Could you please help me understand the logic behind solving this problem below. I would much appreciate it!
Term Yrs / Spot Rates
R (2) - 1.5%
R (4) - 1.9%
R (6) - 3.0%
R (8) - 4.0%
You are exploring a 4yr forward contract in which the underlying is a 2yr zero-coupon bond, which is trading at $90.09 per 100 of par. Using the forward model, is there arbitrage.
A. does not exist
b. profit of $0.56
c. profit of $2.80
This makes no sense: the bond matures 2 years before the forward expires.
Please recheck your numbers.
This is exactly how the question is layed out!
a 4yr forward contract in which the underlying is a two year zero coupon bond. This means find F(4,2).
So, if I understand this correctly, when the forward expires in 4 years, you can buy or sell a 2-year zero at 90.09.
Weird way of presenting it.
In any case, you need to calculate the 2-year forward rate starting 4 years from today (implied by the current spot rates) and compare that to the 2-year rate implied by the price on the zero.
The former is calculated as:
(1 + 2f4)² = (1 + s6)^6 / (1 + s4)^4
(1 + 2f4)² = (1 + 3%)^6 / (1 + 1.9%)^4
(1 + 2f4)² = 1.1075
1 + 2f4 = 1.0524
2f4 = 5.2358%
If you discount the zero at that rate you get:
100 / (1 + 2f4)² = 100 / 1.1075 = $90.30
So it appears that there’s an arbitrage profit of $0.21, which, alas, isn’t listed.
What’d the official answer say?
Correct answer is B = $0.56
This is how they get to it.
Find the price of a F(4,2) = wait 4 years and enter into a 2 year loan.
Calculated Forward Price: P(4) = 0.90297
Currently trading at = 0.9009 (arbitrage exists!!!)
Profit: .90297-.9009 = 20bps (WRONG).
They take the Calc forward price P(4) & presen value it: 0.90297 * 0.927477(which is the R(4).
After PV both prices, the get $0.56
Calc Fwd Price (0.90297 * 0.927477) = .83748
Trading (0.9009 * 0.927477) = .843077
.843077 - .83748 = 0.005597 *100 = $0.56
It appears that the author cannot multiply correctly.