## Saturday, June 16, 2012

### Into the Belly of the Whale: Basis Risk

In our last post, “Into the Belly of the Whale: Curve Balls”, we looked at the term structure of the probability of default and looked at how a “curve flattener” trade pays off when the term structure flattens.
We now apply this knowledge to some of what has been proposed with respect to JP Morgan’s derivative activities and derive some lessons that we can take with us.

It’s a Hedge After All
According to Matt Levine’s assessment, JPMorgan had a significant amount invested in debt securities of other firms.
We have already examined how to price a Credit Default Swap in “Into the Belly of the Whale: Hedging and Credit Default Swaps”.
 Figure A
In theory, we can price a bond using the risk free rate if we know the same factors that go into the Credit Default Swap calculation – default probabilities and recovery/loss rates. Figure A shows this expected value calculation in “tree form”.
Using this methodology, the upper leg of the tree is worth \$999,519 (\$1,050,000 x (1 - 1%) x 0.962) and the lower leg is worth \$4,038 (\$1,050,000 x 1% x 0.962 x 40% recovery rate), for a total expected value of \$1,003,558. This compares to a risk-free bond (i.e. a bond that will pay out with 100% certainty) valued at \$1,009,615 (\$1,050,000 x 0.962).
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 Figure B
The difference between the risky bond and the risk free bond price is \$6,058. Figure B shows our Credit Default Swap pricing calculation, which comes to the same amount - ah, all is right with the world!

But It Ain’t Perfect
 Figure C
If we extend the term of the risk free and risky bonds to 2 years, assuming an annual payment, then the risky bond will be priced according to Figure C. Using this methodology, the risky bond is valued at \$983,177, and the risk free bond is valued at \$1,000,458. This is a difference of \$17,280.
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 Figure D
Running our Credit Default Swap pricing (Figure D), we come up with a slightly different value of \$17,486, for a difference of \$206 versus our Bond Pricing methodology. This difference is attributable to a couple of different factors. If there is a default in time 1, then there will be no interest payment nor recovery of it in time 2, whereas for the risk-free bond this would not occur. If there is a default in time 2, we have already earned the time 1 interest payment on both sets of bonds, while the Credit Default Pricing deals only with one set amount which does not vary from period to period.
The valuation difference is a little over 1% of the total value, so there is still a fairly good tracking of the Credit Default Swap pricing versus the Bond Pricing, but there is a difference. In hedging terminology, the fact that there is some fundamental difference between the hedge instrument pricing and the pricing of the item being hedged is called “basis risk”.
 Figure E
Let’s see what happens if the curve flattens. If we increase the year 1 probability of default to 5% (thereby inverting the probability of default curve) from 1%, the Credit Default Swap pricing jumps from \$17,486 to \$41,717 (see Figure E). The Bond Pricing for the risky bond is now \$959,770, which creates a difference to the risk-free bond of \$40,688. The difference between the two methods is now 2.5% of the Bond Pricing valuation, up from 1% previously. Thus, because of the basis risk the hedge can become less effective as things change through time.

JP Morgan described the hedge they established as a “macroeconmic hedge”, which would suggest that we can interpret it as follows – “we have investments in some bonds, and in general these things will lose value if the default curve flattens, so we will use CDS index to hedge this, but there is an element of basis risk in the hedge”.
Matt Levine suggested that JPMorgan had up to \$1 Trillion in corporate loan exposure. If this were hedged using just our simple example worked out above, the movement of the basis risk between 1% to 2.5% would create a \$15 Billion shift in value. So maybe they should be happy if the losses are only \$3 Billion!

The Moral of the Story
My purpose in this series of posts was to explore the pricing mechanics of Credit Default Swaps and how they might be used to hedge a debt security investment, and to determine whether a sensational story can be made out of a seemingly prudent undertaking. It seems that it can.

This is not meant to expunge JPMorgan from any wrongdoing. There are a lot of other factors that have been reported about JPMorgan’s hedge which can contribute to the loss other than what we have explored to this point, and not being privy to the gory details leaves me in a position where I cannot fairly judge.
However, we have seen that a simple element such as basis risk can have a large impact on the bottom line if we are dealing in large numbers, and it is therefore important to consider. Many of the spectacular blow-ups in the past, such as Long-Term Capital Management, have basis risk as part of the underlying story as to why they occurred.
For this reason, risk management is something that needs to be executed with an understanding of what may or may not occur under a number of different scenarios. When markets are moving fast, it may be too late to correct for changes in the basis risk inherent in your risk management program.

Key Takeaways
Risk Management is not a precise and exact science. There are often differences between what a business needs to hedge and the securities available to execute it, leading to basis risk. In order to understand potential risks related to the risk management effort, scenario analysis of extreme, sudden, and unexpected market movements should be performed in order to keep our firms from being surprised by the results of our risk management efforts.
Questions
·         Do you think JPMorgan’s losses were the result of speculation or the realities of imperfect hedging solutions?