Indy Telecom & Industrial Media

…EVER!

While normal distributions are nice and wonderful, they aren’t really feasible in the world of finance. This is because the market can be so volatile and fickle that variances become meaningless.

So, enter fat-tailed distributions. These are distributions where events deviate significantly from the mean in comparison to normal distributions. What this means in terms of the stock market is that assets and investments are prone to jumps (in either directions).

On this topic, Paul Kedrosky links to an interesting presentation on Fat Tailed distributions by Northfield, the guys that make analytical and investment software.

It’s quite interesting and talks about some work that’s being done in this area.

On a related note, another area of application for Fat tailed distributions is the CRM arena. Contact-centers and self-service applications (i.e. IVRs) receive millions of calls a day, and there is just as much variation in C-sats, agent performance, AHT and so on.

It would be interesting to apply some of these tools and techniques to call-center analytics and see how well those work.

Sometimes, I just amaze myself — as a follow up to my previous blog post, my Dad just sent me this article that talks about how the RBI has eased the currency outflow norms to contain the rise of the Rupee against the US Dollar.

From the article –

In a bid to neutralise the impact of huge capital inflows and check the sustained rise in the rupee’s value against the dollar, the Reserve Bank of India (RBI) has further liberalised the foreign exchange norms to boost the outflow of funds from India. The RBI has now allowed resident Indians to transfer up to $2 lakh (around Rs 80 lakh) a year abroad without its approval under the Liberalised Remittance Scheme (LRS). The earlier limit was $1 lakh (Rs 40 lakh) a year. Now Indians can transfer $2 lakh to acquire and hold immovable property, make investments in financial instruments or purchase any other asset abroad without any prior approval.

Worried muchly about what FIIs might do, me hearties? And of course, there are those exporters who will be taking a hard hit otherwise, too.

I found this interesting article that talks about how hedge funds in India part-take in currency arbitrage. From the article –

Hedge funds - known for their high-risk, high-return short-term investment plays - are taking bets on the upward and downward movement of the rupee against the dollar under the pretext of investing in equities.

As one of my friends recently commented, this is probably a good time to invest in the USD, since it seems to be at an all-time low. While there are speculations that it may go still lower, you can always rely on the various national reserve banks to peg the dollar before it goes down too low.

Last June and early July, most analysts said the rupee could not continue appreciating and the RBI would intervene to ensure that the rupee corrects a bit. This view was shared by many foreign brokerage houses as well.

The RBI did intervene, but only to stop the rupee from appreciating further. The hedge funds also believed that the rupee would fall against the US dollar.

Of course it did. You know, it just might make everyone’s life easier if RBI allowed free dollar convertibility within India. When will these people learn?

No, really. The former chairman of the federal reserve meets our very own tongue-in-cheek comedian. Greenspan makes a rather a interesting comment:

“What a sound money system does is to stabilize all the elements in it and reduces the uncertainty that people confront.”

I really think he should meet this guy.

(Thanks to PD for the link.)

PD recently recommended two excellent books by Nassim Nicholas Taleb (homepage), the mathematician turned philosopher turned epistemologist. I am half way done with one of them, Fooled by Randomness and I have a brand new copy of The Black Swan sitting right here on my desk.

While I was reading the books, one thing that stuck me was this — within a given system, how many such quant funds (such as Taleb’s old firm, Empirica Capital LLC) does it take for Taleb’s risk-based hedge funds to succeed? Or inversely, how many is too many that would cause the system to fall down upon itself?

To find a way to answer these questions, I am interested in starting with finding out the possible success rates for these firms.

Let me explain myself. Let us assume that there are 100 quant firms that invest the way Taleb’s old firm did. This would mean that you have a hundred firms slowly bleeding to death, waiting for that one Black Swan, when things work out for them.

Now, for the sake of argument, let us assume that only half of these firms are going to succeed to some extent while the other half are going to fail.

The probability of all fifty of these firms having the exact same degree of success is quite low. In fact, it is more likely that within their given domain, these fifty firms have some sort of distribution of success-rates.

Let’s assume that two kinds of distributions are possible here — the first, obviously, is a Bell-curve, assuming a normal distribution. Going this route, we could try and apply the 68-95-99.7 rule and get the following distribution (courtesy Wikipedia):

So, let us assume that 68.2% of the quant firms are good enough for us to work with. This would leave us with:

This leaves us with about 34 firms which may perform well enough. Of course, the other interesting thing would be to see how much longer they can bleed themselves (assuming a decaying function) and seeing what percentage of these 34 companies actually “decay” themselves out. But that’s for later.

Now going back to our problem, the second distribution is more interesting. What if we had a log-normal distribution? Or better yet, let us assume a Log Levy distribution, which is more indicative of financial models (and of the stock market). This would be one where they have sharp peaks (for success) and long-tails (for the long periods of failure).

Since the stocks themselves are likely to show a Levy distribution, it would not be wrong to assume that our quants mirror this pattern.
If that is the case, our graph for a stable Levy distribution would look something like this (courtesy Wikipedia):

Now, we have a few cases to consider. If we consider then it becomes a normal distribution, which we just talked about. On the other hand, for all other values of , we could have heavy-tailed distributions.

So, here are my questions –

• What would be a logical assumption among the various values of alpha for our Levy distributions?
• What does this entail for our “functioning quant firm” numbers, i.e. where does that leave ?
• Assuming a standard decay rate for both normal and Levy distributions, which would be more effective (i.e., a better density function)?

Quite obviously, I am trying to back-track from a series of assumptions to evaluate the feasibility of having more than an optimal number of quant-based hedge funds. And I am also interested in evaluating the success and failure thresholds for such numbers.

Finally, I am looking for the Black Swan that will throw these numbers into quant hell.

(Yes, I am quite well aware that this post has a lot of inconsistencies and assumptions, and that I have completely ignored the injection of new blood into the system — quite obviously, this is an exercise in theory, so forgive me while I meander.)