Swaps

[ShaktiRathore]

Thread on swaps:
A swap is an agreement to exchange cash flows at certain specified future times according to certain specified rules.
example An agreement by X to pay fixed rate of interest of 5% per annum for 6 months for a 6 month libor for 2 years on a notional principal of 100 million dollars. Suppose today is 1st march2012 and 6 month libor rate is 4.5% and X enters into the swap agreement as cited above. Than cash flows exchange will began after 6 months for every 6 months for 2 years. Thus payments will be as:
1Sept2012: payment by X: 5%/2=2.5% receipt by X:4.5%/2=2.25% so X makes a net payment of 2.5%-2.25%=.25%. Libor today is 5%
1March2013: payment by X: 5%/2=2.5% receipt by X:5%/2=2.5% so X makes a net payment of 2.5%-2.5%=0%. Libor today is 5.5%
1Sept2013: payment by X: 5%/2=2.5% receipt by X:5.5%/2=2.75% so X makes a net payment of 2.5%-2.75%=-.25%. Libor today is 4%
1March2014: payment by X: 5%/2=2.5% receipt by X:4%/2=2% so X makes a net payment of 2.5%-2%=0.5%. Libor today is 5.5%
From above its clear that Libor rate today determines the payment 6 months afterwards. While the payment by X remains the same as 5% for 6 months on notional principal.


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[ShaktiRathore]

Swaps are used primarily for below purposes:
1. Convert a fixed rate liability to a floating rate liability.
2. Convert a floating rate liability to a fixed rate liability.
3. Convert a fixed rate investment to a floating rate investment .
4. Convert a floating rate investment to a fixed rate investment .
X has fixed rate liability and Y has a floating rate liability. Now X wants to convert its fixed rate liability to floating rate liability and Y wants to convert its floating rate liability to fixed rate liability. Suppose now two parties X and Y enters into a swap agreement.In swap agreement X will pay a floating rate Libor% to other party Y and receive a fixed rate of x% from Y , the fixed rate payment X passes on to fulfill its liability while paying the floating rate to Y. So in a sense X now has a floating rate liability to Y. So X has converted its fixed rate liability to floating rate liability.
Similarly Y pays fixed rate of x% to X and receive flaoting rate Libor from X which Y passes on to fulfill its Libor liability but now has a new fixed rate liability to X. So be entering into an agreement of swap both parties have converted their liabilities at the same time fulfilling their liabilities.
Similar understanding applies to investments.

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[ShaktiRathore]

Lets start discussion on comparative advantage:
Suppose two parties A and B with following rates available to them:
Fixed Floating
A: 4% 6-month LIBOR-.1%
B: 5.2% 6-month LIBOR+.6%
Now A wants to borrow floating and B wants to borrow fixed. Than A and B can enter a swap agreement wherein A pays B floating and B pays A fixed rate.

A pays B Libor and recieve 4.35% from B.
B pays A 4.35% and recieve libor from A.

A enters into fixed rate liability of 4%. Overall Net reciept by A is 4.35% and A pays a floating rate of LIBOR% in the swap so finally overall pay by A is 4%-4.35%+LIBOR=LIBOR-.35%. This rate is floating so A has overall converted a flaoting rate liability to LIBOR-.35% from LIBOR-.1% so A has gained an advantage by entering into the swap of LIBOR-1%-(LIBOR-.35%)=.25%.

B enters into floating rate liability of 6-month LIBOR+.6%. Overall Net reciept by B is Libor and B pays a fixed rate of 4.35% in the swap so finally overall pay by B is LIBOR+.6%-LIBOR+4.35%=4.95%. This rate is fixed so B has overall vrated a fixed rate liability to 4.95% from 5.2% so B has gained an advantage by entering into the swap of 5.2%-4.95%=.25%.

In this way both A and B have gained by entering into the swap while entering into the required position of fixed or floating. Had they entered the positions at their own rates the over all fixed/floating rates would had been higher but by entering into the swap the parties have reduced their liabilities by .25%. So both have gained comparatively by entering into the swap agreement. Thus swap gives comparative advantage for the parties who wants to raise money in form of liabilities.

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[ShaktiRathore]

Valuation of interest rate Swap:
Pay 6 month libor and recieve fixed rate of 8% per annum. Suppose the swap life is 1.25 yrs or 15 months. The libor today is 10.2%.
The payment is equivalent to floating rate bond which pays floating rate every 6 months and receipt is equivalent to a fixed rate bond which pays a fixed rate of 4% every 6 months.
So value of Interest rate swap=Value of fixed rate bond-Value of Floating rate bond.
Floating rate bond value(T=1.5yrs)= C1/(1+y1)+C2/(1+y2)(1+y1)+C3+F/(1+y2)(1+y1)(1+y3)
Floating rate bond value(T=1.5yrs)= C1/(1+y1)+C2/(1+y2) (1+y1) +F.(y3)+F/(1+y1)(1+y2) (1+y3)
Floating rate bond value(T=1.5yrs)= C1/(1+y1)+C2/(1+y2) (1+y1) +F.(1+y3)/(1+y1)(1+y2) (1+y3)
Floating rate bond value(T=1.5yrs)= C1/(1+y1)+C2+F/(1+y2) (1+y1)
Floating rate bond value(T=1.5yrs)= C1/(1+y1)+F.y2+F/(1+y2) (1+y1)
Floating rate bond value(T=1.5yrs)= C1+F/(1+y1) so value of floating rate bond is par value immediately after the next payment.
payments are as follows:
after(months) | Fixed |Floating |PV of fixed | pV of floating
6 | 4 | 105.1 | 3.901 | 102.505
12 | 4 | 0 | 3.697 |
15 | 104 | 0 | 90.64 |
So net value of fixed bond= 3.901+ 3.697+ 90.64= 98.238
value of floating bond= 102.505
net value if interest rate swap,
=98.238-102.505=-4.267


