Chapter 7: Swaps Flashcards
If we have have a payment date at September 5 2021 when is the 3-months LIBOR rate than set?
On September 5 the floating rate that will be received/paid has been set 3 months prior - that is on June 5
What is the loan principle used for when valuing swaps?
The principal is not exchanged - it is only used to calculate interest rate payments
Explain how swaps can be used to transform a liability
If company A has debt with a principal of $100 million and it pays 5,2% in interest then the company can enter into a swap where it receives the floating LIBOR rate. If so, company A has these three cash flows:
1: it pays 5,2% to its outside lenders.
2: it pays LIBOR under the terms of the swap.
3: it receives 5% under the terms of the swap.
These three transactions net out to a net payment of LIBOR plus 0,2%.
Explain how a swap can be used to transform an asset
If company B owns bonds that pays 4,7% it can enter into a swap contract, which gives the following three cash flows:
- it receives 4,7% on the bonds.
2: it receives LIBOR under the swap contract.
3: it pays 5% under the swap contract.
These three transactions net out to LIBOR minus 30 basispoints (0,3%).
What is the comparative-advantage argument?
Consider the borrowing rates below:
Assume that BBBCorp wants to borrow at a fixed rate and AAAcorp wants to borrow at a floating rate linked to 6-month LIBOR.
The difference between the two fixed rates are greater than the difference between the two floating rates. BBBCorp pays 1.2% more than AAACorp in fixed-rate markets and only 0.7% more than AAACorp in floating-rate markets. Therefore, it is said that BBBcorp has a comparative advantage in the floating-rate market.
Now, assume that AAAcorp and BBBcorp enter into a swap contract where AAACorp agrees to pay BBBCorp interest at 6-month LIBOR on $10 million. In return, BBBCorp agrees to pay AAACorp interest at a fixed rate of 4.35% per annum on $10 million.
AAAcorp now has the following three cash flows:
1: it pays 4% per annum to outside lenders.
2 it pays 6-month LIBOR to BBBcorp.
3: it receives 4,35% per annum from BBBcorp.
The net effect is that AAAcorp pays LIBOR minus 0,35% per annuum. This is 0.25% per annum less than it would pay if it went directly to floating- rate markets.
BBBcorp has the following three cash flows:
1: it pays LIBOR + 0,6% to outside lenders.
2: it pays 4,35% to AAAcorp.
3. it receives LIBOR from AAAcorp.
The net effect is that BBBcorp pays 4,95% per annum. This is 0.25% per annum less than it would pay if it went directly to fixed-rate markets.
In this example the swap has been constructed so that both companies save 0,25% per annum, but it could also be that AAAcorp would require that it saves 0,30% and BBBcorp 0,20% as AAAcorp can borrow cheaper in both fixed- and floating rate markets.
How is a swap rate calculated?
A swap rate is the average of (a) the fixed rate that a swap market maker is prepared to pay in exchange for receiving LIBOR (its bid rate) and (b) the fixed rate that it is prepared to receive in return for paying LIBOR (its offer rate).
How can a bank earn the 5-year swap rate on a certain principal?
1: Lend the principal for the first 6 months to a AA borrower and then relend it for successive 6-month periods to other AA borrowers.
2: Enter into a swap to exchange the LIBOR income for the 5-year swap rate
This shows that the 5-year swap rate is an interest rate with a credit risk corresponding to the situation where 10 consecutive 6-month LIBOR loans to AA companies are made.
What is the LIBOR zero curve?
LIBOR rates are only directly observable for maturities out to 12 months. One way of extending the LIBOR zero curve beyond 12 months is to use Eurodollar futures. Typically Eurodollar futures are used to produce a LIBOR zero curve out to 2 years—and sometimes out to as far as 5 years. Traders then use swap rates to extend the LIBOR zero curve further. The resulting zero curve is sometimes referred to as the LIBOR zero curve
When is the value of a newly issued floating-rate bond that pays 6-month LIBOR equal to its principal value?
This is the case when the LIBOR/swap zero curve is used for discounting. This is because the swap provides a rate of interest equal to LIBOR and LIBOR is used as the discount rate. We say that the bond is priced at par.
When valuing swaps in terms of bond prices what is the equation that gives the swap value from the perspective of the floating-rate payer?
The formula is seen below. Note that this is equal to a long position in the fixed-rate and a short position in the floating-rate.
When valuing swaps in terms of bond prices what is the equation that gives the swap value from the perspective of the fixed-rate payer?
The formula is seen below. Note that this is equal to a long position in the floating-rate and a short position in the fixed-rate.
How is the value of the fixed-rate and floating-rate bonds determined?
The fixed-rate bond is easy to value. Just calculate the “coupons” and discount them at the correct rate back to time 0.
To value the floating-rate bond, we note that the bond is worth the notional principal immediately after a payment. This is because at this time the bond is a ‘‘fair deal’’ where the borrower pays LIBOR for each subsequent accrual period. Suppose that the notional principal is L, the next exchange of payments is at time t, and the floating payment that will be made at time t (which was determined at the last payment date) is k. Immediately after the payment B_fl = L as just explained. It follows that immediately before the payment B_fl = L + k. The floating-rate bond can therefore be regarded as an instrument providing a single cash flow of L + k* at time t. Discounting this, the value of the floating-rate bond today is (L + k)e^-r x t , where r* is the LIBOR/swap zero rate for a maturity of t*.
What is a fixed-for-fixed currency swap?
It involves exchanging principal and interest payments at a fixed rate in one currency for principal and interest payments at a fixed rate in another currency.
It is “fixed-for-fixed” if the interest rate in each currency is at a fixed rate.
How can a currency swap be used to transform liabilities?
Suppose that IBM can issue $15 million of US- dollar-denominated bonds at 6% interest. The swap has the effect of transforming this transaction into one where IBM has borrowed £10 million at 5% interest. The initial exchange of principal converts the proceeds of the bond issue from US dollars to sterling.
How can a currency swap be used to transform assets?
Suppose that IBM can invest £10 million in the UK to yield 5% per annum for the next 5 years, but feels that the US dollar will strengthen against sterling and prefers a US-dollar-denominated investment. The swap has the effect of transforming the UK investment into a $15 million investment in the US yielding 6%.
When valuing currency swaps in terms of bond prices what is the equation that gives the swap value from the perspective of the USD receiver?
The formula is shown below.
B_F is the value, measured in the foreign currency, of the bond defined by the foreign cash flows on the swap.
B_D is the value of the bond defined by the domestic cash flows on the swap.
S_0 is the spot exchange rate (expressed as number of dollars per unit of foreign currency).
When valuing currency swaps in terms of bond prices what is the equation that gives the swap value from the perspective of the USD payer?
The formula is shown below.
B_F is the value, measured in the foreign currency, of the bond defined by the foreign cash flows on the swap.
B_D is the value of the bond defined by the domestic cash flows on the swap.
S_0 is the spot exchange rate (expressed as number of dollars per unit of foreign currency).
