Hedging a Fixed-Rate Loan

Let us continue with our discussion on the different types of basic static hedges one might encounter. Another

TABLE 7.2 The hedging of a fixed-rate loan.

Instrument type

Pay/Receive

Leg structure

Fixed Loan

Receive

Fixed Swap Leg

Pay

Floating Swap Leg

Receive

Result

Receive

exposure one would want to hedge, for the same reason outlined in the case of the bond, is the one to a fixed-rate loan.

In Table 7.2 we present the situation where the institution has extended a fixed-rate loan and therefore receives a stream of fixed cash flows made of a coupon and a principal repayment. Note how in the first line of the table we have written the expression for the loan in a way different from the previous ones in the sense that we have omitted any reference to the survival probability of the borrower. This is because in this section we want to highlight the dealing with interest rates and FX-related risk: we assume that the credit risk of the borrower is dealt with elsewhere (we shall discuss it in Section 7.3.2) and here we only concern ourselves with the interest rate sensitivity due to a fixed or a floating rate.

At this point one could ask: why didn't we do the same when dealing with the hedging of the fixed coupon bond? Why didn't we leave the discount factor correction aside and only treat the interest rate component?

A bond, as opposed to a loan, is a securitized instrument: this means that the price of the bond is a market price that cannot be easily broken. At most, as we have done before, we can imply certain things. A loan is not a securitized instrument and the discussion around the fair value of loans (see Section 3.3.1) shows that there is not a single official way of valuing these instruments.

To hedge the exposure to the fixed rate of the loan, the institution would enter into an amortizing swap where it would pay the same fixed rate of the loan and receive a stream of floating rates plus spread where the spread would be chosen so that the two transactions (loan and swap) are financially equivalent. The sum of these three legs results in a net stream of floating cash flows.

As we have said before (see Section 4.3.2), when hedging a loan with a swap, not only are there considerations such as the one we have just illustrated above about the fair value of the loan, but there are others more important about what happens to the combined hedge (swap and loan) in

TABLE 7.3 The hedging of a bond in a foreign currency issued to borrow capital.

Instrument type

Pay/Receive

Leg structure

Foreign Currency Bond

Pay

Foreign Currency Swap Leg

Receive

Domestic Currency Swap Leg

Pay

Result

Pay

case of the default of the borrower or the swap counterparty. Loans are, we have repeated many times, nonsecuritized instruments, meaning that many of the features of the agreement are set between lender and borrower on an almost ad hoc basis.[1] Swaps on the other hand, although there are specific deviations such as the waiver on collateral payment for some institutions, have much more standardized features, in particular those dealing with the situation of default. The presence of these different features, such as if the loan is accelerating or nonaccelerating,[2] would have an impact on the solidity of the hedge.

  • [1] Although each lender certainly has a standard set of loan types, it is not technically impossible that each loan would have different important features.
  • [2] We remind the reader that an accelerating loan is one where at the moment of the default of the borrower the lender calculates the recovery value on the outstanding principal; in a nonaccelerating loan, the recovery is calculated on the present value of the outstanding amount.
 
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