Sunday, May 20, 2012

Credit Default Swaps for Dummies - Part I: Single Name CDS

A few people have asked me about what a Credit Default Swap is and what J P Morgan did with them.  As for the latter question it is not clear that we know the specifics yet but the articles that I have linked to below shed some light on what they may have done.  As for the former question that takes a bit of work.  So here is my version of Credit Default Swaps for Dummies (Part I).

Say you buy a bond from IBM.  You pay 100 USD for it today.  They promise to pay you your 100 USD back in May 2014 and along the way they will pay you  1USD per year in coupon payments.  That 1 USD per year reflects two components (1) the general level of return that you would demand from a risk free lender like say the US Government and (2) a risk premium above the risk free return that you will demand because it is possible (unlikely but possible) that IBM could default on you.

Now you are pretty happy with receiving 1 USD per year for lending your money but you are a bit nervous that IBM could default on you or that the bond otherwise loses value.  So what you really would like to do is hedge away some of the risk.  Before looking at how to hedge the risk let's look at what these risks are again.  You face two primary risks by holding that IBM bond 

(1) there is the risk that the general level of interest rates go up and the price of your bond will then go down.  If you hold the IBM bond to maturity you will still get your 1 USD per year and your 100 USD back in two years.  However if you tried to sell the bond before maturity you would find that you would get less than 100 USD for it.  Why?  If the general level of interest rates has gone up then you could go out into the new bond market and pay 100 USD for a new bond which pays 100 USD at maturity and pays MORE than 1 USD per year along the way (remember we assumed interest rates went up).  So no one is going to pay you 100 USD for your bond that only pays a measly 1 USD per year when they can pay 100 USD for a new bond that pays more than 1 USD per year.  Hence the value of your bond will fall below 100 USD.  That is interest rate risk.

(2) there is the risk that IBM will in someway default on your bond - or in CDS speak that they will experience a "credit event".  Maybe they miss a coupon payment along the way or they don't pay you back your 100 USD at maturity.  There is also the possibility that IBM gets their credit downgraded along the way.  Now IBM getting their credit downgraded does not necessarily mean you don't get your 100 USD at maturity and your 1 USD along the way - but if you tried to sell your 1 USD bond prior to it's maturity the chances are that you would not get 100 USD for it.  This is credit risk.

So now say you want to hedge the risk on your bond how would you do that?  Well there are many ways to hedge the interest rate risk (shorting US Treasuries, selling US Treasury futures, US Treasury futures options, Eurodollar futures and options - these are huge very liquid markets).   But hedging the credit risk of IBM is a bit more difficult.  You could try to short another IBM bond but that may be cost prohibitive.  You could ask someone to write you a put option on your bond.  So in that case if the value of your IBM bond falls below some value (say 90 USD) you could put the bond back to the person who sold you the option in return for 90 USD.  Of course you don't get the option for free - you would have to pay some premium for the option.  The problem with the put option is you have to get someone to write you an option on the specific bond that you hold - and that may be expensive.  Furthermore you are paying them to insure you against both credit risk and interest rate risk when there are cheap ways to hedge away the interest rate risk.  What you really want is a way to specifically hedge away the credit risk.  Enter the credit default swap!

So you go to your local credit default swap dealer and ask him to write you a credit default swap (CDS) on IBM.  You want is a single name CDS ie a CDS which is specific to IBM as opposed to a basket or index or more complicated structure.  There are also two types of CDS physical settle and financial settle.  The original CDS were physical settle and they are easier to understand...but today in the US most CDS are financial settle.

How does a physical settle CDS work?   You would agree to pay your local CDS dealer a coupon rate (say 0.2% per year) on a notional amount (we want to protect 100 USD) for a certain amount of time (in our case two years).  So you would pay the dealer (100 USD*0.2% =  ) 0.20 USD per year for two years.  If at any point prior to the expiration of the CDS if a "credit event" occurs then you would have the right to hand your IBM bond over to the CDS dealer in return for the principle value of the bond (100 USD) and then the CDS ends.  The agreement with the CDS dealer will spell out exactly what constitutes a credit event as well as exactly which bonds you can hand over to the dealer - you may have a choice of a few bonds.

