The CDS valuation models and the Crisis - some specifics

I was going through this semi-mathematical paper by semi-academicians on valuation of Credit Default Swaps. The paper was published by, none other than, Lehman Brothers. With the benefit of hindsight it was even more interesting how these guys valued this instrument in 2003-2004 when it was just starting its meteoric rise in the financial markets. The CDS markets (total notional - I'll touch upon that in this post) increased from ~2 Trillion US $ to about 45 Trillion US $ in the early part of 2008). Consider the fact that this is about three times the size of the US GDP and you get an idea of how huge the market was. So why was everyone running after this?

What is a CDS? 

There are plenty of resources that would explain in much detail what a CDS is. However, I'll touch upon it keeping in mind the valuation aspect - which will form the meaty part of this post. 

So assume that you are a small bank who lends out mortgage to some guy. However you are not really sure about the creditworthiness and think that he might not honor the payments in the future. So you go to a say AIG. The conversation goes something like this -

You - Hey! I am not really sure if the guy will pay up. Can you help?
AIG - Sure we can! If you pay us a small premium (usually called a CDS spread in finance parlance) we will make sure that you get your loan amount back.
You - Great! But don't you think it is risky for you too. Why do you want to do this?
AIG - Oh we think that the house prices are going to go up. In case of a credit event (this is the term used to denote say a default or bankruptcy of the home owner) we can always sell off the houses quickly and recover the money.

Now let us look at how this affects You. The protection buyer.

1. The first impact is that it tells you that you don't really need to worry about the credit-worthiness of the home owner. In case of a default you are going to receive the money anyway. You are willing to pay a small premium to AIG for this because it is more than off-set by the commissions and the interest that you will receive - how?

The interest charged on homes is typically 4-5% higher compared to the premium you pay to AIG. Even if you receive interest payments for half the maturity of the loan - you are good to go.

2. The thought that house prices will go up in future means that you are willing to make loans that are under-collateralized. The bank usually demands a collateral of say 120k for a loan of 100k. However, since the house itself is the collateral and you think that its prices will shoot up in future you are willing to lend much more - based on the wrong assumption that the increased house price will cover the loan amount fully. The number of sub-prime loans increase!

The way it affects AIG - specifically its incentive structure is as follows.

1. It thinks that housing prices will continue to go up.  This simply means that the chances of defaults - or the probability of credit event is extremely low. It then makes perfect sense for them to write as many CDS as possible. The funny thing about CDS is that anyone can buy it for any underlying asset. This would mean that people who think that housing prices will tumble (and there would be multiple credit event) can go and buy these CDS from AIG. These are not protection buyers but speculators or as they were called euphemistically - Investors.

2. It assumes that the houses can be sold immediately. If this were the case the losses should be reduced since the recovery rate (the % of asset vale recovered on sale - the asset value is the notional amount - the amount insured for) would be higher. However, this was again proven wrong as a contagion suddenly clogged the housing market and the asset recovery took more than an year!

The valuation model 

The model given by the two guys at Lehman Brothers is quite mathematical in nature. However, I will try to capture the essence of the model and focus more on the assumptions - that I think were severely misplaced. 

The model has two parts - 

1. The valuation is done from the point of view of the protection buyer.

The protection buyer pays a premium and receives a big payoff in case of a default or a credit event. Now the idea is that a net payment of 100 - Recovery rate is made to the protection buyer. This can happen anytime during the life of the CDS. So the key is to estimate when will the default occur. 

The basic idea is to assume a continuous time period in which the probability of default is given by some function of the hazard rate. This is defined as follows - 

The probability of the credit event (say the party defaults) in a given small time period dt is given by k(t)dt - where k is the hazard rate. How is the hazard rate calculated? 

The amount of premium that the CDS buyer pays is indicative of the likelihood of default. A high premium simply means that the seller of the protection thinks that the mortgage buyer has a high probability of default. In a liquid market these spreads are quoted for different maturities and this can be used to get the value of k. For the purpose of this post we assume it as give. However, the exact computation can be seen here. This can be now used to calculate the probability of default for any time period - say in the next 1 year. Let us call it Q. 

