5.5. USING FORWARD CONTRACTS (4): MINIMIZING THE IMPACT OF MARKET
IMPERFECTIONS 199
DoItYourself problem 5.4
Here is a proof without words. Add the words—i.e. explain the proof to a friend
who is obviously not as bright as you are. We denote the risk spreads byρandρ∗,
respectively.
more,
swappedhcloan yields the same, if
less,Ft,T
1 +r+ρ×
1
St>=
<1
1 +r∗+ρ∗
m
1 +r
1 +r∗1
1 +r+ρ>=
<1
1 +r∗+ρ∗
m
1 +r
1 +r+ρ>=
<
1 +r∗
1 +r∗+ρ∗
m
1 +r+ρ
1 +r<=
>
1 +r∗+ρ∗
1 +r∗
m
ρ
1 +r<=
>ρ∗
1 +r∗. (5.10)
5.5.4 Swapping for Legal Reasons: Replicating Back-to-Back Loans
In the examples thus far, we used the swap to change the effective denomination of
a deposit or a loan. We now discuss reasons to work with a stand-alone swap. The
main use of this contract is that it offers all the features of back-to-back loans (that
is, two mutual loans that serve as security for each other), but without mentioning
the words loan, interest, or security. We proceed in three steps. First we explain
when and why back-to-back loans may make sense. We then establish, via an
example, the economic equivalence of a swap and two back-to-back loans. Lastly
we list the legal advantages from choosing the swap representation of the contract
over the direct back-to-back loan.
Why Back-to-back Loans may make Sense
The most obvious reason for a back-to-back-like structure is providing security to
the lender.
Example 5.22
During the Bretton Woods period (1945–1972), central banks often extended loans
to each other. For example, to support thegbpexchange rate, the Bank of England
(BoE) would buygbpand sellusd. On occasion it would run out ofusd. Hoping