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[ShaktiRathore]

Valuation of interest rate Swap(using Forwards rate agreements):
The fixed and floating rate payments in the future can be considered as a series of forward rate agreements FRA's which whereby two parties agree to exchange fixed rate for floating rate payment on a certain principal at prespecified dates. FRAs are valued with assumption that today's forward rates are realized into the future.
payments are as follows:
FRA1: exchange 8% for floating rate in 6months.
FRA2: exchange 8% for flaoting rate in 12months..
FRA3: exchange 8% for flaoting rate in 15months..
So if interest rate swap is a series of FRAs than its value is sum of values of the above FRAs IRS=FRA1+FRA2+FRA3.
=>value of IRS=value of (FRA1+FRA2+FRA3)
=>value of IRS=value of FRA1+value FRA2+value of FRA3

after(months) | Fixed payment | Floating | Netcashflow | pV of Netpay
6 | 4 | 5.1 | -1.1 | -1.073
12 | 4 | 5.522 | -1.522 |-1.047
15 | 4 | 6.051 | -2.051 | -1.787

Total net value =sum of PV of net pay=-1.073- -1.047- 1.787= -4.267

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[ShaktiRathore]

Now we consider the currency swaps:
The currency swap is an agreement that allows both sides to exchange cash flows in different currencies at pre-specified dates with the exchange of notional principal at the initiation and end of the swap contract. Currency swaps facilitates to convert liability in one currency to the liability in another currency and investment in one currency to the investment in another currency.
The comparative advantage holds in currency swaps too. Two entities X and Y with X wants to make investment in Y's country in AUD and Y wants to make investment in X's country in USD. The Prevailing exchange rates are:
| USD | AUD
X | 5% | 8%
Y | 7% | 7.6%
X can enter into currency swap with Y to borrow AUD from Y at 7.6% and Y can borrow USD at 5%. Both X and Y benefits from the exchange because now they can borrow the foreign currency at cheaper rate that the rate available in their own countries. By entering into a currency swap both X and Y have advantage.


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[ShaktiRathore]

Currency swaps can be values as the difference in the value of two bonds or a portfolio of forward contracts.
Consider a currency swap where 5% is received in yens and 8% is paid in dollars.Payments are made annually. principals are 10milion dollars and 1200 million yen. Current exchange rate is 110yen/dollar. Swap lasts for 3 years.
after(years) | CashFlow($)| PV of CashFlow($) | CashFlow(Yen) | PV of CashFlow(Yen)
1 | .8 | .7311 | 60 | 57.65
2 | .8 | .6682 | 60 | 55.39
3 | 10+.8 | 8.243 | 1200+ 60 | 1117.2

Value of swap=PV of cash Flows $-PV of cash Flows Yen
Value of swap(in$)=PV of cash Flows $-PV of cash Flows Yen*current exchange rate
Value of swap(in$)=9.6439-1230.55/110
Value of swap(in$)=9.6439-11.186
Value of swap(in$)=-1.543
In terms of forwards contracts(valuation)
after(years) | CashFlow($)| CashFlow(Yen) | ForwardExchangeRate | CashFlow(Yen in $) | Net cashFlow($) |PV of net CashFlow
1 | .8 | 60 | .009557 | .5734 | -.2266 | -.2071
2 | .8 | 60 | .010 | .6028 | -.1972 | -.1647
3 | 10+.8 | 1200+60 | .01052 | 13.3 | -2.83 | 1.91
Value of swap($)=sum of net cash flows=-.2071-.1647+1.91=1.543

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[ShaktiRathore]

Wants to conclude the topic of swap discussing the type of swaps.
1. CDS(Credit Default Swap): X has exposure to Y and wants to mitigate the risk of default from Y so X buys CDS from third party Z which provides protection to X in case of default from Y. X pays a periodic interest to Z who bears the default risk and in exchange Z has to compensate X in case of default by Y.
2. Total Return Swap in which buyer of the swap A will get total return and cash flows associated with the asset from B and in return A will have to pay periodic interest payments to B.
3. Swaption is the option on the swap in which holder has the option to enter into the swap in future but not an obligation.
4. A variance swap that allows the parties to exchange cash flows based on volatility. One leg pays pay based on a strike volatility and other leg will pay based on realized volatility thus the net pay of the swap is given by

.Where Nvar is notional principal.
5. Equity Swap in which one leg called floating leg pays a Libor and the other leg called equity leg pays return on equity or equity index. The parties in equity swap exchange the above cash flows associated with floating and equity leg.
6. Commodity swap is a swap in which a floating price(spot price) is exchanged with a fixed price of a commodity over a period.


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[ABFRM]

Thanks Shakti Rathore for explaining Swap in the lucid manner. Can you tell me the difference between Forex swap and Currency swap? If there is difference. Can u elaborate it by giving example?