The overall value of the swap - in terms of the likelihood of default then becomes - 

Integrate [(1-R) * Q * Discount factor *(1-k)ds] over the maturity of the CDS

The protection seller pays a net amount of (1-R) in case of a default. The entity has survived till a given time (Q) and could default in the next small time period (1-k). Integrating this over the maturity period gives the expected cash outflow. 

2. From the point of view of the protection seller - the cash inflow is the premium that he receives over the life of the CDS -until there is a default. 

The value is simply - Spread (in bp) * Total number of payments* Probability of survival in the time period

Equating the above two equations will give us the unknown - Spread (in bp) that would be charged by AIG. To put things in perspective - 

1. The spread will decrease as Recovery rate increases. The more amount of money AIG thinks it will be able to recover - the less it would charge to its clients. 

2. The spread will decrease as the survival probability increases. This also makes sense. The propensity to charge increases as the underlying becomes more risky. To put some numbers to it - The spread on CDS sold on Spanish debt as the underlying was around 2000 basis points (a very high value compared to the usual values of 100-150 bp). It then becomes a gamble not whether the country would default but on how soon it would default. 

Now on to the assumptions.

1. The recovery time - The time it takes for the asset to be recovered is assumed to be at a maximum of 72 days. The model itself was built on the assumption that this could happen in no time. The assumption leads to a severe underestimation of the CDS spread. In 2008 as the systemic risk skyrocketed the whole housing market suddenly dried up. Asset recovery became extremely time consuming ( about an year). Worse still - this was happening when house prices were depreciating rapidly.

2. The asset value - The authors have done some simulations in which the recovery amount is estimated to be about 70 - 80 %. When Rob Shiller talked about irrational exuberance - he talked about the biases that we have developed about stock prices always moving upward. Housing was thought to be a killer investment and again these recovery rates were affected by the enormous expenses that the banks faced in liquidating the houses.

3. Speculation - The model has been built primarily considering two counter-parties. But in 2008 these CDS were sold to investors far far away in different countries. These investors (buyers of CDS) included Hedge Funds who merely would have got huge pay-offs if the housing market crashed. Imagine the enormous amount of pressure it puts on the house prices. A decline in the house prices would create immense benefits to these investor by triggering a credit event. This is something that has been completely ignored.

4. The hazard rate - The hazard rates have been calculated based on CDS spreads quoted for varying maturities. But in an environment where the whole CDS market is in a disarray and the quotes beyond an year are not even available in the market how does one value these instruments?

The 4 points that were made bring out one important thing. CDS as an instrument is like a market clearing tool. By transferring risk from people who don't need it to people who can afford it - it brings some order in the financial markets. The problems come when these risk intermediaries become greedy. Imagine if your salary was based on the number of CDS you could sell to investors. Would you really care to evaluate the likelihood of defaults or would your focus be just on volumes. The distorted incentive structures are the key issues.

Derivatives are not weapons of mass destruction in themselves. They become dangerous when they are in the hands of wrong people. 

The new world order - Will it succeed?

The IMF and the World Bank are what we think of when we think about countries needing money to bridge their deficits or when they are in need of covering their balance of payments gaps. However that is all set to change very soon. In fact, it has already begun.

BRICS - The top 5 emerging economies of the world recently collaborated and created a 100 billion $ fund that would primarily serve two purposes -

1. Be a source of funding for infrastructure and other large scale projects in the developing economies.
2. Be a source of bailout for the economies when they face a balance of payment crisis.

Well, it also has a third - subtle but more important reason - Driven mainly by China and Russia (due to the Kiev issues probably?) this might be the beginning of a new world order - wherein the emerging economies, which make up for a little over half of the global output move away from the US dominated financial system.

Whether this will be successful or not - Only time will tell. But we can always have our opinions (or biases).

It is unclear how this will be better for the 5 nations compared to world bank and IMF as being their primary lenders in the past. Their funding has required stricter and stricter norms to be followed by borrowing nations. The amount of money that the nations borrow from these facilities depends on the severity of crisis, the credibility of the borrower and whether or not the borrower is likely to honor the rules laid down by the lender. This is also one of the primary reason for the BRICS making such a move. Should we call this more of a political move rather than a step towards fiscal freedom?

CHINA Problem - Inequality

Clearly, China has exerted a strong influence in the formulation of the BRICS development bank. The country will be the largest contributor to the bank - almost twice as much as all the others. The sheer size of their economy and their continued rivalry with US might mean that it could have a vested interest in being the harbinger of more problems of US - Not fighting the so called financial dominance of the West but to be a launchpad for its own dominance in the world economy.

