Wednesday, May 23, 2012

Into the Belly of the Whale: Hedging and Credit Default Swaps

Upon first hearing the news of JP Morgan’s derivatives loss I was somewhat puzzled as it was termed a “hedge”.
In risk management, a hedge is a term used to describe transactions that offset some other set of transactions, with the net effect being that as a whole we are unaffected by the activity. If JP Morgan lost $2 Billion on a hedge, they should have made $2 Billion somewhere else.
Was the media sensationalizing one piece while ignoring the whole?
Let’s start from the beginning…

What is a Hedge?
According to Wikipedia, “a hedge is an investment position intended to offset potential losses that may be incurred by a companion investment”.
Suppose we are a cereal manufacturer – we buy corn and make corn flakes. We sell our corn flakes to supermarkets under contract. Our current contract lasts one year and we sell each box for $3.99.
Each box of cereal requires half a bushel of corn to produce. The current price of corn is about $6.50, so our cost is $3.25 (we are assuming that is our only cost in this example) per box.
At today’s price, we make $0.74 per box.
We purchase corn every day of the year. Our problem is that the price of corn will vary day by day, whereas our revenue will not. If the price of corn goes above $7.98, we lose money on every box of corn flakes we sell.
In order to protect ourselves from loss, we enter into an agreement with someone (called a “counterparty”). The terms of this agreement are that they will pay us the day’s market price for corn and we will pay them $6.80. This is known as a floating to fixed swap – one party’s payments “float” (which means they can change every day) and the other party’s payments (in this case ours) are “fixed” – they do not change.
By fixing our price of corn at $6.80, our cost per box is $3.40, so we have ensured that we will make $0.59 per box over the life of our contract.
For us, this transaction is a hedge, because we have executed a financial transaction in order to avoid losses from occurring.

If You Have a Hedge, the Gain or Loss Does Not Matter
Sticking with our corn example just a little bit longer, let’s see what happens under some different price scenarios.
If corn goes to $9.00, the margin on our cereal business loses $0.51 per box ($3.99 - $4.50). On our financial hedge, we have a gain of $1.10 per box ($9.00 received minus $6.80 paid, divided by 2). Adding together our loss of $0.51 on the physical transaction and the gain of $1.10 on our financial transaction, we arrive at $0.59 per box.
Now we will look at what happens if corn goes to $5.00.  The margin on our cereal business is an astounding $1.49 per box ($3.99 - $2.50). The results of our financial hedge, however, are abysmal, a loss of $0.90 per box ($5.00 received minus $6.80 paid, divided by 2).
At this point, the headlines scream out “Corn Flake Manufacturer loses $0.90 per box on derivative transactions”. There is a hue and cry, our share price tanks in the market, Congress subpoena’s our CEO, etc.
Yet, the derivatives loss is part of a well-functioning hedge. Combining our loss of $0.90 with our corn flake profit margin of $1.49 results in a net position of……$0.59 per box! The same amount when the market went the other way!

Figure A
Whether the hedge is a gain or loss is irrelevant – the fact that we wind up at $0.59 every time is the objective. We wanted to protect our profit margin against price fluctuation in our raw material supplies, and we have. A hedge cannot be looked at in isolation, it must be viewed in conjunction with the item we are attempting to protect.
To show this, in Figure A, the brown line is the hedge gain or loss while the orange line is our net position, which remains constant no matter the price.
So when first hearing of the JP Morgan saga I wondered if it was just being sensationalized by focusing on the loss, and the fact that it was a hedge was being downplayed.

Enter Stage Left – The Credit Default Swap
Figure B
The securities at issue in the JP Morgan hedge were Credit Default Swaps (CDS), so in order to understand something of what happened we need to understand these securities.
Similar to our corn example, a Credit Default Swap is an exchange between two parties. This is depicted in Figure B.
Party A seeks to protect themselves against a credit loss, and therefore enters into a contract with Party B who is willing to pay Party A in the event Party A suffers a credit loss. In order to induce Party B to take on this risk, Party A makes quarterly payments to Party B.
There are a number of factors involved in this transaction. The loss can be for a specific company or an index representing a “basket” of companies.
The loss itself is also defined in the agreement. It can be a failure to pay on a specific identified security (e.g. X Corp. Series A 4.9% Due 2017) or on a class of securities (e.g. Any X Corp. Senior Unsecured Debt Obligations). It can be the bankruptcy of X Corp., or the restructuring of X Corp.’s securities. Or it can be all of the above.

