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Theory of reflexivity

Beating The Street

Devangshu Datta  |  New Delhi 

George Soros adopted and adapted Karl Popper's philosophical theory of reflexivity to explain market movements.

Reflexivity can be understood in engineering terms as a feedback loop, the reinforcement of a trend by its effect on itself.

In this context, the obvious example is how an initially small rise in prices creates more demand for stocks, thus leading to further price rise.

In the reverse case, prices may fall drastically because an initially small drop in prices leads to more sales.

Stripped of nuances, reflexivity suggests that price movements often swing beyond the rational; sometimes way beyond. Reflexivity implies equilibrium is an unusual state "" market prices will usually be above or below fair valuation.

Soros realised that, if this was true, positions could be safely held beyond the point of rationality. When trends developed they would continue well beyond "fair value".

The theory of reflexivity flies in the face of conventional market models such as capital asset-pricing models, and other calculations of fair value by discounting returns versus risk-free debt.

Soros has also made far more money than conventional traders, so his beliefs have to be treated with some respect.

If true, reflexivity accounts for some of the irrationalities we see, especially bubbles. Soros-Popper provides an interesting explanation of the lost decade of 1992-2002, when long-term returns were negative.

The reflexivity of the Harshad Mehta boom created a massive bubble, which took a full decade to deflate.

By some measures, prices stayed above fair value through all but a few months of the decade. We can calculate fair value as the reciprocal of risk-free returns.

Since the risk-free return is equivalent to earnings divided by price (E/P), the reciprocal, or P/E is approximately fair-value. If rates drop, fair value rises. It also rises if earnings rise. Earnings rose through the decade and rates fell towards the end.

The risk-free interest rate was 15 per cent during those glory days of 1991-92. So fair equity values were then around P/Es of 7. The Sensex peaked at average P/Es of 55 (4450 points) in April 1992. The following bust saw a 58 per cent dip inside 12 months.

But even at the decade's lowest prices (1900 Sensex) in April 1993, average P/Es were 25, way above fair-value.

In the next boom, prices peaked at Sensex 4600 in September 1994, equivalent to P/Es of 45. Dropping rates meant that fair values were then around 8.

In each subsequent bust, P/E levels declined more since earnings grew steadily. Rates also fell, especially after 1998. In late 1998, average P/Es dropped to around 9-10 at Sensex values of 2700-2800 points. This was close to fair value.

In September 2001, prices declined to P/E levels of about 13 and nominal Sensex levels of 2600 (the index had been rebalanced causing the anomaly versus 1998). Rates dipped. So, fair-value would then have been 11-12.

Recently valuations did drop below fair-value at around 2900 Sensex in April 2003, when average P/Es hit 12. The current run up has pulled the Sensex to 14 P/E with risk-free rates down to 7.

So the market has pulled upto fair-value. Given reflexivity, this bull-run surely has plenty of steam left.

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First Published: Sat, August 02 2003. 00:00 IST