These are also some of the issues that led to such a long delay in the formulation of this facility. India has done well in showing some resistance to such moves by China.

All in all, it is a good move by the 5 emerging economies. The reduced funding from Fed will also be hedged by these nations with this move. However, the imbalance due to differing contributions and variations in sizes of the economy will be a key issue. Moreover, more consolidation on the policy front will be needed in future!

The stock market - Budget '14 anamoly

So it was kind of weird that other day when the budget came out. It was better than the last one where subsidies had really strained the fiscal deficit and added to that, no clear strategy of reviving growth made things bleak for the economy. The market reacted accordingly. They declined the day the budget was out. More precisely, they were unhappy that -

1. Govt. had no plans of reviving growth. The manufacturing and Industrial production was low. The sectors were not given investment opportunities through FDI.
2. Increased non-plan expenditure would lead to widening the deficit - which the center by the way promised to bring down to 4.8% of the GDP.
3. Increased non-plan expenditure would cause inflation. This would be both demand pull and supply push.
4. To bridge the fiscal gap the government would increase taxes. Bad news for businesses.

The 2014 budget was much better. Focused and it had some bitter stuff in it. The FM promised to bring down the deficit to 4.1%, implement GST, control inflation through fiscal policy (good news for businesses like RE where the interest rate exposure is high). The stock market still fell! Why?

Being ambitious is Ok. But being over-ambitious is not.

The first thought that comes to our mind is that perhaps the markets were over-expecting from the budget and things somehow fell short. This would be reasonable considering the hype that Modi got with him. However this is not the case. It is completely the opposite of that.

The market thinks that the budget is over-ambitious and based on unreasonable assumptions. Of particular importance are -

1. The tax revenues that the govt. forecasts are higher. The current tax revenues of the govt. are not good. And to be able to get the Fiscal Defficit down to 4.1% will be a challenge. This divergence of views when it comes to fiscal deficit is the major cause of the fall.
2. The markets were positive about the govt. having a clear long term view on reducing subsidy bills.
3. The markets also think that the implementation of GST will take longer then expected. The FM hopes to implement it in the next 8 months. The market thinks it'll take 2-3 years.

Besides this, the fiscal deficit number itself looks audacious. In the coming days as the govt. takes measures to show it's commitment, the market should react positively.

MACD - One of the best indicators - but not used?

The debate between whether one should use technical indicators or resort to fundamental analysis of the company in arriving at the decision of investing or not investing has a long history. However, sometimes these indicators can work very well - IF USED INTELLIGENTLY.

One of the good indicators that I have come across is the MACD - Or the moving average convergence-Divergence. I don't say that it is the go-to indicator for making your decisions - but what I like about it is -

1. The signals it gives are more reliable then others.
2. The signals - beyond the crossovers - are often leading indicators and can enable you to buy the security/sell it at its lowest/highest.

Let us take an example to make my point clear. I am not trying to focus too much opn how the indicator is calculated - rather on what it says and how should one interpret it.

I'll take the example of Suzlon - A stock that has rallied tremendously in the past 1 year, Reaching an all time high of Rs. 35 before starting its descent. The question we need to answer is - for someone who bought the stock at, say 25 bucks, could have predict the down-turn at 35 and sold at that point.

The price history of the stock is shown below -

We can clearly see the surge in prices in a matter of a few months. An investor, looking at the stock in Jan-Feb would have been able to buy the stock at Rs. 10. Now let us look at the MACD overlayed on this. 

What is a cross-over - 

The MACD is a simple difference of a 12 day and 26 day Moving average. A negative value (below the neutral line) means that the selling activity is present and the prices are going down at a faster rate. A sell signal. However, if you were to rely on this, you would have sold the stock at 24.5 Rs. -Almost 10 busks below its peak. Not so good then. 

The signal line cross over does a much better job as it measures the MACD relative to its own 9 day Moving average. MACD line below the 9 day EMA (White line in the graph) is again a sell signal. However, based on that signal, the value would still have been about 5.5 Rs below the peak. Can we do better?