What Factors Drive a Credit Default Swap’s Value?
The price of a credit default swap is based on three factors:
·         interest rates,
·         the probability of default,
·         the loss incurred should a default occur.
Interest rates are a factor because the payments Party A makes occur quarterly through time, and therefore are not as valuable as their nominal amounts due to the time value of money.
The probability of default is significant on both sides of the swap.  Party A makes payments so long as there is no default, and Party B makes a payment if there is one.
Finally, the loss given default is significant to Party B's payment to Party A. The obligation of Party B is to make Party A whole on the transaction. If Party A's security pays out 90 cents on the dollar, Party B owes 10 cents. If Party A's security pays out 20 cents on the dollar, Party B owes 80 cents.
Given that there are multiple inputs, there will be variation in how the swap is priced and valued. If you think the loss given default should be 50%, and I think it should be 40%, then we will arrive at different prices for the swap.
By "locking down" some of the factors, we can calculate the others, and perform various sensitivity analysis.

Pricing Example
At the outset of the swap, the value of the agreement needs to be equal for both sides of the transaction. The value to Party A needs to be the same as for Party B. This is usually accomplished by through setting the premium payments from Party A to Party B. It is commonly referred to as the CDS Spread.
In mathematical terms, the swap needs to satisfy the following (where PV stand for Present Value):
For the Contingent portion of the swap, the present value equation is calculated by the following equation:

Figure C shows the calculation of a two year swap with a $1 million notional for a counterparty with a 2% per year default probability with a subsequent value of $19,699.

Figure C

The formula for the Fixed leg looks a little scarier:

A bit of further explanation of this equation:
·       the CDS spread is in basis points means we need to divide by 10,000 to get it into percentage terms to use with the Notional amount
·       the denominator of 4 is used to distinguish the fact that the CDS is an annual figure but payments are quarterly
·       the term after the + sign reflects the fact that a default during the term will mean some payment is due, but not the full amount. If the default probability is equally likely throughout the quarter, then on average the payment will be ½ of the normal quarterly amount, thus the divisor of 2 in that equation term.

So how do we determine the CDS rate that will make this value the same as the Contingent payment? Fortunately, we are able to use algebra to come up with the answer, solving for CDS as follows:
Figure D shows the calculation of the Fixed leg with the CDS rate set to 102.02771 basis points. Notice that the value of this leg matches the value of the fixed leg calculation in Figure C.
Figure D

Until Next Time
In the next Treasury Café post, we will look at sensitivity of the CDS prices to various factors held within the equation. Using this knowledge, we will begin to explore how this security might help establish a hedge, and also why it might not be ideal.

Key Takeaways
We have discussed how Credit Default Swaps are valued. By establishing the basic equations, we are able to analyze a CDS sensitivity to various factors. In addition, knowing the mechanics of this calculation and the variables involved will help us analyze JP Morgan’s situation, which involved hedging investments by using a CDS curve flattener trade.
·         What is your experience with Credit Default Swaps?
·         Do you think they are useful or not?
Add to the discussion with your thoughts, comments, questions and feedback! Please share Treasury Café with others. Thank you!


  1. You raise a oft forgotten point if it is truly a hedge as suggested by JPM management; although why instruct a trader known for outsized bets to develop a hedging strategy. That is pardon the pun where it gets fishy, and additionally this was done in London instead of the US, where prop activities are currently less scrutinized. Does it pass the smell test?

    1. You raise some valid points about "the smell test", and it is perfectly conceivable that this was nothing but a bet rather than a hedge. I am not sure if anyone will ever know for sure (unless the London Whale has already signed a book deal!).

      Thanks for the comments!

  2. Bank auditor seeking answersApril 25, 2013 4:41 AM

    Very useful have a writing style that is simple yet concise!

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