Butterfly Effect

"What happened? 13.2% down in 7 days. It's brutal. It didn't even give you time of adjust your expectations. And all for no obvious reasons. You tune into CNBC and the analysts talk about the correction that was long over due. Correction! all right..but why the **** you didn't tell me that it was incorrect."

I've seen it happening so many times that I've almost lost interest. But I want to answer the question that many people have asked me in past few days.Why did the markets fall?

Do you know about Butterfly Effect?

No?

Ok…Do you know butterfly's wings might create tiny changes in the atmosphere that ultimately cause a tornado to appear (or, for that matter, prevent a tornado from appearing).

No jokes. It a concept from Chaos Theory. The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a dynamical system may produce large variations in the long term behavior of the system.

The concept becomes relevant in investing world because the valuation methods used to estimate value of a stock are ultra sensitive to the initial variable. On top of that we routinely indulge in oversimplification of valuation concepts so that they can be expressed in simple ratios.

Lets talk about P/E. Most of you would know that the ratio is calculated by diving price by earnings. But which year's earning are talking about. You would often see reports stating that the stock is quoting just 8 times its FY08 EPS! Cheap..isn't it?

Even if you calculate by taking the average earnings of last 3 years, as Graham suggested, how would you know if P/E 15 is expensive or not? What's the benchmark?

The benchmark is provided by the risk free interest rate and the estimate of risk premium.

The valuation process is known as Discounted cash flow method.

But the problem with the model is that it takes estimates of highly volatile variables as inputs. There is no way of predicting the growth rate of next 10 years. Nor can you ascertain the trends in risk free interest rates or the right level of risk premium. At best we go by our guesstimates which are susceptible to changes in general mood. When everything looks positive people find 1% risk premium enough to invest in blue chip stocks. At the same time they overestimate the expected growth rate. To see the effect lets take an example.

Suppose you were given a task for estimating these variables for 10 year period and here are the actual results

	Growth	Interest rate	Risk premium
Estimate	22%	8%	5%
Actual	18%	9.00%	6.00%

The interest rate rise a bit. Growth is a little lower and investors little more cautious. By all means you have performed very well. But the result.

You valuation model will show that the value of stock must be 75% of your initial estimate. Its shocking. and it's analogous to Butterfly Effect in chaos theory.

This minor change in initial estimates can cause the estimates of correct valuations to change. The impact is almost always coordinated. That means the changes in these variables impact the valuations in the same direction. For instance when the interest rates rise the estimates of growth are revised downward and risk premium shoots up. The combined effect can be disastrous.

To answer the question..Why did the markets fall? A butterfly flapped its wings, which, through complex chain of intermediate events, caused instability in the world financial system and well......Rest is history

Cheers
Kamlesh

Note: text in italics sourced from wikipedia