A couple of days ago I briefly mentioned my "theory" on how to make buy-and-cell decisions:
My theory is: If the fundamental is completely unknown, you sell on technical weakness as the price drops; If the fundamental is perfectly known, you buy more as the prices gets cheaper and cheaper than the intrinsic value!
It's definitely not a earth-shattering discovery, but it's really behind the decision-making process of many stock investors. Besides, the theory implies completely opposite trade actions depending on whether or not the investor know (or thinks to know) the company's underlying fundamentals.
This kind of trading strategy actually has some justification from a statistician's point of view: if applied properly and without other considerations, the outcome is proven to be statistically the "best" and "unbiased". I am going to elaborate it more here by relating it to what geo-statisticians do when they try to estimate a value of a property such as the grade of ore bodies and the porosity of oil-bearing sandstones in un-drilled locations. After-all geo-statisticians and stock traders are facing similar problems: trying to obtain an unbiased estimate of the value (price) of the property of interest (stock) in un-sampled locations (or in the future). In both cases the only certainty we know is uncertainty!
Below I am going to show how similar methodologies are being used in the two fields, hence the "justification" of the "theory" above.
In Geostatistics:
The Problem: Estimate a property value at an un-sampled location based on neighboring sample data.
Information: (1) data values at sampled locations such as nearby wells; (2) underlying geological information and constraints of the property being studied.
Solutions: The best unbiased linear estimator depends on what you believe about the underlying property.
| Belief |
Methodology |
Best Unbiased Linear Estimator |
|
Property's underlying mean known
|
Simple Kriging (SK)
|
Underlying mean calibrated by data nearby, or simply be the underlying mean if far away from data
|
|
Mean not known
|
Ordinary Kriging (OK)
|
The average of neighboring data calibrated with data nearby
|
|
Mean not known but there is a directional trend in data
|
Kriging with a drift, a.k.a. Universal Kriging (UK)
|
The value on the trend surface calibrated with data residuals, i.e., difference between data and trend.
|
Note that the methodology is mathematically proven to produce the best unbiased linear estimator [given a few very unrestrictive assumptions].
In stock trading:
Problem: Estimate the price of a stock in the not-so-distance future. Sell the stock if the estimated price is lower than the current price and vice versa.
Information: (1) price and volume data, i.e., technical data; (2) Financial data of the company, industry as well as the economy, in other words the fundamental data.
Solutions: a combination of fundamental and technical analyses, depending on how much you believe about the company's intrinsic future value.
|
Belief
|
Methodology (and analogy to geostatistics)
|
Best Unbiased Estimator
|
Decision
|
|
Stock's intrinsic value known
|
Fundamental analysis (SK)
|
The stock's intrinsic value, calibrated with data
|
Buy if price drops below intrinsic value and vice versa
|
|
Intrinsic value unknown
|
Technical analysis (OK)
|
The average calibrated with data, or the range of recent prices
|
hold or buy-low-sell-high in range
|
|
Intrinsic value unknown but there is a directional trend in price and/or volume
|
Technical/trend analysis (UK)
|
Whatever price on the trend line, plus or minus the residuals (local variations)
|
Buy if price trending up and vice versa
|
The ideal case is that we know the fundamental or geology very well, then we don't have to worry about local (daily) variations. But in most cases that's not possible: fundamental data are inherently fuzzy and may not relate to the value to be predicted at all. On the other hand, technical data may be very certain but suffer the drawback of them being local, i.e., temporary, information and using them to infer values at distance or future is certainly risky.
Yet a decision has to be made irregardless of the quality and quantity of data. Integrating all available information certainly will help, but an expert would choose the most important data to use and apply the best methodology accordingly (and understand/document its limitations!). The rest is uncertainty (or risk). If he doesn't make mistakes in other facets (there are many!) of stock investing, the expected accumulated return should be positive and goes higher and higher.
... At least that's the theory!