Three religions of investment

The world of finance is populated by people with very different ideologies. Each makes different assumptions about how markets behave and how they are best treated. None, I think, has succeeded in capturing (even approximately) real market dynamics. I would like to discuss the three paradigms that seem to be the most prominent.

Value investing

This the paradigm with which Warren Buffet is associated. It is the oldest of the three paradigms (according to Mandelbrot) and is generally considered to have been born with Benjamin Graham (Buffet’s hero) and John Dodd. Value investing supposes that there is some fundamental or intrinsic value that a stock or asset possesses. However, the market price of the stock may well fluctuate around this value in the short term.

This fluctuation occurs because the market is irrational. It over- or under-reacts to short-term events and news. It follows bubbles (although bubbles may well be perfectly rational1), it panics, it becomes over-optimistic. However, in the long run the price will always move toward its fundamental value. This may take time (in fact, value investors need it to take time), but the market will realise its error, eventually. The idea is to invest in stocks that are currently undervalued by the market, value stocks. The value of these stocks will increase, not only because their fundamental value increases but because the market corrects its pricing as well, resulting in excess returns.

The trick, of course, is to find the fundamental value of the stock. This is done by a process of fundamental analysis, in which the financial statements of the company will be used extensively. This often involves (but is not limited to) finding various ratios that indicate value in a stock. Often stocks with low price to earnings ratios2 (but with good business potential) are considered value stocks. Many other ratios have evolved and investors have different preferences. Some specific ratios are used for specific industries or types of companies.

Value investing implicitly assumes that markets are not efficient. That is, all relevant information is not taken into account in the price. By studying public information it is possible to beat the market. The problem with finding the intrinsic value of a stock is that it requires assumptions, which may well be wrong. There is no unambiguously correct intrinsic value. Margin of safety is a term introduced by Graham and Dodd, and it indicates buying stocks with low enough valuations that even if your valuation is off a little, you should still make money.

I: Illustration of Allan Gray's investment philosophy (source: www.allangray.co.za)

Allan Gray, a South African firm that follows a value-investing mindset illustrate the philosophy quite succinctly. In the above picture the black line is the intrinsic value of a share over time, the red is the actual market price, which fluctuates around the intrinsic value. Allan Gray buys below the intrinsic value on the gray line (which gives a margin of safety), but does not try to time the market by waiting until the price bottoms out. Similarly it will sell above intrinsic value, but not necessarily at the peak price.

I spent some time this year working at a value-oriented hedge fund, a very rewarding experience as I got one-on-one insight from a real believer (and achiever) in this paradigm. Endless time can be spent trawling through news, looking at the drivers of the industry, trying to figure out if the market price is the right price. The math is simple, really just an indicator. Value investing is a skill, an art, not a science. It is the judgement of the investor that results in superior performance.

Value investing requires you not to follow the market. By definition, only a handful of value investors can outperform. If everyone were value investors, only those with the most skill, the best judgement, or the most luck, would stand out.

Technical analysis

Technical analysts study the price history of a stock (or, very often, exchange rates) and attempt to predict its future movements. The underlying business (and its financial statements) is irrelevant. All that matters is the price (and volume) movement. Business fundamentals, such as how the economy is performing, the level of competition, etc. are ignored. This is ostensibly the second oldest paradigm, though its origins date back to the eighteenth century.

Technical analysis takes a more short-term view than value investing. Trading can happen over months, weeks or minutes, whereas value investing usually has a time period of years. The difference in focus between the two paradigms could be considered the difference between trading (technical analysis) and investing (value investing). The former is concerned only with the price at which a stock can be sold at a future point and the latter worries also about its (real) value. Trading is much more worried about timing – it is important to buy low and sell high. With value investing you “know” the price will go up – you just need to wait.

Like value investing, this paradigm assumes the market is inefficient. With technical analysis we need to assume that the information given solely by past price movements is not fully taken into account in the share price (otherwise we would not be able to predict its future movement). The fundamental factors mentioned above need not be examined because they are all contained in the share price already. Technicians (as they like to be called) have identified various patterns in stock charts and given them names. The pattern of highs and lows give an indication of what the price will do next. Moving averages3 of prices are plotted – there is meaning when a price chart crosses a moving average line.

