"Surely, one of the best-established facts in economics is that changes in stock prices are essentially unpredictable. And just as surely, this fact is one of the least believed and most disliked."
- "Macroeconomics" by Dornbusch, Fischer and Startz.
I shall try to explain one such piece of evidence.
"TIME SERIES ECONOMETRICS"
Regression analysis is a popular statistical method used by many scientists to detect relationships between phenomenas. (Like the link between smoking and lung cancer for example.)
This is a chart showing the relationship between values of the S&P 500 index one month ago and its current values:
(Source: "Macroeconomics" by Dornbusch, Fischer & Startz)
A straight line can be drawn roughly joining all the points on the chart. In fact, all the data points are clustered around this line so much that they look like a smear of black ink blots. Statisticians call lines like that "very good fit on the data". But what does this mean? It means that there is a very powerful link between the past values of the S&P and the current value.
THE EQUATION
An equation can be written to show this relationship mathematically:
"P(t+1)" stands for current stock prices. It can be explained by three factors: "a" is the expected return to holding stocks. "P(t)" is last time period's price. "e" represents the unpredictable random errors that resulted in the "ink blot smear" we observed in the previous diagram. (without the random error, all the data points would have formed up in a smooth line by themselves)
The equation shows a process known to statisticians as a "random walk" or more precisely, a "random walk with drift".
Implications of the equation:
P(t+1) - P(t) = Change in Stock Price = a + e
Hence, other than the very small "a" component, the changes in stock price can be attributed to the unpredictable "e". (Which is relatively small, as seen by how close the data points are from the line.)
Also, changes in stock prices are independent over time: If stocks did well last month, they are no more likely to either do well or do poorly this month than at any other time.
TO BE OR NOT TO BE
The conclusion I formulated from reading such practical evidence is that while stock picking might still be possible, it is unlikely to be an easy source of profit for the common man.
Readers are advised to come to the same conclusion.
5 comments:
Hi economist,
Please correct me! I would think the conclusion to be drawn from article is that the best form of investing is to invest in index.
Statistic works best when the sample size is big. And the only way to invest in large number of stocks is to invest through index funds?
The equation goes:
P(t+1) = a + P(t) + e
P(t+1) - P(t) = a + e
Therefore we have:
Change in P = a + e
e is random and thus unpredictable. However, a is the predictable returns to holding stocks.
In the long run, the noise will cancel each other out and e = 0. Hence, investors stand to earn a.
Mathematically,
Expected change in P = E(a + e)
Expected change in P = E(a) + E(e)
We know E(e) = 0 because in the long run noise cancels out.
Therefore,
Expected change in P = E(a) = a
Index investing might be the way to go. Diversification and holding for the long haul allows e to cancel out and investors to earn a. This is in fact recommended by many economists. (some Nobel prize winners too)
But I have my reservations:
Is stock index investing a sham?
Is e really random? I think I read somewhere that Andrew Lo and another academic have published a book to illustrate that stock prices may not be a random walk after all.
I would hesitate to draw any conclusion from the chart showing the relationship between values of the S&P 500 index one month ago and its current values or the equation.
For example, are changes in stock prices really independent over time? A few paper has argued that using relative price strength or strong one year return strategy can outperform the market as stocks with strong prior year return are likely to have high return in the coming year. If this is so, changes in stock prices may not be independent over time.
A lot of strategies will perform well on data generated with coin tosses too. This is the problem of "data snooping". (Given any set of data points one can always formulate strategies that worked in the past; but not in the future)
The issue is not whether the strategies formulated are valid or not but instead is the fact that we cannot tell workable strategies apart from bogus strategies. So far there are no credible tests to separate the cream from the crap. (Being profitable in the past can be a result of pure luck and thus does not guarantee profitability in the future)
Yes, stock pricing is not a resolved area of financial economics and thus we should not jump to conclude that stock prices are random. However, investors should also not be too quick to conclude that they are.
Many thanks for the valuable input. :)
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