Now it is possible that you could decide to sell your IBM bond prior to the expiration of your CDS agreement or maybe you never even owned the bond in the first place.  But you can still purchase a CDS on that bond.  Then if a credit event were to trigger your CDS agreement you could go out into the market and buy a IBM bond (which should be selling cheap since it is in default or has had its credit downgraded) and turn that bond in to the CDS dealer in return for the principle value ($100) of the bond. In that case you are actually hoping the value of the bond does goes down.  That is called a naked CDS - where you have CDS protection on a bond that you don't actually own. 

How does a financially settled CDS work?  Again you would agree to pay your local CDS dealer a coupon rate (say 0.2% per year) on a notional amount (we want to protect 100 USD) for a certain amount of time (in our case two years).  If IBM were to experience a credit event prior to the expiration of your CDS then instead of you turning your bond in to the CDS dealer in return for 100 USD you would instead receive from the CDS dealer a payment for the difference between the principle amount (100 USD) and what the bond is currently selling for after the credit event has been announced.  In order to decide what the official current selling price for the bond is there is a poll of bond dealers which attaches a price to the bond.  Most US CDS are financially settled now.

So now you have a way to hedge the credit risk on a bond separate from the interest rate risk.

Why did people like CDS so much?

First they do allow you to separate the two components of corporate bond risk and hedge as much or as little of each as we want.

Second they allow someone to speculate on the credit risk of a company.  One can argue whether or not this is a good thing or not.

Finally the general structure of a credit default swaps allows banks to hedge their exposure to one of their customer's company credit.  Say Bank Wobbo loans IBM 1BB USD for working capital.  Bank Wobbo decides  they want to hedge some of that risk.  How could they do that?   One way would be for them to buy a CDS on IBM from another party.  As long as either (1) the bank loan has priority in liquidation over IBMs corporate loans or (2) default on the bank loan constitutes a credit event - if IBM defaults on that bank loan then Bank Wobbo would be able to collect on their CDS.   There are similar CDS like structures which are specific to bank loans but they are less liquid than the standard CDS.  Credit default swaps give banks an easy way to insure themselves against customer's defaulting on them.


The Wonderful World of Synthetic CDO Strikes Again

ZeroHedge has their take on the JPM trade and it sounds fairly convincing.

http://www.zerohedge.com/news/irony-101-or-how-fed-blew-jpmorgans-hedge-22-tweets

I have tried to make this as simple as I can but the simple truth is ...it is not simple.  Their story is

(1)  JPM was looking for a way to hedge tail risk - the risk of a huge disruption where everything goes wrong as once.  Tail risk is always expensive to hedge because no one wants to be left holding the bag when the shit hits the fan.  To see a good example of this look at the S&P skew in the options market where downside insurance is much more expensive than upside insurance.

(2) JPM found what seemed to be a good hedge in senior tranches of a synthetic CDO on the CDX.NA index.  What does this mean?  For a description of how CDS works see my Credit Default Swaps for Dummies Parts I and II.  Recall that for synthetic CDO the first defaults get paid out of the equity tranche.  When defaults have exceeded the collateral of the equity tranche then the next tranche up starts paying out.  It continues upward through the junior, mezzanine, and senior tranches in a similar manner.  The only way a tranche has to pay out is if all tranches below it have been depleted.  So the only way that a senior tranche pays out is if there are a huge number of defaults which was exactly the situation that JPM wanted to hedge.  ZeroHedge hypothesizes that JPM purchased large amounts of the senior tranches of CDX.NA.  Not sure which vintage.

(3) So what factors influence the price of a CDS/CDO tranche?  First most obviously how close we are to default.  Second how much volatility there is in each of the underlying names.  And finally how correlated are the underlying names.  But the correlation affects the various tranches very differently.  Imagine first that the names are completely uncorrelated in their default probabilities.  Then it is very likely that there will be some losses in the most junior tranches but the probability of defaults eating through all junior tranches up to the senior tranche is very small.  Now imagine the opposite that the names are perfectly correlated.  So if one name defaults then they all default.  Now if the most junior tranche gets hit the most senior tranche also gets hit.  So the value of senior tranches are extremely sensitive to correlation while the junior tranches are much less so.  In math speak the dV / d(correlation) is very high for the senior tranches and much less positive for the junior tranches.  By purchasing large amounts of the senior tranche of CDX.NA Morgan  had bought insurance against a crash but at the cost of making themselves very long dV / d(correlation). If correlation fell then the value of their CDX.NA senior tranche positions would fall as well.