An important idea in technical analysis is that of trend – a chart showing and uptrend still fluctuates up and down but is characterized by higher highs and higher lows. Analysts generally trade with the trend, attempting to buy low and sell high (or vice versa). Technical analysis (perhaps unwittingly) does recognize the fractal nature of markets. Within a long-term uptrend you can have a short-term downtrend and trends within that trend. You can trade on different scales.

II: Berkshire Hathaway daily share price in candles with trendline (source: www.freestockcharts.com)

The chart above once again shows daily the share price of Berkshire Hathaway. This time candles have been used to represent the price movements. Blue candles mean the price closed higher on the day and red candles that it closed lower. The top and bottom points of the candle give the highest and lowest prices over the day and the body of the candle (the thick middle part) gives the opening and closing prices.

The red line that I have drawn is a trendline4. It is meant to show the downward trend of the stock, encapsulated by the lower highs. The level of the trend line is the resistance and the stock price experiences a barrier there (support is the term for a level below which the stock is unlikely to trade). Should the stock trade above the resistance (or below the support) it is a sign that the trend may be reversing. I find the use of linear trend lines intriguing. In the world of stocks, things tend to increase exponentially, though they may be approximated in the short term by linear growth. Using a logarithmic scale would, of course, solve the problem.

While the technical trading rules could certainly be mechanically applied, I believe this is not usually the case. There is judgement involved in identifying patterns and their relative strengths. As with value investing, technical analysis, can easily be more of an art than a science.

The trends, support and resistance, etc. represent the psychology of the market. One interesting aspect of technical analysis is that it may be self-fulfilling. If all investors believe it works, then prices will by definition move as they expect them to. For instance, if it is expected that the stock price will go up in the next week, investors will buy before the week is up, increasing demand, causing the stock price to rise. Another example, if the stock is falling to a support level, investors will buy the stock, expecting that it will increase soon. This will ensure that the stock does not actually trade below the support level.

Whether things are really as simple as I have described is certainly a topic that deserves further research. In fact, the opposite may well be true. Following technical rules may result in all the patterns disappearing. It has also been observed that round numbers tend to be important trading levels – it is likely that this is because these are psychological/mental barriers (our minds tend to focus on round numbers and so we will use them in deciding when to trade). Whereas value investing uses time to eliminate market psychology, technical analysis tries to profit from it.

Quantitative analysis

This probably the newest paradigm (and possibly not yet recognised as such). Quantitative analysis attempts to treat the financial markets as a system that can be described mathematically. Quantitative analysts (or quants) use mathematical or statistical models in order to decide what and when to trade. The use of sophisticated computing techniques has become prevalent in this paradigm. Assumptions are made about how markets work, tested (at least they should be), and the models applied to real market data.

This paradigm is far more scientific than the others and has the greatest potential (I think) of truly allowing us to understand market dynamics (if not to make profit). It is also this paradigm, through its practitioners, the quants, that has been blamed for the most recent financial crisis. In my latest post I criticised the models that have been prevalent until now.

The wide range of possible activities and the advanced nature of much of the concepts involved (neither of which I have studied in any depth) mean that I will keep this section short and say no more.


I have not examined articles that study the efficacy of any of the above paradigms. However, it appears there is some evidence that stocks with low PE ratios outperform others, which would support the value investing paradigm, unless the PE ratio is merely a proxy for risk (that is to earn higher returns you still need to take more risk). The evidence for technical analysis appears to be mixed.

I believe it is very hard to obtain conclusive evidence for anything in the markets. There is so much randomness that you can be fooled (for a long time) into believing a pattern exists, where it does not. Even if it does exist, if it becomes widely known and acted upon, it may disappear. For instance, there was an observation that stocks tend to go up in January (I mentioned this in my very first post), which apparently has all but disappeared now as people made use of the trading opportunity it presented.