Let us now also consider the histogram. What it tells us is simply the gap between the MACD and its 9 day moving average. What does that signify? Rising bars in the histogram means that the MACD is moving faster than its average (upwards) and is a strong buy signal. 

Once you see a rising MACD and a falling histogram - it means that the 9 Day EMA is catching up and sooner or later there will be a reversal. I have highlighted the this in the next diagram. 

This time if your are vigilant, you could have sold it for around 32-33 Rs. An improvement of almost 3 Rs./Share. Of course one could combine this with another great indicator like RSI. The overheating is clearly seen before it reaches its peak telling us that it is over-brought. It is actually hard to miss this one! Most of the guys would hve realized this down-trend by the time it touched 32-33. But that is not the case! 

The trading volume actually did not pick up until the value fell to Rs. 30. People were waiting with baited breathe - seen in the abysmally low volumes near the peak - meaning that they would have been continuously monitoring the stock. Had they used MACD - They would have done better! :)

Kidding aside - Some people have this notion that technical indicators are never reliable. However, if you base stuff on solid math they can assist you if not govern your decision making. 

Cheers

Oh Jesus! to Ohh! Jesus?

It's been a while since I wrote something here. What have I been upto? Basically some books, some gaming and some "consulting-investing" in the stock market besides the "Internship".

The internship was not much and I would rather not talk about it. I would rather talk about a recent book I read.

The Book - 

I usually choose the books I read carefully. Management education significantly increases your opportunity costs of spending time in not preparing PPT's but reading books. This time though - I decided to take a leap of faith and decided to judge a book by its cover. The book was - The Last Templar by Raymond Khoury.

Warning - Spoilers ahead.

For those who have not heard the term "Templars" , let me elaborate. If you know about them and would like to know about the book experience, you can skip the next  paragraph.

When I thought of Templars I imagined assassins who were hired by the holy church to protect them and their secrets. But this was partly true. They were trained fighters who were supposed to protect the people who travelled to Jerusalem for pilgrimage. The more interesting thing about them is how they were wiped out after they grew extremely wealthy and powerful - partly because they become too rich and powerful and more interestingly because they knew some big secret about the church - something that could change the way people looked at Christainity, the Church and even Jesus.

Christainity has had a bloody and mixed past. Spreading your relegion and letting people decide whether or not they should embrace it is one thing. The church took it to an extreme - any person who either refused to follow them or did something that was unrelegious was punished severely. Punished how? Well no points for guessing - Crucified. Sometimes upside down. Ouch!

So what would happen if somehow, one day, Jesus himself came down and said -

"Chaps! Whatever has been written in the Bible - you guys are taking it too seriously. I was a simple guy, a carpenter. I am no Son of God and neither did I come back from the dead. Like all men, I too liked a Lady and one day got her pregnant. The Pope is no holier than you guys and this whole christainity is too hyped. I never intended it to end up this way!"

An FBI agent and a beautiful (like they always are) archeaologist hunt for that ultimate truth that could change the world and shatter the way we look are relegion. So far so good!

What I liked & disliked about the book - 

1. Practical - Even though the author is dealing with something that is thousands of year old, he has done a great job at putting things in the current context. Mass killings, Discrediting Science and forcing people into accepting a faith is something that has always been associated with relegion. Even today, we see people who just do not want the world to advance because it is somehow unholy. I mean, who would have thought that Jesus would have issues with Test Tube Babies. He would have a much bigger issue with countries killing in the name of relegion and people attacking each other because they have different beleifs. 

2. Critical - The author has used the storyline, although weak, to really analyze the things that are wrong with the world today. How we know so less about what we believe in. He has made logical arguments, coupled them with verifiable facts to make you think about whether what you believe in is really the truth or merely a (mis)interpretation of some mortal. Now, that would really piss off many!

The book has a weak story line. Basically, the author tried to do a backward induction. He knew the end - an awesome end I must say - and then worked backwards. This meant, a story with a lot of twists and turns - a bit too much to digest at times. The result - A bollywoond story with "firnag characters" who travel around the world in search of the truth - while a love story runs parallely. A story with too many coincidences loses its charm after a point. This book suffers from that. 

Ultimate verdict. If you are super-free and really interested in knowing about relegion - do go ahead and read the book. Some parts are good where an over-informed crazy history professor reveals some unsettling truths.