This article has been written by Arvind Sethi, MD and CEO, Tata AMC.
During the 1990’s derivatives were exotic, and I wondered how all sorts of structures could be offered to clients. Even today, when the D word is mentioned, it brings a sense of dread in boardrooms.
However, once I got a firm understanding as to what zero coupons are, it all fell into place. I would like to share my excitement at how zero coupon pricing technology has made it possible to price any combination of cash flows. And more interestingly, how they can be ‘used’, and ‘abused’.
A zero coupon bond, or ZCB, is exactly what it says - it pays no periodic interest or coupon. Since the ZCB does not pay any interest, an investor would only buy it if it is sold at a discount, and the discount would be expected to be equal to the rate of return an investor expects for the time horizon.
In the example below, by investing Rs 68.06 and receiving Rs.100 after 5 years, the investor would have earned a CAGR of 8% - and the beauty is that the ‘final’ return on this investment would be known today.
Now let’s assume that the investor also had the choice of investing Rs 68.06 in a normal 5-year bond or fixed deposit. The precise return is inherently unknown until the end because she will not know the rate at which interest payments will be invested for Year 5. The jargon for this is ‘reinvestment risk’.
The elegance of a zero coupon instrument is that there is no coupon, and therefore no reinvestment risk - and the return on investment is known immediately. In the example above, by investing Rs 68.05 and getting Rs 100 in 5 years, the investor earns 8% annually compounded - and this is known on the first day. You don't have to wait for 5 years to find out.
Conversely, if you were promised Rs 100 after 5 years, you could pay out Rs 68.06 today (by discounting at 8%). Thus, in the world of interest rates there
would be no difference in value between Rs 68.06 today or Rs 100 in five years, assuming there is no credit risk.
Once a bond has been issued, the coupon is committed and as the expected yield in the market changes, the only thing that can change is its price. So when interest rates go up, the price of the bond must fall and vice versa. But in the world of bonds, thousands have been issued for different coupons and for different maturities. They could be quoting at 112 or 85 - so how do you compare them?
The math of that is YTM, an acronym for Yield to Maturity. This is nothing but the IRR of the cash flows of a bond. At business school we are taught IRR with examples of business opportunities with different cash flows and the IRR allows us to compare them. But IRR is just a measure of value - and just because the IRR of one bond (or project) is higher it does not mean that it is better and nor does it mean that it is the return you will get by investing in that bond. The reason is simple - the bond will pay period coupons and we will not know until the end rate at which they will be invested right until the end. In other words, the return is inherently unknowable.
However, if it was not an IRR but a zero coupon yield (as in the example above) then the return can be know right away - and that is the beauty and importance of zero coupons, and at the heart of derivative pricing.
A practical problem which faced financial engineers was - where do you get a zero coupon yield curve (ZCYC) in a world of illiquid coupon bearing bonds? Hardly any zero coupon bonds get issued - most of the bonds are either with a fixed coupon and there are some floating rate bonds - but very few zero coupon bonds.
As usual, the solutions were ingenious, from bootstrapping, curve fitting (Nelson-Siegel) and other interpolation methods to create a ZCYC. The ZCYC is not an actual yield curve of real bonds, but derived from a yield curve of fixed rate bonds. However, as the methods were refined, the ZCYC corresponded to what may have been a curve of real zero coupon bonds. This curve lies at the heart of the rich structures which swap teams were able to provide.
Once you have a ZCYC it is possible to calculate the value today of Rs 100 after 1 or 2 years or even 2 years and 43 days! The ZCY allowed practitioners to equate any cash flow along the yield curve.
For a start, ZCYC allows you to calculate precisely the forward rate of interest. If the 1-year ZCY is 8% and the 2-year ZCY is 9% then the implied 1-year rate after 1 year is 10% (intuitively, if we are required to pay someone a 9% CAGR for 2 years and are able to earn only 8% in the first year, then we will need to earn 10% between the first and second year – which is the forward rate !).
Using the ZCYC, the bank can derive the forward rate every six months, and then solve for the fixed rate X - such that the implied value of the forward rates equals
the fixed rate. This is a simple fixed to floating swap rate and if you think about it, this innovation is amazing. It permits a derivatives team to, at a point in time, express a floating rate (which is an unknowable unknown!) into a fixed rate. And it is useful for a corporate because it transforms a floating rate loan into a fixed rate loan, or the other way round.
A currency swap transaction is as follows. A corporate with a 5-year USD loan has to pay Libor every 6 months and the principal amount at the end of 5 years. How does this corporate protect itself from changes in $Libor and also changes in the dollar rupee rate?
By entering into a currency swap, the bank says – ok, we will fix the rate at which you need to repay those dollars at today’s dollar rate of Rs 60. We will also pay you the $Libor every 6 months, so that you can pay that to your lender. In exchange you pay us 7% in rupees.
How did the bank calculate this?
It is easy once you have a ZCYC for INR and the USD. The bank calculates what the $Libor payments will be by using forward rates. It also calculates the cost of giving USD to the company 5 years later but at today’s rate of Rs 60. It then solves for the fixed rate of interest which the company will have to pay every six months so that the value of what is paid and what is received is equal – which say, works out to 7%. This enables an amazing transformation of a floating rate USD loan into a fixed rate rupee loan!
