I believe this falls under “Derivatives” and for the life of me, I cannot figure this out. I found an older thread explaining this answer but not clear…
“A bank can borrow or lend at LIBOR. Suppose that the six-month rate is 5% and the nine-month rate is 6%. The rate that can be locked in for the period between six months and nine months using an FRA is 7%. What arbitrage opportunities are open to the bank? All rates are continuously compounded.”
The implied forward rate is 7.8% (if I got this right). Does this mean I can short the bond for 9 months, and simultaneously long the bond and FRA for 5% and 7% respectlvely, because you earn the extra 0.8% on the FRA differential?
If the implied forward rate is too high, you want to pay money at T1 and receive money at T2. So you short the 6m bond and long the 9m bond. You are now short interest rates between T1 and T2, so you can hedge this buy going long the FRA.
Edit: That was kind of vague. Here’s what you are supposed to do. Let’s say your notional is $1000. The question states that the rates are continuously compounded. This makes the calculations more tractable.
t=0: Borrow $1000 for 5% for 6m (short bond). Lend that money for 6% for 9m (long bond). Go long FRA with notional $1025.32 = $1000*exp(0.5*5%) from 6m to 9m, thus guaranteeing that you can borrow at a rate of 7% over this period.
t=6m: You must now deliver $1025.32 = $1000*exp(5%*0.5) from your short bond position. You can fortunately borrow this money for a known rate of 7%, due to the FRA agreement.
t=9m: You receive $1046.03 from your long bond position from t=0. You must pay effectively $1025.32*exp(7%*0.25) = $1043.42, which you locked in with the FRA. Your net arbitrage proceeds are $2.61 in this period.
Also, since the rates are continuous, the forward rate is (0.75*6% - 0.5*5%)/(0.75-0.5) = 8.00%. So, you could also calculate the arbitrage proceeds as $1000 * exp(0.5*5%) * [exp(0.25*8%) - exp(0.25*7%)].
when is the new season coming out? i recently watched the entire thing with my wife from season 1. very refreshing and you pick up subtle messages here and there second time around.
Not until the summer. HBO is going to finish up The Leftovers (also a quality show) while trying to give George RR Martin as much time as possible to get the next book out.