(4)  At some point in time JPM tried to hedge out some of their exposure to correlation.  The hedge instrument that JPM chose was the CDX.NA.IG9.  Since CDX.NA.IG9 includes all tranches it has a much lower dV / d(correlation) than do the senior tranches of CDX.NA.  So JPM had to sell huge amounts of CDX.NA.IG9 in order to offset the long exposure to correlation that they had incurred from their senior tranche position.  Furthermore, the relationship between V and correlation is not linear ie the second derivative of V with respect to correlation is not zero.  This is analogous to the gamma from standard option pricing.  If correlation fell then JPM would have to continue to change their position in CDX.NA.IG9 in order to keep their correlation hedge balanced.  More on this point below.

(5) When the Fed and the ECB took action to reduce the probability of systematic defaults in Europe they effectively reduced the correlation between names.  At this point it is not clear if JPM had fully hedged their correlation.  It is possible that they were not fully hedged - in which case they took a mark to market  loss on their long correlation position in the CDX.NA senior tranches.  In either case since senior tranches are nonlinear in correlation they would have had to rebalance their hedge in CDX.NA.IG.

(5)  Hedge funds saw that IG9 was getting way out of line with fundamentals so they tried to profit by buying IG9 against other indices.  But no matter how much they bought IG9 kept falling as JPM continued selling in an attempt to balance their correlation exposure.  The funds eventually got pissed about the non-convergence and the nicknames The Whale and Voldemort began seeping into the business news.

Ok so what parts of this story still don't make sense to me?

(a) If the original purchase of CDX.NA senior tranches really was a hedge to the JPMs other positions then why change its exposure when correlation changed or hedge out its correlation exposure at all? Yes as correlation fell they would have lost mark to market on their senior tranche hedge but their original portfolio would have been better off - since there would have been less tail risk.  If they could not explain this then how did they explain the rational for the hedge in the first place?

(b) I am no expert in CDO pricing but I think the second derivative of the V with respect to correlation is positive (someone correct me if I am wrong here).  So if correlation increased then dV / d(correlation) should  increase or if correlation fell then dV / d (correlation)  would decrease.   If prior to the Fed / ECB intervention JPM had been hedged then after the intervention (where correlation fell) then they would be short correlation by the second derivative effect.  Hence after the intervention they should have been buying CDX.NA.IG9.  Maybe they were...

(3) Why did JPM's alarm bells not go off when they put on the CDX.NA.IG9 hedge?  It seems like they replaced the tail risk with correlation risk, and then replaced correlation risk with a lot of general directional risk.  Did they not hedge the general direction risk?

I am not sure if I buy the whole story.  Still it is a very interesting hypothesis.

Friday, May 18, 2012

Even More on Morgan's Trade



So the trade was ?
(1) buy protection on a subset of high yield companies
  Possibly CDX.NA.HY.11 which expired last December
(2) sell huge amounts of protection on the general index CDX.NA.IG9
which expires December 2017 as a hedge against (1)

Since the riskier companies have a "credit" beta greater than one J.P. Morgan needed to sell more of the general index to get a market neutral hedge.  Perhaps they have learned rule 1 of stat arb.  Because two assets on average move together does not mean that they always have to move together.

Wednesday, May 16, 2012

Better explanation of the JP Morgan trade


JP Morgan's USD2 Billion-Plus Loss Came On Three-Legged Trade


   By Katy Burne
   Of DOW JONES NEWSWIRES

NEW YORK (Dow Jones) -- The complex web of trades that saddled J.P. Morgan Chase & Co. (JPM) with at least $2 billion in losses had three key components, according to people familiar with the bank's strategy. 

