In our last post, “Into the Belly of the Whale: Hedging and Credit Default Swaps”, we explored what makes a hedge a hedge and then looked at how the ever-so-mysterious Credit Default Swap is priced.

We now take this knowledge and continue exploring the JP Morgan loss of $2 Billion by their illustrious trader nicknamed “The London Whale”.

**What is a “Curve”?**

According to Matt Levine and Lisa Pollack, the JPMorgan trade in question was a “curve trade”. While one might think this involves driving a car on mountainous roads, in the world of finance the term “curve” is used differently.

If you put yourself in the shoes of a borrower, you are faced with a choice of when you would like to pay back the money you borrowed. Do we want to issue 5-year debt, 10-year, or 30-year? Homeowners face this same question when they are considering their mortgage.

Figure A |

The length of time until the debt is due is called the “term” of the debt. Figure A plots these rates out by their term (I added a few extra for completeness). This picture, and the concept of different rates for different terms of debt, is called the “yield curve”.

Figure B |

For Credit Default Swaps, the curve concept is the same, but instead of interest rates the points on the graph represent the Credit Default Swap Spread (for example, the 102 basis points we calculated in our last post for a 2-year CDS).

Because the shape of a curve can change over the course of time, it is possible to buy and sell securities that will make or lose money should this occur. According to Matt Levine and Lisa Pollack, part of the JPMorgan hedge in question was a “curve flattener”. This means the transactions were set up to pay-off if the curve became flatter than what it was.

**Let’s Pull Up Our Bootstraps**

Figure C |

Let’s look at a simple probability event like flipping a coin. If the coin is flipped twice, and if heads comes up then there is default, then we know that there is a 50% probability that by the end of period 1 there will be a default and a 75% probability at the end of period 2. This is shown graphically in Figure C.

Figure D |

What we are missing is the rate for the second period. Yes, we have a two-year rate of 75%, but that incorporates the first year as well as the second. We want to get the rate for the

__second year only__. The bracket in Figure D shows the time period where the rate we need is missing.Figure E |

Figure F |

onedigit.org has been kind enough to provide Visual Basic code so we do not have to go through this process in a tedious, step by step manner.

Figure G |

Figure H shows our valuation for the 10 term swap. The rate of 35.2 basis points for the swap is the correct one in order to get the valuation of the contingent leg equal to the value of the fixed payment leg.

**The World is Getting Flatter?**

The period probabilities are important because these are the drivers of change in the price of the Credit Default Swap. If the curve is going to flatten, then one of several things are going to occur:

a) short-term probabilities increase more than long-term ones,

b) long-term probabilities decrease more than short-term ones, or

c) some combination of a and b.

In order to generate gains when the curve flattens, we need to buy the short-term part of the curve and sell the long-term. The amount we buy vs. what we sell will be different, because for a change in probabilities of default or the CDS rate the change will be different, since one security is much shorter in length than the other, so there is less to impact.

Figure J |

Figure K |

This is by design, the transaction is supposed to make money when the curve flattens, not when the whole thing shifts up and down.

Figure L |

We will continue on into the belly with our next post.

**Key Takeaways**

The term structure of default rates and interest rates can create different impacts depending on the shape of the curve and how it changes. We can execute derivative transactions that take advantage of this.

**Questions**

· In your opinion, was JPMorgan speculating or hedging?

Dave

ReplyDeleteI worked for you a few years ago as your analyst and stumbled upon this website. It is very impressive, I learned a lot reading through the blogs on here. Hope all is well.

Stephanie,

DeleteHow funny, I just thought about you the other day, someone asked about IRR for an equity buyback, and I had to remember how you did that analysis!

Thanks for the compliments on the blog and reading. Hopefully you continue to find it useful.

Hope all is well with you as well - kindergartner this fall or am I off a year?

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