Can someone please explain in detail how to solve the following question. It looks simple but I am missing a critical point. Thank you!
A 4 percent Treasury bond has 2.5 years to maturity.
Spot rates are as follows:
(6 month—0.02); (1 year—0.025); (1.5 years—0.03); (2 years—0.04); (2.5 years—0.06)
The note is currently selling for $976.
Determine the arbitrage profit, if any, that is possible.
A)$43.22.
B)$19.22.
C)$37.63.
Discount the cash flows at the spot rates and compare the total value to the price of the bond.
First calculate the arbitrage-free price of the T-Bill: (Note that the spot rates given are annual yields and that you need to divide them by 2 to get the semiannual yields.)
PV =
20 / (1 + 0,01) +
20 / (1 + 0.0125)^2 +
20 / (1 + 0.015)^3 +
20 / (1 + 0.02)^4 +
1,020 / (1+ 0.03)^5
= 956.78
If the note is currently selling for $976.00 the bond is mispriced by + $19.22.
You could explore this arbitrage opportunity by short-selling the T-Bill and using th e proceeds to purchase strips/ zero coupons equivalent to the T-Bill payment structure. You’ll realize an inmediate risk-free profit of $19.22 as the short-selling liability is offset by the future proceeds of the strips / zero coupons.
Best,
Oscar