Good news for managers - not so useless after-all !

I came across an interview that McKinsey did with the Noble prize winning economist - Robert Solow.

Background and some initial thoughts - 

Economics - before Solow - essentially said that the output depends on two factors - Capital and Labor. These so called factors of production mean different things for different industries. For an auto industry Capital would mean the production facilities, the warehouses etc. whereas labour would encompass man and machine.

Solow said that apart from these what matters is the technological progress. Putting it in slightly mathematical terms would make more sense. Suppose that the output is governed by the following equation -

                                          O = f (t, C, L) 

Apart from the capital and labour, an important factor to consider would be the technological part. Why are some countries with limited access to capital and labour some of the biggest producers of some products? How can China possibly hope to grow at above 7% in the long term? Would it be possible by just deploying more people on the job and/or more capital investments? The answer is no. Even without looking into it too much two reasons justify this answer -

1. Diminishing returns - Putting in more people in the same factory would start leading to overcrowding and ultimately lead to a productivity decline.

2. Deploying more capital and increasing the fixed cost without a proportionate increase in the demand would ultimately lead to lower contribution margins.

So to increase productivity one needs to focus on the technology aspect. Squeezing more out of your capital and labour is the key. In the current state, talking about man-machine coordination exemplifies this line of thought.

Ok.. what about the managers?

The report shows that the in many industries with similar levels of capital, labour and technology - productive efficiencies differ. What could be the possible reasons for this? 

It was seen that resource allocation, better managerial decisions and organizational structures were able to explain these differences. As the countries and various sectors become exposed to competition with increasing globalization, the managers need to push themselves harder to sustain that level of growth in-spite of advances in technologies. 

Moreover, exposing these industries to global best practices is important as that would ultimately drive them to achieve growth by focusing on these marginal gains and improvement in efficiencies. 

I am often bewildered about how growth works. In the present state it feels as if growth and innovation is incremental. 20 years ago, it worked in leaps and bounds - uneven and unpredictable. This makes the case of micro-level management even more important. 

Although the leaps and bounds growth concept is not completely out of the picture. The next technological leap would likely occur when human and machine interaction becomes more seamless... the point where man and machine start working together in a truly integrated manner. However, organizations cannot just wait for this to happen only to be thrown out of the business. Marginal gains would govern profits for them in short to medium durations. 

On the business model front, managers would need to me more pro-active. We have seen entire models being wiped out in a relatively short time period (e-retail replacing the brick and mortar is one prime example). 

The point that managers would need to keep in mind is that technological advances occurring in unrelated areas will affect them - affect them in a big big way! Pro-activeness and not just cognizance is extremely important!

Update - Should Mr. Rajan...

Small update..

Incidentally, I came across this..

http://www.livemint.com/Politics/5ZPiITYBkffR0FwkjTUxDL/Retail-inflation-cools-further-to-552-in-October.html

Interesting..

So it would be interesting to see how the things pan out in the coming months. But hope that it does not pan out like Subbarao-Chidambaram debate..

Is Mr. Rajan justified in not cutting the rates?

The voice, or may I say cacophony, in the business AND political circles is growing with respect to shifting the focus from the inflation-hawk stance to the forward and growth looking stance. The key argument is that we are well on our way to lower inflation where-as the growth has still not picked up.

The financial minister has also argued for a rate cut to fuel growth but the governor has held his ground firm and the rate cut does not look in sight.

Now being neutral is no fun. My stance/opinion is that it is too early. I am with what the governor thinks on this. Why?

Human factors -

1. The 2 gifts that UPA gave us were - stagflation and a weak rupee. Enter Mr. Rajan - we have seen a steadily declining inflation. However, when we look at the global picture - EU, Japan and to some extent US are struggling with lower inflation - or worse deflation. So India seems out of place in this context. More importantly, having a well respected economist who has been the EA to the PM and carries a global outlook should give him enough credibility when it comes to steering us out of this mess.

2. Might I say that the centre does has some vested interests - albiet not so evil. They would much more like to show a higher growth (which would come with rate cuts and more credit supply) rather than just a lower inflation (Something for which they might not get the credit for at all - I would much rather credit Rajan for that). No doubt, My. Jaitley is pushing for a rate cut.

Practical matters -

1. As pointed out earlier - similar economies are struggling with deflationary pressures. Celebrating a lowering inflation may thus be premature for us.

Source: RBI website.

The inflation has definitely eased. However, the inflation has dipped severely mainly because of a sharp fall in oil prices (yellow line). This is something that is not internal to India. The manufacturing inflation is still above 3% - signalling a shortfall in output. We need to be more sure that the economy has come out of these internal and structural problems before initiating a rate cut.

2. I recently read an article in Mint - The cautious central banker. This argues for a conservative central banker when the government does not have a lot of credibility with regards to tackling inflation. The argument goes as follows -

Nominal wages are sticky since it would be difficult for the companies to revies wages every month. However, a government that is looking for growth would be tempted to reduce wages and increase employment and output through an inflation surprise. Now the problem is that consumers will ultimately see a reduction in real wages, especially in a country where the credibility of the government with respect to tackling inflation is low (consider the populist policies of UPA - fuel and food subsidies that strained the budget deficit). This could later lead to an inflation spiral.

The solution is - as suggested by Rogoff - place a cautious and credible central banker. India has that!

Rajan has consistently argued that the so called inflation-growth trade-off is illusionary. Unless we bring down the inflation, growth seems unfathomable. Inflation is hurting rather than limiting growth! So cutting the rates early and risking an above 7% inflation is too risky!

Something funny about delta!

I'll keep this post short and sweet. 

I was plotting some graphs that showed how an option delta behaves with time to maturity and its half brother - volatility when I noticed something funny.

Some basics:

The best way to think about delta is probability of the option expiring in the money.For an option trader it would be the amount he is likely to gain or loose with changes in the value of the underlying. 

So for starters - how does it vary with the amount of time remaining for expiry. Intuitively the more time you have on your hands the more the chances that it would exceed the strike. However, it will depend on whether the option is in-the-money or out-of-the money. So if it has already exceeded the underlying, the probability is much more like 1. I have captured this in the graph below. 

So far so good.

Now let's bring in volatility. I choose vols varying from 10% to 100% and used the same range of time to expiration. The graph looked like this,

Two things are simple to see.

1. For a given maturity delta reduces as vol increases.. however this will depend on whther the option is in or out or at the money.

2. With a lower volatility it takes less time to maturity for the probability of option expiring in the money to approach 1. 

But there's more...

Volatility somehow starts overpowering the time to expiration when we look at very high vols. Contrary to what we might think, delta does not strictly decrease for an increasing volatility. The 100% vol curve lies above the 70% vol curve for T beyond 6 months. 

Possible reason.. implications?

I guess it has something to do with t being in the square-roots. But I am not sure about it.. 

However, for relatively long dated (4-6 months) options a higher vol could be much worse or better for a trader then he might think. Over long terms it makes things much much more volatile. This might push up the hedging requirements in turn.

I should get back to the book now. Too much digression can be bad for health! :) 

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.