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Explanation:
The correct answer is D.
A long position in a 612 FRA is equivalent to a long position in a 6-month bill and a short position in a 12-month bill. This is because a long position in a 612 FRA means that you are agreeing to borrow money for six months starting six months from now at a fixed rate. This is similar to buying a 6-month bill now (which is a long position in a 6-month bill) and selling a 12-month bill now (which is a short position in a 12-month bill). The reason for this is that when you buy a 6-month bill now, you are effectively lending money for six months. When you sell a 12-month bill now, you are effectively borrowing money for 12 months. However, since the 12-month period starts now and the 6-month period starts six months from now, the net effect is that you are borrowing money for six months starting six months from now, which is exactly what a long position in a 6*12 FRA represents.
Choice A is incorrect. The formula suggests that a long position in a 6*12 FRA is equivalent to shorting 6-month bills and going long on 12-month bills. This does not align with the concept of forward rate agreement where the investor borrows for the shorter period and invests for the longer period.
Choice B is incorrect. According to this choice, a long position in a 6*12 FRA equals shorting 12-month bills minus going long on 6-month bills. This contradicts with the definition of forward rate agreement as it implies borrowing for longer term (shorting) and investing for shorter term (long).
Choice C is incorrect. This option suggests that being long in a 6*12 FRA equals being long on both, the 12 month Bills and short on the 6 month Bills which does not support our initial statement about FRAs.
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Q.1525 The forward rate can be defined as the implied rate that makes the return on a period investment and a period investment equal. That is:
It means that if you sold a 5*10 FRA on $50 million, this transaction is equal to borrowing $50 million into 5-month Bills and investing the proceeds into 10-month Bills. Which of the following formulas is supporting the above statement?
A
Long 6*12 FRA = Short 6-month Bills + Long 12-month Bills
B
Long 6*12 FRA = Short 12-month Bills - Long 6-month Bills
C
Long 6*12 FRA = Long 12-month Bills + Short 6-month Bills
D
Long 6*12 FRA = Long 6-month Bills + Short 12-month Bills