So the three legs of the trade were
(1) buy protection on junk bonds expiring ?
(2) sell huge amounts of CDX IG9 expiring 2017
(3) buy protection on investment grade bonds expiring at the end of 2012

I am still not sure I understand what they were doing exactly.  Apparently neither did they.

Double Take


1.  Inflation expectations are running 60bps below target
2.  The real interest rate is negative (yes negative) right now
3.  The ten year treasury yield is at 50 year lows....

And the biggest threat to America is...inflation!!! 
http://www.reuters.com/article/2012/04/10/usa-fed-fisher-idUSL2E8FABGG20120410

This guy is a Federal Reserve Governor?  He seems utterly clueless about what is going on with the economy.

If Uncle Milton were alive I can tell you what he would be counseling us.  M*V=P*Y    Assuming V is constant, as he did, we need to be pumping money into the economy any way we can.  Either inflation will go up - which we can afford right now - or output growth will increase.  Most likely some of both will occur - more output at first and more inflation later. 


Saturday, May 12, 2012

J.P. Morgan's Big Bet

http://ftalphaville.ft.com/blog/2012/05/11/996131/too-big-to-hedge/
http://blogs.reuters.com/felix-salmon/2012/05/11/counterparties-your-massive-guide-to-jpmorgans-failed-hedge/
http://www.marketplace.org/topics/business/easy-street/jp-morgans-loss-explainer#.T60fG7ppJTE.twitter

Assuming Alphaville is correct that it was a short position in the CDX.NA.IG.9 my questions are

(1) how much of the loss was on the original position and how much of the loss was due to trying to liquidate the position?  If it really was a hedge then why liquidate it?

(2) The Marketplace article has me confused.  If JPM was long the corporate bonds then the hedge is to buy protection but all the articles suggest that they sold protection.   If they were long bonds then JPM's CIO has a lot of explaining to do.

(3) If the trade really was a hedge then was it

        (a) a curve trade like Alphaville contends.  If so then we should observe a huge increase in the notional on the other leg of the trade as well.  Do we?  Everyone seems to focus on CDX.NA.IG.9 but  have seen nothing on the other leg of the trade.   Also how much notional would they have had to have on for a curve trade to lose USD2BB.

        (b) a basket of the index versus the underlyings.  If they lost USD2BB on this trade then how far did the index get out of line before they started to liquidate and how much of it did they actually have on (it must have been a lot)?

        (c) short the protection and short the corporate bonds.   Again how much did they have on?

(3) the chart of total notional outstanding suggests the total outstanding notional on CDX.NA.IG.9 has doubled in the last 6 months.  How much of this was due to JPM?

The one case where Alphaville speculated on the specifics of a trade where I actually knew what the trade was...they were wrong.  I'm not saying they are wrong this time but rather it is sometimes difficult to infer the specifics a trade from looking at market activity.  Eventually the true story will come out.

Sunday, May 06, 2012

Brussels We Have a Problem

http://www.bloomberg.com/news/2012-05-06/greek-election-surprise-rejects-barbarism-of-bailout-austerity.html

http://www.bloomberg.com/news/2012-05-06/sarkozy-is-first-french-president-in-30-years-to-fail-reelection.html

http://www.bloomberg.com/news/2012-05-06/euro-falls-to-three-week-low-after-hollande-wins-french-election.html


European markets have not opened yet but you can tell this is not going to be good. 

Cochrane Spin Control

http://johnhcochrane.blogspot.com/2012/05/slow-recoveries-after-financial-crises.html

John Cochrane writes "On my reading list: In the meantime, Jim Stock and Mark Watson do very careful econometric analysis and conclude that this recession really didn't have much to do with the financial crisis: "no new “financial crisis” factor is needed.   They continue, More ominously,  we estimate that slightly less than half of the slow recovery in employment growth since 2009Q2, compared to pre-1984 recoveries, is attributable to cyclical factors (the shocks, or factors, during the recession), but that most of the slow recovery is attributable to a long-term slowdown in trend employment growth"

From these excerpts you would take away that Stock Watson's paper lend support to the Cochrane / Ohanian / Schlaes argument that the recession is not the result of the financial crisis but due to poor policy by the Obama administration.  You might think that if you had not read the paper and just took Cochrane's excerpts at face value...

