Let us start analyzing the delicate problem of correlations used by financial markets by introducing what a correlation is all about through the example below (framed).

**Distinct and separate observations on Pierre**

- The probability of his parents divorcing during the year is around 5%

- The risk of him getting head lice is around 5%

- The “chance” of seeing of teacher slip on a banana peel is 5%

- The probability of winning the spelling contest of his class is 5%

**Simultaneous observations of the two children**

- If the parents of Jacques divorce, what is the probability of that the parents of Pierre do likewise? Still 5%? (We’ll let you take a look around you in order to answer).

- If Jacques has head lice, the risk that Pierre, seated next to him, gets them as well is about 50% which means that the correlation would be around 0,5.

- If Jacques sees a teacher slip on a banana peel, what is the probability that Pierre will see it as well? It will indeed be very high since they are seated next to one another. The probability could be something like 95% which leads to a correlation close to 1.

- Likewise, if Jacques wins the spelling contest of his class, Pierre has zero chance of winning which means that the correlation is negative (-1).

If stock trading was based on the probabilities that are only distinctly applicable to Pierre (see illustration) then all the transactions would be traded at the same price. How would the investors then do to evaluate share prices by taking into consideration several parameters (Pierre and Jacques) that display correlations that are similar to those of our example? In fact, some calamities do not always happen on an individual basis. Take the case for example of a drop in the price of the houses in your area. This will also impact your neighbor and will impact you one day or another.

Now, carry out the demonstration for states (European countries for example) and don’t forget to consult historical data for correlation calculation!

And so, isn’t correlation in finance charlatanry? We can indeed answer positively through four situations that have been observed on financial markets with final investors as well as with asset managers and proprietary traders. The observations deal with asset management, the relation among assets, investment and trading strategies and the complexity of a financial engineering.

### 1. Correlation and Asset Management

Every investor learns that the alpha and the omega of asset management are based on a set of rules. For example, sufficient diversification, being selective in the choice of shares, being regularly defensive by identifying some true safe havens that are underpriced and above all to be decorrelated as much as possible. As far as rules and basic principles are concerned, everything is always simple.

It is needless to build a diversified asset portfolio. It is better to favor assets that are the most liquid, simple and transparentMory Doré and Patrick Jaulent

Anticipating the valuation of some assets (Are they over or underpriced?) supposes that correlations among assets are stable over time. (This is never the case as demonstrated by the situations of Pierre and Jacques). Consequently, the relationship between two assets can never be captured by a unique scalar quantity. The history of the financial markets shows that assets that are apparently decorrelated in stable market conditions are no longer so during crisis situations (Assets that are historically decorrelated become coincidentally brutally recorrelated during periods of stress). This contradicts much of “modern” portfolio asset management as well as the works of Markowitz and Sharpe regarding the normal return/risk distribution with the eternal aim of the efficient frontier (This apparently magical place where risk and return are seemingly optimized and where all asset allocations are considered as optimal).

According to us, it is therefore useless (usually) to build a diversified portfolio (which is consequently statistically decorrelated) since it does not protect against market irrationality, the consequences of forced asset selling on the value of some assets and herd behavior. All those who had to manage supposedly diversified portfolios know what we are talking about. It is consequently better to privilege the most liquid investments (regardless of the anticipations and asset class being considered).It is also necessary to search for simplicity and transparency when choosing an investment.

### 2. Correlations and relations among assets

When one trades, one searches for the right correlations among assets and reference is made towards several approaches that can coexist:

- Market psychology estimation and the proper comprehension of risk aversion among market participants.
- Fundamental analysis through the publication of macroeconomic indicators and the anticipation central bank monetary decisions.
- The analysis of trade flow anticipations and the structure of stock positions for major actors such as central banks, large institutional investors and global macro hedge funds…
- Useful technical analysis when the first three approaches do not allow detecting relevant market movers.

The whole difficulty is about knowing which approach must be overweighted and more importantly how to overweight them?

When trading, the search is for the right correlations among assets. This can often lead to small coincidental wins but also large coincidental lossesMory Doré and Patrick Jaulent

Let us imagine that the market mover on financial markets is the first approach described above (risk aversion) considering the fact that negative US macroeconomic indicators (Increase in unemployment, drop in consumer consumption) will paradoxically strengthen the dollar (the currency which benefits – rightly or otherwise- from an aversion to assets regarded as “risky”) and will consequently lead to a drop in the EUR / USD parity as well as a drop in stock market indices.

However, if the market mover is rather based on fundamental analysis as in approach 2 above, the conclusions will be different. Indeed, the same negative economic indicators will this time lead to an increase in the EUR / USD parity since the perceived economic deterioration will reinforce anticipations of new monetary stimulus (the famous quantitative easing (QE) or money printing of the US central bank). This will most probably cause the value of the dollar to drop. Similar reasoning could be held in the presence of positive US macroeconomic indicators.

We see how complex it can be to take bets on the EUR / USD parity through correlations of the latter with economic fundamentals. This can often lead to small coincidental wins but also large coincidental losses.

*So according to you, does conditioning trading to strong hypotheses on correlation levels among assets liken it to charlatanry? *

### 3. Correlation and investment or trading strategies

Beyond overweighting this or that market mover (Approach 2), it is useless to invest or trade through correlations alone if we are facing situations where the markets are being “manipulated” or in any case are momentarily under the influence of significant actors that have large stock positions and have a P&L (Profit & Loss) that they wise to preserve or boost.

