“Noise”, 1986-07-01 (; backlinks; similar):
The effects of noise on the world, and on our views of the world, are profound. Noise in the sense of a large number of small events is often a causal factor much more powerful than a small number of large events can be.
Noise makes trading in financial markets possible, and thus allows us to observe prices for financial assets. Noise causes markets to be somewhat inefficient, but it often prevents us from taking advantage of inefficiencies. Noise in the form of uncertainty about future tastes and technology by sector causes business cycles, and makes them highly resistant to improvement through government intervention.
Noise in the form of expectations that need not follow rational rules causes inflation to be what it is, at least in the absence of a gold standard or fixed exchange rates. Noise in the form of uncertainty about what relative prices would be with other exchange rates makes us think incorrectly that changes in exchange rates or inflation rates cause changes in trade or investment flows or economic activity.
Most generally, noise makes it very difficult to test either practical or academic theories about the way that financial or economic markets work. We are forced to act largely in the dark.
…The whole structure of financial markets depends on relatively liquid markets in the shares of individual firms.
Noise trading provides the essential missing ingredient. Noise trading is trading on noise as if it were information. People who trade on noise are willing to trade even though from an objective point of view they would be better off not trading. Perhaps they think the noise they are trading on is information. Or perhaps they just like to trade.6
With a lot of noise traders in the market, it now pays for those with information to trade. It even pays for people to seek out costly information which they will then trade on. Most of the time, the noise traders as a group will lose money by trading, while the information traders as a group will make money.
The more noise trading there is, the more liquid the markets will be, in the sense of having frequent trades that allow us to observe prices. But noise trading actually puts noise into the prices. The price of a stock reflects both the information that information traders trade on and the noise that noise traders trade on.
As the amount of noise trading increases, it will become more profitable for people to trade on information, but only because the prices have more noise in them. The increase in the amount of information trading does not mean that prices are more efficient. Not only will more information traders come in, but existing information traders will take bigger positions and will spend more on information. Yet prices will be less efficient.7 What’s needed for a liquid market causes prices to be less efficient.
The information traders will not take large enough positions to eliminate the noise. For one thing, their information gives them an edge, but does not guarantee a profit. Taking a larger position means taking more risk. So there is a limit to how large a position a trader will take. For another thing, the information traders can never be sure that they are trading on information rather than noise. What if the information they have has already been reflected in prices? Trading on that kind of information will be just like trading on noise.8 Because the actual return on a portfolio is a very noisy estimate of expected return, even after adjusting for returns on the market and other factors, it will be difficult to show that information traders have an edge. For the same reason, it will be difficult to show that noise traders are losing by trading. There will always be a lot of ambiguity about who is an information trader and who is a noise trader.
The noise that noise traders put into stock prices will be cumulative, in the same sense that a drunk tends to wander farther and farther from his starting point. Offsetting this, though, will be the research and actions taken by the information traders. The further the price of a stock gets from its value, the more aggressive the information traders will become. More of them will come in, and they will take larger positions. They may even initiate mergers, leveraged buyouts, and other restructurings.
Thus the price of a stock will tend to move back toward its value over time.9 The move will often be so gradual that it is imperceptible. If it is fast, technical traders will perceive it and speed it up. If it is slow enough, technical traders will not be able to see it, or will be so unsure of what they see that they will not take large positions.10
Still, the further the price of a stock moves away from value, the faster it will tend to move back. This limits the degree to which it is likely to move away from value. All estimates of value are noisy, so we can never know how far away price is from value.
However, we might define an efficient market as one in which price is within a factor of 2 of value, i.e. the price is more than half of value and less than twice value.11 The factor of 2 is arbitrary, of course. Intuitively, though, it seems reasonable to me, in the light of sources of uncertainty about value and the strength of the forces tending to cause price to return to value. By this definition, I think almost all markets are efficient almost all the time. “Almost all” means at least 90%.
Because value is not observable, it is possible for events that have no information content to affect price. For example, the addition of a stock to the S&P 500 index will cause some investors to buy it. Their buying will force the price up for a time. Information trading will force it back, but only gradually.12
Similarly, when a firm with two classes of common stock issues more of one class, the price of the class of stock issued will decline relative to the price of the class of stock not issued.13
Both price and value will look roughly like geometric random walk processes with non-zero means. The means of percentage change in price and value will change over time. The mean of the value process will change because tastes and technology and wealth change. It may well decline when value rises, and rise when value declines. The mean of the price process will change because the relation between price and value changes (and because the mean of the value process changes). Price will tend to move toward value.
The short term volatility of price will be greater than the short term volatility of value. Since noise is independent of information in this context, when the variance of the percentage price moves caused by noise is equal to the variance of the percentage price moves caused by information, the variance of percentage price moves from day to day will be roughly twice the variance of percentage value moves from day to day. Over longer intervals, though, the variances will converge. Because price tends to return to value, the variance of price several years from now will be much less than twice the variance of value several years from now.
Volatilities will change over time. The volatility of the value of a firm is affected by things like the rate of arrival of information about the firm and the firm’s leverage. All the factors affecting the volatility of a firm’s value will change. The volatility of price will change for all these reasons and for other reasons as well. Anything that changes the amount or character of noise trading will change the volatility of price.
Noise traders must trade to have their influence. Because information traders trade with noise traders more than with other information traders, cutting back on noise trading also cuts back on information trading. Thus prices will not move as much when the market is closed as they move when the market is open.14 The relevant market here is the market on which most of the noise traders trade.
Noise traders may prefer low-priced stocks to high-priced stocks. If they do, then splits will increase both the liquidity of a stock and its day-to-day volatility. Low-priced stocks will be less efficiently priced than high-priced stocks.15
The price of a stock will be a noisy estimate of its value. The earnings of a firm (multiplied by a suitable price-earnings ratio) will give another estimate of the value of the firm’s stock.16 This estimate will be noisy too. So long as noise traders do not always look at earnings in deciding how to trade, the estimate from earnings will give information that is not already in the estimate from price.17
Because an estimate of value based on earnings will have so much noise, there will be no easy way to use price-earnings ratios in managing portfolios. Even if stocks with low price-earnings ratios have higher expected returns than other stocks, there will be periods, possibly lasting for years, when stocks with low price-earnings ratios have lower returns than other comparable stocks.
In other words, noise creates the opportunity to trade profitably, but at the same time makes it difficult to trade profitably.
…If monetary policy doesn’t cause changes in inflation, what does? I think that the price level and rate of inflation are literally indeterminate. They are whatever people think they will be. They are determined by expectations, but expectations follow no rational rules. If people believe that certain changes in the money stock will cause changes in the rate of inflation, that may well happen, because their expectations will be built into their long term contracts…noise causes changes in the rate of inflation.
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