Post on 27-Dec-2015
transcript
Nature of SwapsNature of Swaps
Agreement to exchange cash flows at specified future times according to certain rules
Example of a plain vanilla swap• agreement by Microsoft to receive 6-month
LIBOR & pay a fixed rate of 5% per annum every six months for three years on a notional principal of $100 million
Cash FlowsCash Flows
---------Millions of Dollars---------
LIBOR FLOATING FIXED Net
Date Rate Cash Flow Cash Flow Cash Flow
Mar.5, 2001 4.2%
Sept. 5, 2001 4.8% +2.10 –2.50 –0.40
Mar.5, 2002 5.3% +2.40 –2.50 –0.10
Sept. 5, 2002 5.5% +2.65 –2.50 +0.15
Mar.5, 2003 5.6% +2.75 –2.50 +0.25
Sept. 5, 2003 5.9% +2.80 –2.50 +0.30
Mar.5, 2004 6.4% +2.95 –2.50 +0.45
Use of SwapsUse of Swaps
Converting a liability from• fixed rate to floating rate • floating rate to fixed rate
Converting an investment from • fixed rate to floating rate• floating rate to fixed rate
Involving a Financial Involving a Financial InstitutionInstitution
F.I.
LIBOR LIBORLIBOR+0.1%
4.985% 5.015%
5.2%Intel MS
Involving a Financial Involving a Financial InstitutionInstitution
Intel F.I. MS
LIBOR LIBOR
4.7%
5.015%4.985%
LIBOR–0.2%
Market Maker QuotesMarket Maker Quotes
Maturity Bid (%) Offer (%) Swap Rate (%)
2 years 6.03 6.06 6.045
3 years 6.21 6.24 6.225
4 years 6.35 6.39 6.370
5 years 6.47 6.51 6.490
7 years 6.65 6.68 6.665
10 years 6.83 6.87 6.850
Comparative AdvantageComparative Advantage
AAACorp wants to borrow floatingBBBCorp wants to borrow fixed
Fixed Floating
AAACorp 10.00% 6-month LIBOR + 0.30%
BBBCorp 11.20% 6-month LIBOR + 1.00%
Involving a Financial Involving a Financial InstitutionInstitution
AAA F.I. BBB10%
LIBOR LIBOR
LIBOR+1%
9.93% 9.97%
CritiqueCritique
10.0% and 11.2% rates available to AAACorp and BBBCorp in fixed rate markets are 5-year rates
LIBOR+0.3% and LIBOR+1% rates available in the floating rate market are 6-month rates
BBBCorp’s fixed rate depends on the spread above LIBOR it borrows at in the future
Swap RatesSwap Rates
6-month LIBOR is a short-term AA borrowing rate
5-year swap rate has a risk corresponding to the situation where ten 6-month loans are made to AA borrowers at LIBOR• Lender can enter into a swap where income
from the LIBOR loans is exchanged for the 5-year swap rate
Valuation of SwapsValuation of Swaps
Valued as the difference between the value of a fixed-rate bond and the value of a floating-rate bond• Fixed rate bond is valued in the usual way• Floating rate bond is valued by noting that it is
worth par immediately after the next payment date
Valuation of SwapsValuation of Swaps
Suppose that:• A bank agrees to pay 6-month LIBOR and
receive 8% p.a. with semiannual compounding on notional principal of $100m
• Remaining life of 1.25 years• 3-month rate 10%, 6-month rate 10.2%, 9-
month rate 10.5%, 15-month rate 11%
What is the value of this swap?
