate the value of this 3X12 FRA at this point. (2 points) E) At expiration, the 270-day LIBORs 4 5% Calculate the payoff en this 3X12 FRA. (2 points) D) Ans:

Answer 1

A   The manager should take a short FRA. In an FRA, a person who agrees to pay the rate is the buyer of                   
   the FRA or the long and the counterparty is known as the seller of FRA or the short. In the given case,                   
   the lender wishes to hedge. Therefore, he is the counterpart and has to take the short FRA                  
                      
B   Price of 3 * 12 FRA today :                  
                      
   3 * 12 FRA means the loan is proposed to be taken after 3 months for a period of 9 months.                  
                      
   Hence, the current FRA rate is calculated by the below formula ,                  
                      
   ((1+ LIBOR 360) / (1+ LIBOR 90) ) - 1                  
                      
   '= (1+ 0.051)/(1+0.01325) -1                  
                      
   0.03726   < for 9 months>              
   0.04968   <when annualised , I.e 0.03726*360/270>              
                      
   Therefore, 4.96% p.a is the current FRA rate that is computed on Jan 1, 2019                  
                      
   Note : LIBOR 90 is 5.30% p.a, Therefore , for 90 days, it is 5.30*90/360, which equals 1.325%                  
                      
C   Price of 3 * 6 FRA today :                  
                      
   3 * 6 FRA means the loan is proposed to be taken after 3 months for a period of 3 months.                  
                      
   Hence, the current FRA rate is calculated by the below formula ,                  
                      
   ((1+ LIBOR 180) / (1+ LIBOR 90) ) - 1                  
                      
   '= (1+ 0.026)/(1+0.01325) -1                  
   0.012583271650629                  
   0.01258   < for 3 months>              
   0.05032   <when annualised , I.e 0.01258*360/90>              
                      
   Therefore, 5.03% p.a is the current FRA rate that is computed on Jan 1, 2019                  
                      
   Note : LIBOR 90 is 5.30% p.a, Therefore , for 90 days, it is 5.30*90/360, which equals 1.325%                  
                      
D   Value of 3 * 12 FRA on Feb 15, 2019 :                  
                      
   Hence, the FRA rate as on Feb 15, 2019 is calculated by the below formula ,                  
                      
   ((1+ LIBOR 315) / (1+ LIBOR 45) ) - 1               < Note -1>  
                      
   '= (1+ 0.04419)/(1+0.01325) -1                  
   0.03054   <for 270 days (315 – 45) >              
   0.04072   <when annualised , I.e 0.01258*360/90>              
   Therefore, 4.07% p.a is the FRA rate that is computed on Feb 15, 2019                  
                      
   The manager has entered into an FRA for 4.96% p.a <which is the price arrived in B>                  
                      
   Therefore, the value of FRA as on Feb 15, 2019 is                  
                      
   Value of FRA at the end of the loan period                '=10000000 * (0.0496-0.0407)*270/360  
   Value of FRA at the end of the loan period=                66,750.00    <in $>
   $ 66,750 is the value at the end of 315 days from today.                  
   Therefore, the value as on Feb 15, 2019 is the present value of $ 66,750 discounted at LIBOR 315.                  
                      
   Value of FRA as on Feb 15, 2019                '= 66,750/((1+(0.0505*315/360)))  
   Value of FRA as on Feb 15, 2019                63,925.30    <in $>
                      
   Note :                   
   1. Since 45 days has passed in the total of 360 days, LIBOR 315 (360-45) days is considered on Feb 15, 2019                  
   Similarly, where LIBOR 90 was used in answer ‘B’, LIBOR 45 is used.                  
                      
       LIBOR 315 = 5.05% p.a              
       For 315 days, it is 5.05%* 315/360 days, I.e 4.42%              
                      
   LIBOR 90 is 5.30% p.a, Therefore , for 90 days, it is 5.30*90/360, which equals 1.325%                  
                      
E   Pay off on the expiration :                  
                      
   Interest savings at the end of the loan period=                '=10000000 * (0.0496-0.0450)*270/360  
   Interest savings at the end of the loan period=                34,500.00    <in $>
   Therefore, pay off as on the date of expiration is the present value of the above computed interest savings                       discounted using LIBOR 270.                  
   Pay off on the expiration         '=34500/(1+(0.0496*270/360))          
   Pay off on the expiration         33,262.63    <in $>