The most famous and widely quoted studies are those done by Ibbotson Associates, which tracks financial market returns typically since 1926. If one were to look at the returns for the US stock market, the average return delivered since 1926 till date is 10.4 per cent p.a.

Eight decades is a long and credible period of time and this number of 10.4 per cent (average annual return for the stock market) is often used by the buy and hold crowd to justify being fully invested and owning stocks over bonds.

One can break down stock market returns into three components: earnings growth, valuation changes (P/E expansion or contraction) and dividend yield. The breakdown of the 10.4 per cent annual return is as follows.

According to Ibbotson, earnings growth over the last 79 years contributed 5 per cent to the long-term average return.

Since P/E ratios were 10.2 in 1926, the effect of the increase in P/Es to 20.7 at the end of 2004 provided .9 per cent to the long-term average.

Finally, the dividend yield averaged about 4.5 per cent over this period. Combining all the three components together, the compounded total return for the US stock market (before transaction costs and all other expenses, etc.) averaged 10.4 per cent.

Using these same three components of return and looking at what they are likely to deliver over the coming decades, one easily comes to the conclusion that long-term returns in the US from here are likely to be significantly below the 10.4 per cent historical average.

First of all, the chances of P/E expansion from the current elevated levels are low, thus straightaway knocking .9 per cent off the expected returns number. In fact, investors in the US will be lucky if they do not experience P/E contraction over the coming decades, which would reduce long-term returns.

As far as earnings growth is concerned, this is closely linked to nominal GDP. Given the outlook for lower inflation, both nominal GDP and earnings growth are likely to be below the average of the past eight decades. Most observers expect at best earnings growth to average 4 per cent.

As for dividend yields, given the current elevated valuation levels, the best case is 2-2.5 per cent, much lower than the 4.5 per cent average of the past 79 years.

Thus, doing a simple break-up of the expected long-term returns of the US equity market from current levels leads to the simple conclusion that investors will be lucky to get much over 6 per cent over the coming decades.

Compared to the 10.4 per cent long-term average this is a big drop, and partly explains the strong and growing interest among large institutional investors in the US to diversify into emerging markets (where expected returns are higher).

While numerous studies like the one above have been done for US markets, what does this throw up for Indian markets?

If one were to invest in the Indian markets today, what returns can one expect taking a decade-long view and breaking up returns into the three components discussed above? This is not an academic issue as retail investors and FIIs are currently flocking to our markets, and it will be interesting to see what type of returns they can logically expect from an index level of 8,700.

First of all, given current valuation levels, with P/E multiples near 20 times 2005, it is unlikely that P/E multiples will expand further over the coming decade. We should count ourselves lucky if we do not get P/E contraction dragging down expected returns.

For earnings growth, as pointed out earlier, it is closely linked to nominal GDP. In fact if one were to look closely at the data, while market earnings track nominal GDP, earnings per share growth trails nominal GDP by about 2 percentage points due to dilution.

My best case for nominal GDP over the coming decade is in the region of 10-11 per cent (6.5 per cent GDP and 4.5 per cent inflation), leading to market EPS growth of about 9 per cent (assuming the same 2 per cent dilution as in the US).

If one expects higher inflation to boost nominal GDP and thus earnings, one should bear in mind that higher inflation will lead to higher interest rates as well, which will drag down P/Es. Thus, whatever is gained from the higher earnings will be more than given up through lower multiples in such a scenario.

As for dividends, the current level of about 2 per cent seems appropriate from a forecasting perspective, as yields are unlikely to rise from here unless multiples contract. Companies do not change payout ratios based on their stock price, thus the same 50 per cent payout gives you a dividend yield of 2.5 per cent at a 20 P/E and 5 per cent dividend yield at a 10 multiple.

Thus, even for the Indian markets, for those investing today it looks unlikely that they will earn much above 11 per cent over the coming decade and that too assuming current multiples hold and we have no P/E contraction. If P/Es were to contract to say, 15, then returns would be below 10 per cent.

As for the flaws in the above arguments, investors may genuinely believe that multiples will expand still further to 25 or even 30 times. While this may even happen over the short term, the history of emerging markets shows that to sustain multiples over 20 for an extended period of time is quite rare.

Investors may also argue that earnings growth in India will be faster than nominal GDP, as the private listed corporate sector is growing much faster than the broad economy. While there is some truth to this argument, the listed equity markets in India have very good sectoral representation, and should mirror the broad economy.

Financial history across geographies also shows the difficulty for market earnings to even come close to nominal GDP, let alone exceed it.

Thus, you have it; looking at the numbers it looks unlikely that anyone buying the Indian market today will be able to get more than 10-11 per cent return p.a. over the coming decade (best case assuming no P/E contraction).