The often repeated story of developments in stock markets continues to be breath-taking. From quarterly average of 3138 points in Oct-Dec 2001, within about six years, the Sensex has reached an average level of 13,227 points in Oct-Dec 2006.

Even after shedding 541 points during the day of the Budget, and more in recent days, the market barometer is still at dizzying heights as compared to levels in those periods of hibernation. Predictions by some market participants about the Sensex reaching 15,000 points were frowned upon at that time, but look less absurd today.

Most market participants today talk of the economic fundamentals and say that as long as the years of unsatiated demand in the country are still there, the growth story will continue. We still have roads and houses to be built, bridges to be erected, cars to be delivered, unheard of places to be shown to tourists and multi-specialty hospitals to be constructed.

People seem to be waiting for weekends to visit one of those swanky malls in the neighbourhood. So, the growth story is expected to continue, isn't it?

But we also know that the stock markets do not react to certain news at all, while reacting wildly even to some rumours. Surely, all those second-by-second movements cannot be based on economic fundamentals.

Indeed, the exponential rise of the Sensex also corresponds to one of the most spectacular periods of growth in the economy. We have an average annual growth of 8.6 per cent for the last three years. Most sectors, except agriculture, have witnessed above average growth.

However, at least some participants are concerned as to whether an asset price bubble is being created. After all, the memories of tech-bubble are not far behind us. A financial bubble arises when the market prices are not reflective of the actual reality.

For instance, when housing prices increase with support from speculators rather than actual investors, a bubble is expected in the housing market, which will burst sooner than later. Similarly, exuberance in the stock market which is not based on economic fundamentals is more likely to be irrational.

So, beyond simple annual averages, how much is the evidence that we have in support of the linkages between the economic fundamentals and various barometers of stock markets? As far as we are aware, there is not much empirical evidence which actually establishes linkages -- at least not in the public domain. We hope to present some statistical evidence.

To begin with, let us compute the statistical correlation between the Sensex and any one real sector parameter, say, the quarterly Gross Domestic Product of the manufacturing sector (Q-GDP) at 1999-2000 prices. In order to make the Sensex comparable with Q-GDP, quarterly averages of the Sensex are taken.

Also, in order to avoid pseudo relationships, the correlation is computed between the incremental Q-GDP and incremental quarterly Sensex. Based on quarterly data from the April-June 2000 quarter to the October-December 2006 quarter, the correlation is 0.55. This is our first linkage.

Next, consider the case of FIIs. One of the widely acknowledged facts of the stock markets is the role of funds brought in by FIIs. The amount to be put in the market in a given period is perhaps decided by them based on profit potentials in other markets vis-�-vis Indian markets.

Unlike resident investors, they do have more liberty and flexibility of going underweight or overweight in any of the economies of the world. This unique feature makes them more or less an independent judge of the economy. Of course, they do have a clear speculative motive. But, how much of their speculation is based on economic fundamentals?

In order to figure this out, the easiest way is to see the correlation between net FII inflows and the real sector indicators, like the Index of Industrial Production (IIP) or Q-GDP. For the ease of comparison, all the variables are taken as quarterly averages.

Again, in order to avoid pseudo relationships, models are built on quarterly incremental values of IIP and Q-GDP. The message here is clear too: FII investments do depend on the performance of the economy. In terms of numbers, statistical correlation between net FII inflows and incremental Q-GDP is 0.65 and that with incremental Q-IIP is 0.61. This is our second linkage.

Now, let us do some serious number crunching. As earlier, the real sectors are captured through quarterly IIP (Q-IIP) and Q-GDP. The markets are captured through quarterly averages of call rate, exchange rate of Indian rupee against US dollar, S&P CNX Nifty, BSE 100 index, and, of course, the BSE Sensex.

Once again, in order to avoid pseudo-relationships, models are built on incremental values of Q-IIP, Q-GDP, S&P CNX Nifty, BSE 100 and BSE Sensex. Original quarterly averages are used for call rates and exchange rates.

We would like to compute statistical correlation between the real sector variables and the market indicators. Since both the sets have multiple variables, how to do it is not obvious.

Here, a statistical technique called canonical correlation is helpful. This technique finds maximum correlation between linear combinations of the first set and the second set. Based on the results, there is a strong correlation of 0.75 between the two sets of variables. This is our third linkage.

Before going for a regression analysis for the Sensex, it is helpful to look at the variables and analyse them in terms of their levels of similarity. This is done using dendrograms, which are basically a tree structure used for studying closeness of variables. The variables that we use are as before, with incremental values, except for call rates and exchange rates.

Summary results indicate that net FII inflows, Q-GDP of manufacturing at 1999-2000 prices and Q-IIP are closely linked. And, as expected, the BSE Sensex, BSE 100 and S&P CNS Nifty form another closely linked set. This means that one each may be picked up from each of the closely linked sets for the purpose of statistical regression.

We then ran a statistical regression for the Sensex on net FII inflows, Q-GDP of manufacturing at current prices, call rate and exchange rate. The regression equation for incremental values is as follows:

BSE Sensex = 9205 - 105 Call rate - 180 Exchange rate + 0.0836 FII + 0.0099 Q-GDP

The t-values are acceptable and the R-square value of the model is 0.40. The model once again establishes the role of economic fundamentals in terms of Q-GDP of manufacturing sector and the widely acknowledged role of FIIs in the incremental Sensex values.

The model provides an added insight into the working of the market in terms of call rates and rupee-dollar exchange rates. This is our fourth and final linkage.

Our analysis using the quarterly data for the last five-six years clearly indicates that the developments in stock markets are in sync with macro-numbers and, as of now, there is no reason for worry -- not yet.

Views expressed here are personal. Authors can be contacted at nkunnikrishnan@rbi.org.in.