Final word

From my (very) limited experience in the industry, it seems that people follow these paradigms like they do religions, and with as little proof of efficacy. I myself am biased toward the quantitative. However, I will try to remain objective.

Some references

On value investing

  • Allan Gray. (2011). Allan Gray investment philosophy: Theory of share price and intrinsic value. Retrieved from http://www.allangray.co.za/Assets/swf/investment_philosophy.html.
  • Investopedia. (2011a). Value Investing. Investopedia. Retrieved from http://www.investopedia.com/terms/v/valueinvesting.asp.
  • Wikipedia. (2011a). Value investing. Wikipedia. Retrieved from http://en.wikipedia.org/wiki/Value_investing.

On technical analysis

  • Investopedia. (2006). Technical analysis. Investopedia. Retrieved from http://www.investopedia.com/university/technical/#axzz1Rs0f1lul.
  • Wikipedia. (2011b). Technical analysis. Wikipedia. Retrieved from http://en.wikipedia.org/wiki/Technical_analysis.

On quantitative analysis

  • Investopedia. (2011b). Quantitative Analysis. Investopedia. Retrieved from http://www.investopedia.com/terms/q/quantitativeanalysis.asp.
  • Wikipedia. (2011c). Quantitative Analyst. Wikipedia. Retrieved from http://en.wikipedia.org/wiki/Quantitative_analyst.

Mandelbrot’s book

  • Mandelbrot, B., & Hudson, R. (2004). The (Mis)behaviour of Markets. London: Profile Books.

1 As long as others are buying the share its price can be expected to go (irrespective of the underlying worth of the share) and so it is rational to buy the share now to sell a little later – value investors may, however, disagree.
2 This is the ratio of the price per share to the earnings (or net profit) per share.
3 This is constructed by replacing every price point with the average of itself and some points surrounding it.
4 I am no technician. If I have drawn the line incorrectly, please let me know.


Prophet Mandelbrot

I recently read a very entertaining book written by Benoit Mandelbrot and Richard Hudson, called The (Mis)behaviour of Markets. It is a popular science text, attempting to explain Mandelbrot’s fractal views on markets in simplified terms and with no maths. For years Mandelbrot has argued that conventional finance is wrong. This very fact was one of the lessons taken from the latest financial crisis (although it is yet to be seen if it will stick).


What is interesting about the book is that it was written in 2004, before the latest financial crisis. Mandelbrot argues that conventional financial theory (based on normal distributions) could not be more wrong. Markets are wilder than these models could imagine. Continuing to use them may result in further financial crises (guess what, it did).

What is more surprising, perhaps, is that Mandelbrot has been saying this for over thirty years (and no one seems to have listened). Even before modern portfolio theory was developed, Mandelbrot argued against the mild view of risk posed by models based on the normal distribution. Like Taleb in 1987, Mandelbrot may have had some right to feeling smug given the events of 2007 onward.

What is wrong with conventional models?

Conventional financial models make a number of false assumptions that have been known for some time to be incorrect. However, in the absence of better models, they have continued to be used.
  1. People are rational: people most certainly are not rational and do not always take into account all the information available. People tend to feel losses more heavily than gains which means we take different decisions when faced with choices framed in terms of losses as opposed to gains.
  2. All investors are similar, apart from their appetite for risk: Investors are very different. Some are speculators in it only for a day, some are in it for the long run. Some believe in value investing, some are technical analysts. Return and variance are not the only things that matter to all investors (which is what the theory assumes). Some investors are big (able to influence prices), others are small (the theory assumes everyone is small).
  3. Prices are continuous: This means they move smoothly. However, in reality it appears more likely that prices can jump erratically, moving from say 5 to 10 without hitting any number in between.
  4. Prices changes (more accurately the logarithm of price changes) follows a normal distribution: in actual fact there are both far more boring pricing changes (very small) and wild changes (that is, fatter tails) than this model would predict.
  5. Prices are independent over time: This means the price change yesterday does not impact it today. Mandelbrot argues that volatility tends to cluster with large price changes tending to be followed by more large price changes. He also argues that there is a long-term dependence in prices. The movement in prices today may still have an impact 100 years from now.
  6. Volatility is constant: this is one critical assumption of the ubiquitous Black-Scholes formula for valuing option prices. This assumption is wildly wrong that quants have started modelling the intricate variation in the so-called implied volatility (if the model were correct there would be no such variation). This is ludicrous, in my opinion. Empirical evidence shows that volatility itself is very volatile.
A number of hacks have been made to work around some of the problems. For instance, the modelling of the volatility ‘skew’ in point 6 above. Complicated models such as GARCH and FIGARCH have been developed that allow for volatile volatility and long-term dependence. Mandelbrot argues that this is just tacking sticky tape onto a broken vase. Something entirely new is needed. His main premise for this seems to be that his models exhibit much greater parsimony (that is they need fewer parameters) – which is a way of saying they are more beautiful or elegant – and that they start with observations of actual market behaviour.

