Between January 1991 and January 2008, the compounded annual growth rate of the Sensex (ex-dividend) was over 19 per cent. Now, after a fall from over 21,000 points to below 9,000, the CAGR has dropped to 13 per cent. Since 18 years, equity has generated a risk premium of 3 per cent or more above the concurrent bank fixed deposit rates.

The CAGR hit a low of below 10 per cent in 2003. The highs are deceptive because the surges of the early 1990s pushed the CAGR above 30 per cent between 1991-96. In the next 13 years (Jan 1996 onwards) however, the top-end of CAGR has been 19-20 per cent. The average divided yield has been about 1.5 per cent.

Can one use CAGR fluctuations as a long-term buy/ sell indicator? It looks to be possible because like many other features of equity markets, the CAGR is mean-reverting. The returns tend to correct towards the average value. The average return has tended to be around 15-16 per cent if we discount the excesses of the early years. The median return has been around 14.5 per cent.

The index has been worth buying whenever the CAGR has dropped below the median. If that signal is cross-referenced with more traditional mean-reversion indicators like price book value and price earning ratios, we get a simple and easily actionable set of long-term signals.

The average PE of the Sensex has been about 17 since 1996. The market has rarely been able to sustain PEs ranging beyond 20 and it has rarely seen dips below the 13 PE levels. Single-digit PEs have been rare. Every time the market has dropped below 13 PE, it has been a good buy. It's trading at around 12 PE now.

Similar number-crunching with respect to price book value leads to the conclusion that the market is a good buy whenever the PBV is below 2.5. It's hovering around 2.5 levels right now. Similarly, a dividend yield of over 1.5 per cent is usually a reliable buy signal. The current yield is at 1.9 per cent.

Combining these mechanical signals, this appears to be one of those moments when the odds are heavily in favour of buying and holding index funds for the long term. Out of these four variables, three are clear buys and the fourth is on the cusp.

It is true that the bear market has been very severe and there are no apparent fundamental signals of recovery. It is possible that we haven't hit bottom yet. In fact, a downside is likely, given what is happening in the global economy.

But there is powerful historical evidence that buying at a similar combination of valuations has always been successful strategy for investors with a three-year perspective. Logic suggests that instead of trying to time the exact bottom, an investor should start buying now and continue buying and averaging down.

Another interesting thing is that it is equally easy to build a set of sell signals from this basic data. You get a sell signal if the CAGR is over 19 per cent. You get a sell signal if the dividend yield is below 1 per cent. You get a sell signal if the PE ratio is over 20. You get a sell signal if the PBV is over 4.5. In combination, these sell signals have been correct an overwhelming majority of the time.

Can one actually use these two sets of buy and sell signals to invest and disinvest with long-term perspectives? There are many ways to slice and dice the data. But any set of logical rules that follows these signals seems to generate returns in excess of the expected CAGR. The buys get in fairly close to bottom and the sells trigger fairly close to tops.

What is more, rules based on these signals will keep equity investors invested for long periods, which is supposedly necessary to smooth out volatility of returns. For every six to 12 month period when the investor is forced out of the market, there tends to be periods of 25 months when the investor is committed.