Understanding Central Bank Liquidity Swaps

This is part 7 of a 10 part series on currency swaps and interest rate swaps and their role in the global economy. In part 7, we illustrated how companies use swaps in the global market place, but on a company-to-company basis. In part 8, we’ll explain the purpose of swaps on the central bank level and when they’re used.

As established earlier in this series, a currency swap is an agreement to exchange principal interest and fixed interest in one currency (i.e. the U.S. Dollar) for principal interest and fixed interest in another currency (i.e. the Euro). Like interest rate swaps, whose lives can range from 2-years to beyond 10-years, currency swaps are a long-term hedging technique against interest rate risk, but unlike interest rate swaps, currency swaps also manage risk borne from exchange rate fluctuations.

Banks and companies aren’t the only parties using currency swaps. A special type of currency swap, a central bank liquidity swap, is utilized by central banks (hence the name) to provide their domestic country’s currency (i.e. the Federal Reserve using the U.S. Dollar) to another country’s central bank (i.e. the Bank of Japan).

Central bank liquidity swaps are a new instrument, first deployed in December 2007 in agreements with the European Central Bank and the Swiss National Bank as U.S. Dollar funding markets ‘dried up’ overseas. The Federal Reserve created the currency swap lines to assist foreign central banks with the ability to provide U.S. Dollar funding to financial institutions during times of market stress. For example, if the Federal Reserve were to open up liquidity swaps with the Bank of Japan, the Bank of Japan could provide U.S. Dollar funding to Japanese banks (just as the Bank of England would provide liquidity to British banks, etc).

As the world’s most important central bank (next to the Bank of International Settlements, considered the central bank for central banks) in one of the world’s most globalized financial markets, the Federal Reserve has a responsibility of keeping safe financial institutions under its jurisdiction. Thus, when factors abroad (such as the European sovereign debt crisis) create funding stresses for U.S. financial institutions, the Federal Reserve, since 2007, has opened up temporary swap lines.

Generally speaking, currency liquidity swaps involve two transactions. First, like currency swaps between banks and companies (as illustrated in part 7), when a foreign central bank needs to access U.S. Dollar funding, the foreign central bank sells a specified amount of its currency to the Federal Reserve in exchange for U.S. Dollars at the current spot exchange rate.

In the second transaction, the Federal Reserve and the foreign central bank enter into agreement that says the foreign central bank will buy back its currency at a specified date at the same exchange rate for which it exchanged them for U.S. Dollars. Additionally, the foreign central bank pays the Federal Reserve interest on its holdings.

Unlike regular currency swaps, central bank liquidity swaps are rare and only occur during times of market stress. The first such occurrence, as noted earlier, was in December 2007, as funding markets started to dry up as the U.S. economy entered a recession as the housing market crashed.

More recently, on November 30, 2011, the Federal Reserve announced liquidity swaps with the Bank of Canada, the Bank of England, the Bank of Japan, the European Central Bank, and the Swiss National Bank, after the European sovereign debt crisis roiled markets throughout the fall. These swaps are set to expire in February 2013.

What necessitated the Federal Reserve’s most recent round of central bank liquidity swaps? The ongoing crisis in Greece, which in fact was onset by a series of ill-advised interest rate swaps with U.S. bank Goldman Sachs.

In part 8 of 10 of this series, we’ll discuss the role of interest rate swaps in more recent times: the Euro-zone crisis (as well as answer the question in part 5 about Goldman Sach’s role with Greece’s demise).

Swaps: A basic Q and A

This is part 5 of a 10 part series on currency swaps and interest rate swaps and their role in the global economy. In parts 1 through 4, we discussed the differences between interest rate swaps and currency swaps, as well as the pricing mechanisms for fixed-for-floating, floating-for-floating, and fixed-for-fixed swaps. In part 5, we’ll review the basics before looking at some real world examples in parts 6 and 7.

We’ve fielded some basic questions on interest rate swaps and will provide some clear, succinct answers to make this complex financial instrument a little more understandable.

What is a swap?

