Financial Time Series Characteristics: Crucial knowledge as always

Recently while studying for my Life Risk Management Exam coming fall I went off syllabus to studying market risks. I have always felt that financial models tend to have too many subtle assumptions that should always be borne in mind while working with them and the no-arbitrage principle tops that list.

The section on “Characteristics of financial time series” in the “Financial Enterprise Risk Management” Book (Chapter 14) had some interesting information that I felt would serve as rule of thumb in financial modeling. My regular perceptions on the subject did change dramatically.

Firstly;

“In spite of the assumptions in many models to the contrary, market returns are rarely independent and identically distributed.”

I have always felt the same as markets tend to be driven by common perceptions and copy cats a lot. Also there are many instances where markets go over kill with an idea and then subsequent corrections start to take place gradually. Also, mean reversion is always there very much observable. So does this mean models assuming a random walk process as in the Log-normal model is wrong?

Then;

“Whilst there is little obvious evidence of serial correlation between returns, there is some evidence that returns tend to follow trends over shorter periods and to correct for excessive optimism and pessimism over longer periods. However, the prospect of such serial correlation is enough to encourage trading to neutralise the possibility of arbitrage. In other words, serial correlation does not exist to the extent that it is possible to make money from it – ……..”

Ummm…. so does that mean the use of a random walk process is justified?

But then;

“Whilst there is no apparent serial correlation in a series of raw returns, there is strong serial correlation in a series of absolute or squared returns: groups of large or small returns in absolute terms tend to occur together. This implies volatility clustering. It is also clear that volatility does vary over time, hence the development of ARCH and GARCH models.”

From WIKI, Volatility Clustering infers that "large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes" (Mandelbrot, 1963). This I understand as it being very much obvious in periods of financial crisis and depressions; often high downturns are followed by strong uplifts. But to me this implies more of a systemic risk.

And then all of a sudden:

“The distribution of market returns also appears to be leptokurtic, with the degree of leptokurtosis increasing as the time frame over which returns are measured falls. This is linked to the observation that extreme values tend to occur close together. In other words, very bad (and very good) series of returns tend to follow each other. This effect is also more pronounced over short time horizons.”

This is where I felt I had actually learnt something. My pessimism with simple stock models that do not embed volatility clustering has been in infancy. There is no reason to call them incorrect I suppose. The Black Scholes assumption of risk neutrality and expected growth being equal to the risk free return makes sense now. The returns would very much linger around the risk free interest rate and would not deviate much further.

The return distribution (in normal circumstances) therefore is much narrower than I thought and so assuming extreme events to be outliers, simple models can provide a good fit. However, being risk professionals our interest lies in the tails which for a leptokurtic curve are longer.

So moving on;

“Correlations do exist between stocks, and also between asset classes and economic variables. However, these correlations are not stable. They are also not fully descriptive of the full range of interactions between the various elements. For example, whilst the correlation between two stocks might be relatively low when market movements are small, it might increase in volatile markets. This is in part a reflection of the fact that stock prices are driven by a number of factors. Some relate only to a particular firm, others to an industry, others still to an entire market. The different weights of these factors at any particular time will determine the extent to which two stocks move in the same way.”

This has me asking too many questions at the same time:

• Is it ok to model stock performances based on a recognized index?
• Should we be modeling each type of stock individually and is it practical / possible?
• Can systemic risk occurrences be built in a probability model or is scenario testing the only way?
• Are we wasting our time on Complex volatility clustering models? Would a random walk process suffice along with intuitively designed scenarios for changes in the business environment or systemic risk?
• Can economic scenario generators (ESG’s) embed that level of complexity to relating economic factors, business trends, commodity prices, etc for economic capital purposes?
• Should fund managers improvise for cutting edge performances with clever fund compositions or should they just match the market beta (market composition) and be happy with it (go with the flow and a track-able index)?

WHY DID I WASTE MY BREATH ON THIS:

Being a Valuation Actuary primarily I am obsessed with Gross Premium Valuation Models, i.e. models that make real time sense. However, the asset side has never quiet been addressed by us (or other non-finance actuaries). Also, working in a company running traditional insurance business that credits bonuses based on the complete asset portfolio returns make life a great deal harder. It is imperative that a consistent approach to modeling portfolio performance (consisting of long term debt instruments, stocks, money market instruments, etc) is adopted, specifically for Economic Capital purposes.

This has also led me to understand that I should not have been fooling around in Economics, if scenario designing is the way to go I should have my facts straight. Also I shall be tinkering with ARCH and GARCH soon.