Question

You are a manager of Short Term Capital Management (STCM). You observe that the interest rate on 3 year notes is 5.5 percent, while the interest rate 3.25 year notes is 5.70 percent. You know for sure for sure that the two interest rates will converge in six months to some value X. You also have the ability to go short $400 million face in any note you choose. Given all this, describe your profit making arbitrage strategy. Then graph the amount of money you will make if the interest rate converges to X, X a percentage rate between 0 and 10 percent^. Please make sure you don’t have negative returns!

First note that if you have negative returns, you can simply reverse strategy! Make sure your graph is done in EXCEL, has at least 50 data points, and not too much empty space.

Answer 1

The strategy to be followed should be take a 3-year, $400 million loan @5.50% and deposit the amount for 3.25 years @5.70%

After 6-months, if the interest rate converges to X, where X is:

case a) below 5.50%, say 5%: close out both the loans. Receive: (5.70-5.00)*400*6/12 = $1.40 mn on deposit and pay: (5.00-5.50)*400*6/12 = -$1.00 on 3-years loan. Therefore, receive a net amount of (1.40-1.00) = $0.40mn

case b) between 5.50% and 5.70%, say 5.60%: : close out both the loans. Receive: (5.70-5.60)*400*6/12 = $0.20 mn on deposit and again receive: (5.60-5.50)*400*6/12 = -$0.20 on 3-years loan. Therefore, receive a net amount of (0.20-0.20) = $0.40mn

case c) above 5.70%, say 6.00%: close out both the loans. Pay: (5.70-6.00)*400*6/12 = -$0.60 mn on deposit and receive: (6.00-5.50)*400*6/12 = -$1.00 on 3-years loan. Therefore, receive a net amount of (1.00 - 0.60) = $0.40mn

From these above scenarios, we can see that we have a risk-free return of $0.40mn through the strategy adopted.

Graph: