Can somebody share a very simple example to illustrate that the no-arbitrage rules hold and the investor is indifferent to investing at spot rate or investing at the spot rate and then rolling over to the forward rate. Thanks
The forward price on a zero coupon bond will be the spot price increased by the risk-free rate for the term of the forward. The investor can either:
- Buy the bond today at the spot price, or
- Enter into the long position in the forward contract and invest the spot price at the risk-free rate; when the forward expires, he pays the forward price with the balance in the investment account.
Either way, the investor buys the bond by investing the spot price today: he’s indifferent to the investments.
Thank you.
Could you please make up a hypothetical numerical example. That will make me understand the concept a lot easier. An example which justifies that the return and price of both ways is the same. I really appreciate your participation
Suppose the following rates:
r(0,2) = 0.05 is the 2 year rate starting today and ending in period 2
r(0,1) = 0.04 is the 1 year rate starting today and ending in period 1
F(1,2) = 0.06 is the 1 year rate starting in period 1 and ending in period 2
The arbitrage condition states the above rates will hold becuase the investor is indifferent between investing at the spot rate for 2 yrs at r(0,2)^2 or investing at the 1 yr spot rate at r(0,1)-=0.04 and rolling the investment over to the forward rate F(1,2) =0.06 (which was locked in at time 0.
We can see that this is true because: 1.05^2 = 1.04(1.06).
Note that F(1,2) actually equals 0.0601 but I rounded above.
Thanks a lot. Now I have understood the concept.