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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.

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  • $\begingroup$ note futures are settled daily so at time T1 it doesn't account for further days discounting while forward is cleared once $\endgroup$
    – numerairX
    Oct 10, 2018 at 18:13
  • $\begingroup$ @Jojo Tang can you please elaborate in an answer. $\endgroup$
    – advocateofnone
    Oct 10, 2018 at 18:17
  • $\begingroup$ If you are saying that there are some subtle differences between FRA and ED which make them not equivalent, you are right. $\endgroup$
    – nbbo2
    Oct 10, 2018 at 23:35

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Futures trading are settled on a daily basis meaning in the end of day, your account will be adjusted by your PnL. So of course your payment on T1 is not discounted. However forward is settled only once at expiration, hence you discount the whole duration.

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I think he does mention this caveat in the last paragraph of Example 6.3, saying that a hedger could slightly reduce the size of the hedge to account for this. As for your question in particular, I feel like the problem is that you are assuming the forward rate is the same as the futures rate, while they don't necessarily need to be the same, and you are also assuming the realize spot rate at $T_1$ is greater than the forward rate.

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