Valuation of SwapsValuation of Swaps
* e-0.1(0.25) # 0.5 x 0.102 x 100 = 5.1
Value of swap: 98.238 – 102.505 = –4.267m
Time Bfix CF Bfl CF Discount
factor
PV Bfix CF PV Bfl CF
0.25 4.0 105.1# 0.9753* 3.901 102.505
0.75 4.0 0.9243 3.697
1.25 104.0 0.8715 90.640
Total 98.238 102.505
Valuation of SwapsValuation of Swaps
Alternatively, can be valued as a portfolio of forward rate agreements (FRAs)• Each exchange of payments in an interest
rate swap is an FRA• FRAs can be valued on the assumption that
today’s forward rates will be realised
Valuation of SwapsValuation of Swaps
* e-0.1(0.25) # 0.5 x 0.102 x 100 = 5.1 † using rate [0.105(0.75) – 0.10(0.25)/0.5] = 0.1075 convert to semiannual compounding: 0.1044
Time Fixed CF
Floating CF
Net CF Discount Factor
PV Net CF
0.25 4.0 -5.100# -1.100 0.9753* -1.073
0.75 4.0 -5.522† -1.522 0.9243 -1.407
1.25 4.0 -6.051 -2.051 0.8715 -1.787
Total -4.267
Currency SwapsCurrency Swaps
Agreement to pay 11% on a sterling principal of £10,000,000 & receive 8% on a US dollar principal of $15,000,000 every year for five years• Principal is exchanged at the beginning and
the end of the swap, unlike in an interest rate swap
Currency SwapsCurrency Swaps
Year
Dollars Pounds$
------millions------
2001 –15.00 +10.002002 +1.20 –1.10
2003 +1.20 –1.10 2004 +1.20 –1.10
2005 +1.20 –1.10 2006 +16.20 -11.10
£
Use of Currency SwapsUse of Currency Swaps
Conversion from a liability in one currency to a liability in another currency
Conversion from an investment in one currency to an investment in another currency
Comparative AdvantageComparative Advantage
General Motors wants to borrow AUD Qantas wants to borrow USD
Can be valued either as the difference between two bonds or as a portfolio of forward contracts
USD AUD
General Motors 5.0% 12.6%
Qantas 7.0% 13.0%
Alternative SwapAlternative Swap
GM F.I. QANUSD 5.0%
AUD 11.9% AUD 11.9%
AUD 13.0%
USD 5.0% USD 5.2%
Swaps v ForwardsSwaps v Forwards
Swaps can be regarded as a convenient way of packaging forward contracts
“Plain vanilla” interest rate swap in earlier example consisted of six FRAs
“Fixed for fixed” currency swap in other example consisted of a cash transaction & five forward contracts
Valuing Currency SwapsValuing Currency Swaps
Suppose that:• Term structure of LIBOR/swap rates is flat in
Japan and the US• Japan rate is 4%, US rate is 9% p.a.
(continuous compounding)• A bank enters a swap paying 8% and
receiving 5% p.a., USD10m against JPY1.2bn• 3-year swap, current rate USD1 = JPY110
What is the value of the swap?
Valuation as BondsValuation as Bonds
Value of swap: 1,230.55/110 – 9.6439 = USD1.5430m
Time USD CF
PV ($) JPY CF
PV (¥)
1 0.8 0.7311 60 57.65
2 0.8 0.6682 60 55.39
3 0.8 0.6107 60 53.22
3 10.0 7.6338 1,200 1,064.30
Total 9.6439 1,230.55
Swaps v ForwardsSwaps v Forwards
Value of a swap is the sum of the values of the forward contracts underlying the swap
Swaps are normally “at the money” initially• It costs nothing to enter into a swap• It does not mean that each forward contract
underlying a swap is “at the money” initially
Valuation as FRAsValuation as FRAs
Time USD CF
JPY CF
Forward Rate
JPY CF in USD
Net CF in USD
PV
1 -0.8 60 0.009557 0.5734 -0.2266 -0.2071
2 -0.8 60 0.010047 0.6028 -0.1972 -0.1647
3 -0.8 60 0.010562 0.6337 -0.1663 -0.1269
3 -10.0 1,200 0.010562 12.6746 2.6746 2.0417
Total 1.5430