Mathematicians (and practitioners) love normal distributions and so tack on anything they can to make them work as it saves them the trouble of starting from scratch (It’s hard to admit that a hundred-year-old body of academic literature is largely defunct). Certainly I agree this is the wrong way to go about things. However, parsimony is also not the only measure of a model’s worth. Something things are just complicated (financial markets especially). Like Einstein we should not overcomplicate. Things should be as simple as possible, not simpler. Mandelbrot may well have given us a simpler, better foundation.

Fractal markets

Mandelbrot is most famous for his work on fractals (he coined the term ‘fractal’) and he applied it in many areas. Finance is one area to which it is naturally suited. However, it has not yet caught on, probably because the maths is harder and less well developed. I do not quite understand all the workings myself (not having gone through the math, yet), but the basic premise is that markets behave similarly on any scale (or most scales at least).

Consider a graph of the prices of a certain stock. The graph will look very similar, in terms of its swings, erratic movements and proportional price changes whatever period you look at, whether it be a year, a month or a day. That is, you can zoom in on one part of a price graph and get a miniature (statistical) replica of the whole graph (that is, it is equally “wiggly”). This can be seen in the following graphs of our old friend Berkshire Hathaway (from freestockcharts.com). Can you order them by length of period covered?




The first chart shows the daily price over about 2 days, the second the hourly price over a little more than 3 months and the last the daily price over a period of almost 2 years. Except for random variation, they are pretty much indistinguishable.

This would break down at very small time periods (over a minute, say, – prices may be constant) and over large time periods (the upward trend of stocks is likely to show more clearly and the progression may be smoother). It would also not, I would add, work for illiquid stocks where the (realised) price changes very infrequently (you can still think of the price moving in the fashion described, but only being observed when the stock is traded).

If you are a regular reader, you may also remember that in a previous post I discussed power-law distributions. Mandelbrot first suggested these might fit cotton prices, and since then many other price series. Power-laws display a scaling behaviour, which is a fractal property.


The book attacks every paradigm of finance in existence today. It even says value investing, espoused by Warren Buffet (and Benjamin Graham before him), is mistaken. Technical analysis (which I have not heard many talking fondly of) is also debunked.

While I agree conventional finance has got things wrong and have my doubts about both the above paradigms (more so with technical analysis), Mandelbrot’s arguments could not convince me entirely. Mandelbrot’s view of technical analysis appeared to be a straw man (perhaps he needed to do so in order to make the book accessible) and I still have unanswered questions regarding technical analysis. However, it is a good beginning for my quest to understand the operations of the markets.

Final word

Though the book is not perfect, I would still recommend it to anyone in finance, to instil a sense of caution and of questioning. Too many people follow blindly what the ‘experts’ say. We still know very little about the markets (perhaps they are unknowable) and much work still needs to be done. I for one am rather excited that I might get to play a part.

Some references

Mandelbrot’s book:

  • Mandelbrot, B., & Hudson, R. (2004). The (Mis)behaviour of Markets. London: Profile Books.

For Taleb's account of the crash in 1987:

  • Taleb, N. N. (2007). The Black Swan. Penguin.