For accounting or tax reasons, a corporate may say - I’m ok with paying the Libor cost every 6 months because U.S. interest rates are low, but I want to hedge the principal amount at today’s rate of Rs 60/$. The derivatives person says - ok that's fine. To buy USD 5 years forward the premium would have been, say, Rs10 and the cost to the company would have been Rs 70. However, we will sell you those dollars at Rs 60- and the Rs 10 cost we will recover from you by charging you (for example) 5% every six months.
In the world of ZCY’s that is easy because the bank has to calculate what the today’s value of Rs 10 after 5 years, and solve for Y - the percentage rate they need to charge the customer every 6 months to recover it - which in this example is say 5%. This is called a Principal Only Swap (PoS) and in simple terms, the corporate has bought USD 5 years forward and paid the hedging cost by paying 5% every 6 months.
It could be that the corporate says that I don't mind leaving the principal unhedged, because the rupee will get strong but we would like to hedge the Libor payments every 6 months because $Libor could rise. The bank can easily calculate those $Libor payments using USD forwards and equate them into a 6 monthly rupee interest cost - and in this example it would work out to 2%. So in exchange for 2% paid in INR every 6 months, the bank would pay the company $ Libor and the company would use that to repay interest on its dollar loan. This is known as a Coupon only Swap - CoS.
The PoS was (ab)used in an interesting way during the mid 2000’s. At that time interest rates had come down to 8% and many corporates had loans at around 11% and were looking at ways to reduce their cost. There was a strong view in the market that the rupee would strengthen. Companies wanted to short sell the dollar, but they needed to have an underlying exposure like an export. And not all companies had significant exports!
A novel solution to circumvent the regulation was to show the rupee loans as the underlying liability against which a PoS was executed. However, instead of the corporate paying the rupee fixed rate (as in the example above, which means that they commit to buy USD in future) they received the rupee fixed rate, paid $Libor every six months, and effectively sold USD forward. This view turned out to be a winner and during the period of the swap the corporate not only earned the fixed rate (say 7%), and since the INR strengthened they also bought the USD back at a profit.
However, views do not always go right and suppose the company loses $1 million on the swap. The trick then would be to go the derivatives desk and say - can we “restructure” the swap? For the ZCYC wizards the calculation would be to amortize the loss over the term of the new swap and add it to the cost. It would be easy, with a ZCYC, to solve for - how many basis points do we need to charge the client every six months so that it would equal $1 million. If that number came to 0.40%, then instead of the client paying Libor he would pay Libor +0.40%! QED.
Fortunately, the regulator latched on to this trick and has closed that loophole.
Italy and Greece used swaps to reduce their budget deficit and in one of the most interesting cases Enron used it to reduce the leverage on its balance sheet.
Amongst the many tricks which Enron used was a Deferred Payment or Prepaid Swap. What does this mean, exactly? Going back to a basic interest rate swap, say for 3 years, the agreement would be - the company pays a fixed rate of interest every six months and receives a floating rate (Libor) every six months. Enron asked the derivatives team to restructure a swap as follows - instead of paying each other interest cash flows every six months, why don’t you give me all your payments upfront and we will pay you our interest obligations at the end.
This is a relatively simple calculation in the world of ZCYC’s - because all you need to do is work out the present value of the payments the bank would have made, and the future value of all the payments the company would have to make. In other words there would be no intermediate payments - the bank would pay everything on day one and the company would pay everything at the end.
But wait a minute does that not look suspiciously like a zero coupon bond - because the company receives money in the beginning and pays it at the end? It is - but by showing it as a swap, to which the auditor fraudulently agreed, it was booked as an off balance sheet item and not a loan, and therefore escaped the scrutiny of most analysts. Enron got away for a while - but when the time
came to make the payments on the final day of the swap, banks realized that it would be ‘payable only if able’!
Greece and Italy use variations of similar structures. In these deals the exchange rate used was not the market rate! In the case of Italy, the Finance Minister, Gustavo Piga, there was a Yen200 billion bond (about $1.6 bn at the time) which was In The Money - meaning that the Yen had weakened since the bond was issued and was, if marked to market, profitable.
A swap was executed in which the profit was paid upfront and Italy agreed to pay the bank Libor + 16.77%, when the market rate for Yen Libor was about 5%! In other words they took the gain upfront, and paid for it in periodic (higher) interest rate payments. This, along with other similar deals allowed them to show a lower debt and meet the criteria for joining the EU.
Greece did similar deals, where the exchange rate for the swap was done at ‘off market’ rates. Information about the Greek deals is less clear, but the rate was set so as to take some money upfront and reduce the size of the debt; or they were done in a way to reduce the interest cost and lower the debt servicing cost.
In any case, the motive was to restate the cash flows and once you have a ZCYC then it is easy. An analogy would be that suppose you have a loan of Rs110 but were only allowed to show up to Rs100 - then it could be ‘structured’ so that the books show it as Rs 100, and you pay a higher interest rate to compensate the lender for the Rs 10 which you did not show in the books!
A little tip for someone reading this is that if you see ridiculous rates being paid or received, then it is a sign that ‘daal mai kuch kaala hai.’