Can anyone help me explain why using a spot rate give a no-arbitrage price of the bond? Having an example will be much appreciated! Thanks.
You can think of a coupon paying bond as a bunch of smaller zero coupon bonds.
Example: A 3 year, 5% coupon bond could be four different bonds (stripping the coupons and selling them). Call this Bond XYZ
Bond 1: 1 year, $5 face value
Bond 2: 2 year, $5 face value
Bond 3: 3 year, $5 face value
Bond 4: 3 year, $100 face value
If you had the following yearly spot rates: 2%, 3%, 4% then which do you discount them by?
If you discount them all by 4% then an investor could buy Bond XYZ at $102.78
If you use the spot rates the price is $105.76
An investor could make risk free profits by buying the $102.78 bonds, selling the $105.76. They keep the $2.98
I see. Thank you
I am struggling to calculate the no arbitrage price of the bond at $105.76 using those spot rates. Maybe I am looking at your example wrong but I am reading it as the 1 Year spot rate= 2%, 2 year= 3%, and 3 year=4%.
Using those spot rates to find the non arbitrage price of a bond, wouldn’t you use the formula:
5/(1.02) + 5/(1.03)^2 + 105/(1.04)^3 = $102.96
What formulas are you using to find $105.76?
Thanks for the help
Oh no. You’re right! I was treating the 3% and 4% as forward rates. Ex. f(1,1) and f(2,1). That’s my fault.
Zroubal, you’re right. The cash flows are
5/(1.02) + 5/1.03^2 + 105/1.04^3
For PV of 102.96.
The YTM equivalent to the 2/3/4 spot rates is 3.935%.
At any other YTM underlying the bond such as the 4% of MGreg99 there is a mispricing as the spot rates per nganh96 are indeed the no-arb rates.