A swap is a financial derivative in which two parties (called counterparties) exchange future cash flows of the first party’s financial instrument for the future cash flows of the second party’s financial instruments.

What is the most common type of swap?

The most common type of swap is a plain vanilla swap, or an interest rate swap, and is when one party exchanges its fixed rate obligation with a second party’s floating rate obligation. Currency swaps, sometimes referred to as cross-currency swaps, are also very common, especially in the realm of international financing.

I only recently heard of swaps, how long have they been around for?

The first swap, a currency swap, was a $290 million agreement between the World Bank and IBM, in 1981.

How big is the swap market now?

As the world’s deepest financial derivatives market, the over-the-counter (OTC) swaps market has a notional value of $415.2 trillion as of 2006, according to the Bank of International Settlements (sometimes referred to as the central bank for central banks). At that figure, in 2006 dollars, that would make the swaps market approximately 8.5 times the size of global GDP – combined!

Over-the-counter, what does that mean?

Over-the-counter, or OTC, is off-exchange trading of financial instruments, not just swaps, but stocks, bonds, and commodities as well, directly between parties. While most of the swaps market is OTC, meaning it is without a centralized exchange, interest rate swaps can be standardized contracts regulated by exchanges, like futures.

Who uses swaps?

Swaps are utilized by two groups of people: hedgers and speculators. Bona fide hedgers are using swaps to insulate themselves from future risk, whereas speculators are without hedging need and are in the market for the sake of making money. Under CFTC Regulation 1.3(z), no transactions or position will be classified as bona fide hedging unless their purpose is to offset price risks incidental to commercial cash or spot operations and such positions are established and liquidated in an orderly manner in accordance with sound commercial practices.

So bona fide hedgers come from futures trading?

No! Actually, the first hedge exemption was granted by the CFTC to a swaps dealer for OTC index-based exposure where the swaps dealer writing the swap establishes a futures position to hedge its price exposure on the swap. Sounds complicated, but really, the swaps dealer proved he was protecting his capital rather than using it to speculate on swaps.

I have a fixed rate but I really want a floating rate – what do I do?

If your financing is within your borders and you are using your domestic currency, a domestic fixed-for-floating swap is the type of swap you would initiate with another party. This is known as a plain vanilla swap (see above), and is the most common type of swap.

But I’m not using these funds in my country – I’m funding a project aboard

In this case, this would be a fixed-for-floating currency swap, or a cross-currency swap, and it would require a counterparty in the country in which you’re seeking to finance a project.

I remember where I’ve heard swaps before – didn’t Greece get in trouble with swaps?

This is a complicated subject but we will cover it extensively in part 8 of this series.

In part 6 of 10 of this series, we will lay out simple real world examples of how companies would use swaps to hedge against risk in domestic projects as well as projects abroad.

Fixed-for-Floating Swaps: Domestic and Foreign Currency Transactions

This is part 3 of a 10 part series on currency swaps and interest rate swaps and their role in the global economy. In parts 1 and 2, we discussed the beginnings of swaps as well as the differences between interest rate swaps and currency swaps. In part 3, we’ll discuss fixed-for-floating swaps. 

Fixed for Floating Swaps

This is a chart provided in the March 1987 Federal Reserve paper “Interest Rate Swaps: Risk and Regulation,” by J. Gregg Whitataker. It remains perhaps the simplest and best diagram to date on how a fixed-for-floating swap works.

But before we jump into some math, we should reestablish the basic motivation behind swaps: comparable advantage. For example, if the party (party A) holding the floating rate instrument believes rates will increase in the short-term while the party (party B) holding the fixed rate instrument believes rates will decrease in the short-term, they might swap obligations. Thus, once the swap is complete, party A is ‘long the fixed rate, short the floating rate,’ while party B is ‘short the fixed rate, long the floating rate.’

The aforementioned example is a plain vanilla swap, a fixed-for-floating swap involving only one currency (i.e. a swap agreement involving two companies using the same domestic currency). Let’s say party A wants to take out a loan, at 12% and a floating rate of LIBOR +2% (but would really prefer a fixed rate). Conversely, party B wants to take out a loan, at 8% and a fixed rate of LIBOR +4% (but would really prefer a floating rate). By using a fixed-for-floating swap, both party A and party B can exchange obligations and receive their respective desired interest rates.

