No arbitrage case of spot and forward interest rates

[haiderraza]

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

 

[S2000magician]

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.

 

[haiderraza]

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

 

[dwheats]

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.

 

[haiderraza]

Thanks a lot. Now I have understood the concept.