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Wednesday, May 31, 2006

Taking Stock

Ever wonder about this pseudo-paradox?

The stock market goes down by x% and the goes up by the same x%. Does it recover its original value?

No, it only reaches a value of 1-(x/100)^2 of its starting point. The percentage positive increase has to equal x/(1-x/100) for a full recovery. Ratchets have a definite mechanical advantage for pulling investors across the bumpy plateau.

Although, or perhaps because, I don't have a significant fraction invested in the stock market and mutual funds, this property has always spooked me. It always seems that any large percentage drop in value takes a much larger counter-ratchet to recover. In a non-growing, oil-limited economy, it seems to me that this inevitably leads to a downward spiral.

Sorry for the pedantic post, but time off has rendered me to refitting the old training wheels. Tom Friedman has also pulled out his training wheels and begins to make some sense by looking at basic math and realizing that GM hasn't a clue.


Professor Anonymous Anonymous said...

Have you investigated the Random Walk theory, MO? I thought it might appeal to your mathematical bent. (Lots of academic work behind it.)

Basically says that it is impossible or very difficult to do better than the market average. Therefore, it's better to avoid transaction costs and invest in an index fund. This was the inspiration behind Vanguard, the most consumer-friendly of the mutual fund companies.

I find the theory very persuasive. Index funds are also much less stressful than individual stocks.

The only problem is that the theory is designed for the 20th century U.S. economy. Wouldn't have worked so well for the stocks in the Austrio-Hungarian Empire in 1912. May not work too well if energy and environmental and US-dollar crises shake the economy.


8:55 PM  
Professor Anonymous Anonymous said...

The Random Walk theory has been debunked by many, exhibit A would be Warren Buffett's 40 year record. There are many other managers who show decades of investment experience that far outpace the market averages. No need to fear the fact that a 20% decline requires a > 20% rise to come back to even. Annual rises in stock markets are much more frequent than annual declines. Markets go up over time because economies keep growing, and earnings grow along with the economy. Sure, sharp drops in markets can scare the bejebus out of anyone, but over nearly all 5 year periods markets provide real returns of about 7-8%.

Want to learn about markets and market risk from the guy who has the lowest risk adjusted returns, and is an amazing font of knowledge - see
John Hussman's site and pick up the weekly commentaries in /wmc.

12:44 PM  
Professor Anonymous Anonymous said...

Random Walk has not been debunked. Look at the proliferation of index funds. Look at the academic papers on the subject.

The number of investors and mutual funds that consistently outpace the averages is very low indeed. Especially when you subtract transaction costs and mutual fund fees.

I agree with the statement of the previous poster that the U.S. economy kept growing during the 20th century, and on the average stocks went up.

And yet...

There were 10-year periods where that didn't happen. And the experiences in some non-U.S. countries were very different.

I'm uncomfortable extrapolating the behavior of the U.S. stock market from the 20th century into the future. The last century was the century of oil and U.S. predominance - those factors underlay the growth that made possible the stock market gains. Will they continue?

In unsettled conditions, I think active management WOULD make sense -- though not the heavily advertised funds most people are likely to purchase.

Diversification looks like a very good strategy to me - for example bonds (especially bonds indexed for inflation) and paying down debt.


4:03 PM  
Professor Blogger WHT said...

Thanks for the good analyses. The mixture of mathematics and psychology makes it an intriguing yet daunting task to get right or even close.

5:51 PM  

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