While fixed-for-floating swaps involving one currency are simple, they become slightly more complicated when involving more than one currency. As the name suggests, fixed-for-floating swaps in different currencies involve exchanging a fixed rate in one currency (i.e. U.S. Dollars) for a floating rate in another currency (i.e. Euros).

For example, if a company A has a fixed rate $50 million loan at 6.5% paid monthly and a floating rate investment of €75 billion that yields EUR 1M LIBOR +75-basis points monthly, and is worried about exchange rate fluctuations, it may choose to enter a fixed-for-floating currency swap with another firm, company B. In this example, company A wants to ensure profit in U.S. Dollars as they expect one of two things to occur: either the EURUSD exchange rate to drop; or the EUR 1M LIBOR to drop. By entering a fixed-for-floating currency swap with company B, paying EUR 1M LIBOR +75-basis points and receiving a 7.0% fixed rate, company A secures 50-basis points of profit and reduces its interest rate exposure.

In part 4 of 10 of this series, we’ll discuss floating-for-floating and fixed-for-fixed swaps.

Interest Rate Swap Tutorial, Part 2 of 5, Fixed Legs

Interest Rate Swap Fixed Legs

Now that we know the basic terminology and structure of a vanilla interest rate swap we can now look at constructing our fixed leg of our swap by first building our date schedule, then calculating the fixed coupon amounts.

For our example swap we will be using the following inputs:

  • Notional: $1,000,000 USD
  • Coupon Frequency: Semi-Annual
  • Fixed Coupon Amount: 1.24%
  • Floating Coupon Index: 6 month USD LIBOR
  • Business Day Convention: Modified Following
  • Fixed Coupon Daycount: 30/360
  • Floating Coupon Daycount: Actual/360
  • Effective Date: Nov 14, 2011
  • Termination Date: Nov 14, 2016
  • We will be valuing our swap as of November 10, 2011.

Swap Coupon Schedule

First we need to create our schedule of swap coupon dates. We will start from our maturity date and step backwards in semi-annual increments. The first step is to generate our schedule of non-adjusted dates.

swap coupon dates unadjusted

Then we adjust our dates using the modified following business day convention.

swap coupon dates adjusted

Note that all the weekend coupon dates have been brought forward to the next Monday.

Swap Fixed Coupon Amounts

To calculate the amount for each fixed coupon we do the following calculation:

Fixed Coupon = Fixed Rate x Time x Swap Notional Amount

Where:

Fixed Rate = The fixed coupon amount set in the swap confirmation.

Time = Year portion that is calculated by the fixed coupons daycount method.

Swap Notional = The notional amount set in the swap confirmation.

Below is our date schedule with the Time portion calculated using the 30/360 daycount convention. More on daycounts can be found in this document titled Accrual and Daycount conventions.

Note the coupons which are not exactly a half-year due to the business day convention. If our business day convention was no-adjustment all the time periods would have been 0.5. This is a difference between swaps and bonds, as bonds will generally not adjust the coupon amounts for business day conventions, they will simply be 1/(# coupon periods per year) x coupon rate x principal.

swap schedule with daycount

The coupon amount for our first coupon will be 1.24% x 1,000,000 x 0.50 = $6,200.00. Below are the coupon amounts for all of the coupons.

swap coupon schedule

Now that we know our coupon amounts, to find the current fair value of the fixed leg we would present value each coupon and sum them to find the total present value of our fixed leg. To do this we calculate the discount factor for each coupon payment using a discount factor curve which represents our swap curve. We will build our discount factor curve later in this tutorial series.

Thanks to our sister company Resolution for providing us with this series of posts.

Next Article: Swap floating legs including calculating forward rates

Interest Rate Swap Tutorial, Part 1 of 5

This is the first in a series of articles that will go from the basics about interest rate swaps, to how to value them and how to build a zero curve.

