# Difference between settlement of Eurodollars and FRA

I am going through J.C. Hull's chapter on FRA and EuroDollar Futures.

• Taking the case of FRA. I assume $$T_0$$ is the time when two parties entered into a FRA to fix interest rates they get on a principal $$P$$ for the time between $$T_1$$ and $$T_2$$. I also assume they fixed the rate to be $$R_F$$. Now say time elapses and we are are time $$T_1$$. The market interest rate is $$R_M$$. Let us say $$R_M > R_F$$. Talking from perspective of the party who entered as a borrower, he will be paid at $$T_1$$, $$G = P*(e^{R_M(T_2-T_1)}-e^{R_F(T_2-T1)})*e^{-R_M(T_2-T_1)}$$ ( assuming all rates are expressed in continuous compound). This makes sense to me as the borrower can borrow $$P$$ from market at $$T_1$$ ( to $$T_2$$ ) and paying $$L = P*e^{R_M(T_2-T_1)}$$. Plus he can also invest amount $$G$$ he got for $$T_1$$ to $$T_2$$ again at rate $$R_M$$ earning $$G^{'} = P*(e^{R_M(T_2-T_1)}-e^{R_F(T_2-T1)})$$. So in net he will pay back $$L-G = P*e^{R_F(T_2-T_1)}$$. Which is what was intended ( assuming rate of borrowing and investing is same).
• In case of Eurodollar Future, the payment made at time $$T_1$$ according to hull is $$P*(e^{R_M(T_2-T_1)}-e^{R_F(T_2-T1)})$$. It is not dicounted. Doesn't this make the above scenario more favorable for the borrowing party ? If I repeat the same process above the amount the party pays back would be less than $$L-G$$ ( so that the party borrowed at a rate less than $$R_F$$, which is not what was agreed in the contract).

Did I misinterpret the book ?

PS: I am beginner. I apologize if I used something incorrectly or vaguely. Just having a hard time with this chapter being complete novice to finance.

• note futures are settled daily so at time T1 it doesn't account for further days discounting while forward is cleared once – numerairX Oct 10 '18 at 18:13
• @Jojo Tang can you please elaborate in an answer. – sashas Oct 10 '18 at 18:17
• If you are saying that there are some subtle differences between FRA and ED which make them not equivalent, you are right. – noob2 Oct 10 '18 at 23:35