What Stock and Watson actually say is "The main contributions to the decline in output and employment during the recession are estimated to come from financial and uncertainty shocks.  ....Taken at face value, this suggests an economy being hit in close succession by a sequence of unusually large shocks, all of which have been experienced before, but not in such magnitude or close succession: an initial oil shock, following by a financial crisis, financial market disruptions, and prolonged uncertainty due in part to policy uncertainty....given the value of the factors in 2009Q2, the DFM [Stock Watson's model] predicts nearly two years of sub-trend employment growth following the 2009Q2 trough.  In fact the DFM predicts a slower employment recovery from the 2009Q2 trough than actually occurred, that is, the current recovery in employment is actually faster than predicted; from the perspective of the DFM forecasts, the puzzle, if there is one, is why the recovery was a strong as it has been."

Their paper is more nuanced than the excerpts that I have pulled out here.  Here is the idea:  Stock and Watson look at a large number (198) of macroeconomic variables and posit that there are a small number of underlying factors which drive them all.  They first estimate how many underlying factors there are (six) and how much each of the six underlying factors contributes to explaining each of the 198 macroeconomic variables.  Some of the macroeconomic variables are predicted very well by the six driving factors and some less so. 

Next they ask if this recession is different from other recessions in terms of what underlying factors drove the recession.  They ask if there a seventh factor responsible for the most recent recession or do the same six factors which have been responsible for previous recessions do a good job of explaining the most recent recession as well.  They reject the existence of a seventh factor.  In other words this time is not different in terms of what the factors are that drove the recession - although the size of the shocks to those factors was unprecedented. 

Finally they try to distinguish what types of shocks actually drive their factors.  The six shocks they consider are: oil, monetary policy, productivity, uncertainty, liquidity / financial risk, and fiscal policy.  They find that the productivity, monetary, and fiscal shocks had small impact on the 2007-2009 recession.  Oil shocks - depending on how one defines them - may have contributed at the start of the slowdown.   The two shocks which seem to have most impact are liquidity / financial risk as represented by the TED spread and corporate bond spreads, and uncertainty as represented by the VIX and BBP economic policy uncertainty variable.  The TED spread represents the spread between bank borrowing rates and US Treasury.  During the 2007-2009 financial crisis the TED blew out as banks equity collapsed and fears of lending between banks took over.  That was the financial crisis.  Other recessions have seen a  widening of the TED spread, the corporate bond spread, and an increase in the VIX, but this most recent recession saw extreme moves in all three. 

Finally they note that part of the reason that the recovery has been so slow is that that trend component in labor force participation slowed greatly between 1965 and 2005.  The initial 2007-2009 decline was deeper then any previous downturn back to the Great Depression and given our slowed secular growth rate  in labor force participation it will take a while to get back to pre-recession levels.  That sounds about right to me.

Stock Watson conclude:  "Three main conclusions emerge from this work.  First the recession of 2007-2009 was the result of shocks that were larger versions of shocks previously experienced, to which the economy responded in a  historically predictable way.  Second, these shocks emanated primarily but not exclusively from financial shocks and heightened uncertainty.  Third while the slow nature of the subsequent recovery is partly due to the shocks of this recession most of the slow nature of the recovery in employment and nearly all of the the slow recovery in output is due to a secular slowdown in trend labor force growth.  This slowdown in labor force growth provides and simple explanation for the jobless recoveries of 2001 and 2007 recessions."

Saturday, October 23, 2010

What I am reading: Hicks Classic Paper

Mr. Keynes and the "Classics"; A Suggested Interpretation - J. R. Hicks (1937)

This is the paper that introduced the IS-LM apparatus as Hicks interpretation of Keynes General Theory.  Hicks is frequently criticized for abandoning Keynes focus on the financial market speculation as a driving force behind booms and busts but the revolutionary element of this paper is pretty apparent when you compare it to what else was going on at the time.  In this paper Hicks created the framework that macroeconomics would build around for the next 40 years.  He does this by constructing simple equilibrium models representing what the "Classicals" (read Pareto, Marshall, Pigou) had argued and what he interpreted Keynes to be saying (at least in part) in the General Theory.

