Wednesday, August 24, 2011

Still haven't bought any stock

Summary: This post tells a formula for deciding if you should postpone purchases in times of a looming crisis.

Update: Added a paragraph on probabilities.

After I finished reading Saarion sijoituskirja, the Arvopaperi OMXH index showed that Finnish stock prices had moved -10% since 1.1.2011. I postponed purchasing stocks because of the following calculation. It had two scenarios:

(1) Greece crisis becomes acute with probability P(crisis).
(2) Orderly recovery happens with probability P(recovery) = 1 - P(crisis).

Let the change in stock prices be C(crisis) or C(recovery). We should postpone purchases if

P(crisis) * C(crisis) + P(recovery) * C(recovery) < 0

When Lehman Brothers collapsed, the prices decreased by 40%. Let C(crisis) = -40%. By contrast C(recovery) = 10% - 20% since recovery is usually slower.

Avoiding probability estimates

We can pick stock price changes from historical data. Regarding probabilities, let's look at the equation at 0 when it doesn't matter whether we postpone investment or not.

P(crisis) * C(crisis) + (1 - P(crisis)) * C(recovery) = 0
P(crisis) * C(crisis) + C(recovery) - P(crisis) * C(recovery) = 0
P(crisis) ( C(crisis) - C(recovery) ) = - C(recovery)
P(crisis) = C(recovery) / (C(recovery) - C(crisis))

With C(recovery) = 15% and C(crisis) = -40%, the equation gives P(crisis)= 15% / 55% = 27%. This means that we should postpone investment, if we estimate that P(crisis) > 27%. We should invest now if we estimate that P(crisis) < 27%. It doesn't matter if we invest or not if we estimate that P(crisis) = 27%.

How it turned out

What in fact happened was that Greek crisis materialized but it was an orderly restructuring and prices collapsed only by 20%. The debt and the budget deficit are still simmering.

The situation now is almost the same, but the 'risk scenario' is 2008-style banking crisis. Only this time, goverments are part of the problem and no longer part of the solution. I'm still postponing investment.

If stock prices recover from current -30% to -10% in the next 3 months, then I suck at predicting and am better off investing to index funds. Stock traders divide profit to 'alpha' and 'beta'. 'beta' is the profit from market. You get beta profit from index funds, because stock prices on average rise with economic growth. 'Alpha' is the profit from skill. It is negative if you suck at predicting. Finding your own alpha by making successful and failed predictions is called alpha discovery.

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