Introduction to Interest Rate Swaps

An interest rate swap is where one entity exchanges payment(s) in change for a different type of payment(s) from another entity. Typically, one party exchanges a series of fixed coupons for a series of floating coupons based on an index, in what is known as a vanilla interest rate swap.

The components of a typical interest rate swap would be defined in the swap confirmation which is a document that is used to contractually outline the agreement between the two parties. The components defined in this agreement would be:

Notional –  The fixed and floating coupons are paid out based on what is known as the notional principal or just notional. If you were hedging a loan with $1 million principal with a swap, then the swap would have a notional of $1 million as well. Generally the notional is never exchanged and is only used for calculating cashflow amounts.

Fixed Rate – This is the rate that will be used to calculate payments made by the fixed payer. This stream of payments is known as the fixed leg of the swap

Coupon Frequency – This is how often coupons would be exchanged between the two parties, common frequencies are annual, semi-annual, quarterly and monthly though others are used such as based on future expiry dates or every 28 days. In a vanilla swap the floating and fixed coupons would have the same frequency but it is possible for the streams to have different frequencies.

Business Day Convention – This defines how coupon dates are adjusted for weekends and holidays. Typical conventions are Following Business Day and Modified Following. These conventions are described in detail here.

Floating Index – This defines which index is used for setting the floating coupons. The most common index would be LIBOR. The term of the index will often match the frequency of the coupons. For example, 3 month LIBOR would be paid Quarterly while 6 month LIBOR would be paid Semi-Annually.

Daycount conventions – These are used for calculating the portions of the year when calculating coupon amounts. We’ll explore these in more detail in our discussions on fixed and floating legs. Details of different daycounts can be found here.

Effective Date – This is the start date of a swap and when interest will start accruing on the first coupon.

Maturity Date – The date of the last coupon and when the obligations between the two parties end.

Thanks to our sister company Resolution for providing us with this series of posts.

Next Article: Constructing fixed legs including calculating coupon amounts.

Interest Rate Swap Tutorial, Part 5 of 5, building your swap curve

Swap Curve

In the final article in this series, we will continue to build out our discount factor curve using longer datedpar swap ratesPar Swap rates are quoted rates that reflect the fixed coupon for a swap that would have a zero value at inception.

Let look at our zero curve that we have built so far using LIBOR rates.

zero curve

We are now going to build out this curve out to 30 years using par swap rates. These rates are as of Nov 10, 2011, and reflect USD par swap rates for semi-annual LIBOR swaps. The daycount convention is 30/360 ISDA.

par swap rates

Also keep in mind that these rates reflect the settlement conventions, so the one year rate is for an effective date of Nov 14, 2011 and termination of Nov 14, 2012. If we were to price a one year swap from the curve we have built so far, we can derive the 6mo discount factor, but we are currently missing the 1year factor. Since we know the swap should be worth par if we receive the principal at maturity, then the formula for a one year swap is:

1 year par swap rate resized 600

Notice that the T’s would be adjusted for holidays & weekends and are calculated using the appropriate discount factor. We can rearrange our formula to solve for df(1year).

swap bootstrapping

Using our example data:

discount factor par swap

We calculate the missing discount factor as: 0.99422634. But, this for a swap which settles on November 14th, and we are building our curve as of November 10th. So we need to multiple this by the discount factor for November 14th to present value the swap to November 10th. So the discount factor we use in our curve for Nov 14, 2012 is 0.9942107.

We continue by calculating discount factors for all the cashflow dates for our par swap rates. The next step is to calculate the discount factor for May 14, 2013. Our first step is to calculate a par swap rate for this date as it is not an input into our curve. We linear interpolate a rate between our 1 year and 2 year rates.

1.5 year par swap rate = 1 year + (2 year – 1 year)/365 x days

= .58% + (.60%-.58%)/365 x 181 = 0.589918%

We now can solve for the missing discount factor, continuing our bootstrapping through the curve.

zero curve construction

Thanks to our sister company Resolution for providing us with this series of posts.