Hicks assumes in both models an IS equation representing equilibrium in the market for loans i(r)=I = S(Y,r).  He then argues that the major difference between the Classicals and Keynes is in the specification of money demand.  The Classicals attribute money demand to a transactions motive as represented by the Cambridge equation M=k*Y while Keynes argues that money is held as an asset - in simplest form M=m(r).  Hicks extends this to the "General" theory M=m(r,Y) which is our modern LM equation.  Note that in the Classical model M -> Y without any involvement of r.  r and I are then determined by Y and the IS equilibrium.  In Keynes shocks to M are passed through to Y at least in part via M's impact on r.  Keynes simple case says M->r->Y and Keynes general case says M->(r,Y) two equations in two unknowns which must be solved simultaneously.

Finally Hicks asks how we are to reconcile this model with Keynes view that monetary policy was ineffective in escaping major downturns.  Hicks posits the liquidity trap - an L shaped LM curve with a horizontal portion on the left and a vertical portion on the right.  If the IS-LM equilibrium (r,Y) currently lies on the horizontal portion of the LM curve then manipulating the money supply shifts the LM right / left but leaves the (r,Y) equilibrium unchanged.  Fiscal policy however will shift the IS along the horizontal LM leading to a change in Y while leaving r unchanged.   If the current IS-LM equilibrium (r,Y) currently lies on the vertical portion of the LM curve then monetary policy will again be effective.

Next up Modigliani...

Sunday, October 10, 2010

I am reading: All About High-Frequency Trading

All About High-Frequency Trading - Michael  Durbin

If you want to know what high frequency trading is all about and what some of the issues are surrounding high frequency traders then this is a nice book.  If you want to set up your own high frequency trading firm this book is not going to get you too far - although perhaps that is too much to ask from any book.

One of the questions touched on this book is - are high frequency traders good or bad for the industry?  That is not a well framed question.  High frequency trader refers to a large class of  traders running many different strategies, and their good or badness is dependent on the particular strategy employed.   The book describes some of the strategies that high frequency traders may use.  Some of these strategies are versions of market making (clearly a good) while other strategies profit at the expense of customer orders (arguably a bad).  Some strategies are stabilizing while others can be destabilizing (read trend followers).

I work with a number of high frequency traders and in general I see them as a positive force for the industry as they provide liquidity into the markets and keep price relationships in line with fundamentals.  Large orders can then come into the market without causing significant price disturbance.  However there is always the fear of the single runaway black box or of black boxes getting stuck in a self reinforcing negative loop.  And the speed at which these negative effects could potentially come into play is concerning.  This is what the industry is still trying to get their arms around.

Saturday, September 18, 2010

I am reading: Would a stock market drop affect consumption?

Wealth and Consumption: Would a Stock Market Drop Really Cause a Recession - Stephen Cecchetti (2000)

A few facts 1990-2000
  • US household wealth doubled to $44 Trillion
  • the value of the stock market increased 300%
  • household consumption increased 60% to $6.2 Trillion
  • the ratio of savings to disposable income fell from 7.8% to 2.4%
Cecchetti notes that post 1995 the ratio of consumption to wealth dipped below the normal range of 17-21%. By 2000 from the perspective of a consumption to wealth ratio people were consuming as though the stock market were 25% lower that it actually was. This may have been due to a time lag to adjust consumption or uncertainty about the state of the stock market. He hypothesizes that a 25% drop in the stock market should have little impact on consumption - unless it generated a panic.

I am reading: Aggregate wealth and aggregate consumption

The Wealth Effect in Empirical Life-Cycle Aggregate Consumption Equations - Mehra (2001)

main results (approximately):
  • cointegration / error correction model.
  • in long run a $1 increase in annual disposable income -> $0.55 increase in annual consumption.
  • in long run a $1 increase in wealth -> $0.04 increase in annual consumption
These are not stunning revelations as they confirm previous results. However it is something to think about given the size of the swings in the stock and housing markets that we have experienced over the last decade.