I need explanation regarding forward rates for the following specific example.
A zero coupon with spot rate $s_0(1)=.08$ and $s_0(2)=.09$ are available.
a), Smith borrows $1$ and is obliged to pay back $1.08$ at the end of the year. Using that money he reinvests and purchases a bond for $1$, which at the end of the second year he receives $1.1881$.
b), Jones borrows $1$ and is obliged to pay back $1.881$ two years from now. Using that money he reinvests and purchases a bond for $1$, which at the end of the first year he receives $1.08$
Find the forward rate for both situation.
The book I am working on suggests that these two answers are supposed to be the same, but I intuitively think that case b) would lose money...
can someone explain this to me?
Thank you.
The fact that they borrowed to buy the bond is immaterial. At the end of the first year, Smith is $-1.08$ and will have $1.1881$ at the end of year 2. He promises his creditor the $1.1881$, an interest rate of $\frac {1.1881}{1.08}$ At the end of the first year, Jones is $+1.08$. He needs $1.1881$ at the end of year 2, so he needs an interest rate of $\frac {1.1881}{1.08}$ to satisfy that.