Let us take once again the example of the EUR/USD parity (even if we know that the currency market is the one that can be least manipulated). If a major participant only sees a short term exit through a fall of the dollar, he will spread the market propaganda that goes along with it in the simplest and most efficient manner.

- Bad economic figures resulting from the US economic condition will require an accommodating monetary policy from the FED. This will cause anticipations of new QE and will auto justify the desired fall of the dollar. The most respected analysts will spread this message.
- On the contrary if the US figures are positive, this would mean that American economic recovery is taking shape and this will allow for the anticipation of an increase in risk appetite. The dollar will then lose its allure as a safe haven leading to an expected drop in its value.

It is useless to invest or trade through correlations alone if we are facing situations where the markets are being “manipulated” or in any case are momentarily under the influence of significant actors.Mory Doré and Patrick Jaulent

All this will not prevent the same significant participant or another one to spread the opposing propaganda if necessary some trading sessions later. This time will be about justifying the rise of the dollar against all odds. We will once again be able to count on the most respected and seasoned analysts who will explain the opposite of what they were “selling” some days before (you were talking about a financial crisis: let’s rather talk about a crisis in finance which is nonetheless not our enemy).

- The bad US economic indicators will imply an increase in risk appetite and consequently an increase in demand for the dollar. We will this time avoid putting forward QE risks for the greenback
- The bad US economic indicators will imply an increase in risk appetite and consequently an increase in demand for the dollar. We will this time avoid putting forward QE risks for the greenback

*So according to you, does the observation of some correlations to provide credibility to some investment or trading strategies account to charlatanry? *

### 4. Correlation and financial engineering complexity

Between 2004 and 2007, traditional investment vehicles which are OECD state loans and corporate and corporate and banking bonds with small risk premiums no longer meet return expectations of investors. Investment banks will use this context as an argument to “build” structured credit products that provide higher returns than traditional investment vehicles (thanks to or because of the leverage). Among these structured credit products, we have seen the CDOs (Collateralized Debt Obligations), securities backed by various types of debt instruments or rather derivative instruments on debt.

The high demand for these structured products stemming from the herd behavior of investors (who are confronted to ridiculously high return expectations) will quickly lead to a drop in returns. The investment banks will then develop products that are more and more complex with an ever bigger leverage in order to maintain the appearance of a subsidized return. If 100 euros were invested on a classic investment product that only yielded 0.5% (or 50 bp (basis points where one basis point = 0.01%) above the money market rate when the return objective was maintained at 200 basis points above the market, the challenge would consist in creating a product on 400 euros that are invested at Euribor + 50 basis points. This would lead to selling to the investor a structured product of 100 euros at the Euirbor rate + 2% (200 bp). The problem is that by doing this, leverage is being carried out (here we are taking 4 times the notional: 100 euros of cash that are really invested and 300 euros that have been borrowed to take on risk via derivative products).

It is not mathematics that are the problem but those that use them without understanding despite the various warnings.Mory Doré and Patrick Jaulent

These structured products have in reality been strongly depreciated as from the end of 2007 for at least two reasons that defy the mathematical hypothesis on which they had been built.

- First of all, many of these structured credit products were built on a logic that was radically different than what is taught to a novice investor. The logic stated that the more risky markets became with an increase in the risk premium on the issuers, the more you would borrow to take on risk and vice versa. That is taken on the basis that risk premiums or the credit spreads of issuers always converge back towards an average (probably an unverified statistical law that caused so many trading and arbitrage catastrophes).
- Then, the hypothesis of an absence of correlation among these types of debt that were backed on these products has run its course. Just like we were explaining at the beginning of this article, what was statistically decorrelated brutally recorrelates during periods of stress. When we shall be able to include the fear of investors, herd behavior, and risk aversion in financial models, a major qualitative leap will have been done in risk management.

*So according to you, can conditioning the development of financial engineering to unrealistic and irresponsible hypotheses of decorrelation among financial assets be considered as charlatanry? *

### Conclusion

To conclude, please allow us to remind you of the story of David X.Li. This illustrious Chinese mathematician had during the 2000s a genius idea, at least during a few years. His idea was simple: since correlations are a problem in themselves, why don’t we try to create a map of the different correlations and calculate all the relations? It does not matter if we mix different correlations along them. The only thing that counts is the final correlation after all (In other word, a random variable called the “survival time between each default” and a correlation coefficient between the survival times). This is the summary of the main aspects of his “genius” idea on correlations.

During 5 years, Li’s formula, known as a Gaussian copular function enabled the modeling of extremely complex risks with an ease and precision that were never seen before. Before his magical mathematical trick, Li has helped in expanding financial markets to unimaginable levels. This was the result of Wall Streett, rating agencies and even regulators using his idea.

But in 2007, cracks started to appear when the financial markets had a different behavior from that imagined by our illustrious genius. In 2008, the initial cracks became huge gaps by causing abyssal losses with the resulting major consequence of a destabilization of the world financial system. Li had simply forgot that correlations between them are notoriously unstable (He was however not alone). The approach of Li did not take unpredictability into account at all.

But is it really Li’s fault and that of his mathematical formula? As far as we are concerned, the answer is clear. It is not mathematics that are the problem but those that use them without understanding despite the various warnings.

We could not conclude this article without mentioning this extract of Shakespeare’s Hamlet on which we shall leave you to ponder : *There are more things in heaven and earth, Horatio, than what our philosophy can dream about*.