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The Hebner Model: Why Prices Change

by Mark T. Hebner February 11, 2011

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The Hebner Model attempts to simplify free market forces into 3 simple variables: Price, Expected Return and Economic Uncertainty (News). In short, prices move in the opposite direction of economic uncertainty so that expected returns at a specified level of risk can remain essentially constant and the only way to alter the expected return is to alter the risk of a diversified portfolio held and rebalanced to maintain the risk of the whole portfolio over time.

At the foundation of the model is Eugene Fama's Efficient Market Hypothesis, which says that market prices are fair. This implies the price fully reflects all available information or news, including economic uncertainty at the moment of the trade, new information concerning the investment, and the predictions on the probabilities of future information.

See this interview of Eugene Fama.

Fair prices lead to fair returns, which means that investors should be compensated for their risk exposure over a risk related appropriate period of time and that in the short term future prices are just as likely to go up as to go down. There is a slight advantage for the buyer of risk, with about 51% of the daily equitiy index returns being positive returns and 49% being negative, over about 30,000 days. Investors are primarily investing to get a return, so a future fair return for the risk is an indication of the fairness of the price at the time of the trade. However, nobody can see the future with certainty, so there will be an approximate normal distribution (bell shaped curve) of Simulated Passive Investor Experiences over the long term (see here).

To summarize the above statement: Fair Price = Fair Return. So, before you trade, ask yourself, "Who is on the other side of this trade, why do you know more than they do and is this a fair price?" If there are many willing buyers and sellers, by definition, it is a fair price.

From a fair price investors should expect:

(1) a fair outcome, which would be a risk-appropriate or fair return.
(2) an equal chance of being greater than or less than that fair return.
(3) the further the return is from a fair return the lower the probability of the event. [see here]

You can consider this the random distribution of the errors of the resulting monthly returns and the price that creates those returns relative to what was the investor expected at the time of trade, watch the video below.

Why do prices change?


The bell curve is the Law of the Frequency of Error and is a kind of cosmic order of disorder or order among chaos (see the Normal Distribution and The extreme gains and losses in short periods are not important to long term passive investors if they realize that extremes short term outcomes are normal in markets where human emotions of fear and greed meet money decisions. If passive investors hold for the proper period of time there have been no losses in the last 50 years and there are few if any extreme events beyond 3 standard deviations (see here).

Efficient markets move with the news, which is random and therefore the price changes have no exploitable trends. So any speculation using trading systems or active investment strategies, such as stock, time, manager, or style selection, will only detract from future market returns, relative to a market or risk appropriate return. In other words, the excess expected return from speculation starts at zero and becomes negative when you include expenses, taxes and mistakes.

Also, in an efficient market, investors cannot expect to earn above-average returns without assuming above-average risks. In other words, the risk of an investment is the source of it's expected return, not price speculation. Market efficiency does not suggest that investors can't "beat a market (or a risk appropriate benchmark.)" Over any period of time, some investors will beat a market, but the number of investors who do so will be no greater than expected by chance, and chance, or luck, does not persist. In addition, it is therefore impossible to know who will be the lucky manager in the future.

This does not mean that prices are perfect; some prices may be too high and some too low, but there is no reliable way to know at any point in time. Under such conditions, investors should consider the current price the best estimate of the right price to earn an expected return, considering the risk of the investment and the current news or information set. Forecasting the future has proven to be very difficult, so a better solution is to capture the wisdom of many very smart people who are backing their opinions with their money.
The accuracy of the collective wisdom of all of us is eloquently detailed in the book: The Wisdom of Crowds : Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations by James Surowiecki. The book is a thoroughly accessible and readable explanation of applied behavioral economics. The author is interviewed on the video on the left.

Many economists, such as Friedrich von Hayek, Ludwig von Mises, and Milton Friedman, have argued that market economies are the result of spontaneous order, which results in a more efficient allocation of societal resources than any design could achieve. They claim this spontaneous order is superior to any order human mind can design due to the specifics of the information required. In a market economy, price is the aggregation of information acquired when people are free to use their individual knowledge. Price then allows everyone dealing in a stock, bond, commodity or its substitutes to make decisions based on more information than they could personally acquire, information not statistically conveyable to an indivdual trader, trading firm or a centralized authority. Interference from a central authority which affects price will have consequences they could not foresee because they do not know all of the particulars involved. In other words, the wisdom of the crowds will exceed the wisdom of any individual or small group of individuals. This is illustrated in the concept of the invisible hand proposed by Adam Smith in The Wealth of Nations. Thus as the result of spontaneous order, information is embedded in prices with greater detail and accuracy than possible for any other source, a more efficient economy is created to the benefit of a whole society. (Source: Wikipedia)

This is why we often hear that the news or information is already "Baked in the Cake", meaning that there is no need to assume you know something that is not already included in the price.

Click to enlarge

An example of Baked in the Cake:

This is an interesting description of prices from cafehayek: “Prices are beautiful.  We have a tendency to view prices as deception, a trick played on consumers to scam us into paying more than we like.  Prices are information.  Like ants tracing pheremones, prices provide signals for the billions of buyers and sellers that we call “the market.”  These prices guide our savings, our production and our consumption.  Isn’t it marvelous how we can use a price to evaluate all 3 of those functions?  Prices are like a universal language!"

The job of free market participants is to set prices so that investors will be compensated for the risk they bear. So as long as markets are free, investors should be confident that future periods (days, months, quarters, 1, 5, or 10 years), have relatively constant expected returns (Er) for that length of period, given a certain investment (i). In other words, for each investment there is some probability distribution of future returns, where the average of that distribution is the expected return and there is a 50/50 chance that future returns should be above or below that expected return. The more extreme the deviation from the average, the less likely it's occurrence. In other words, the S&P 500 has an average annual return of about 10% and a standard deviation of about 20%, therefore annual gains greater 50% or annual losses greater than 30% should occur about 2.5% of the time for each, or about twice in 80 years. (Note: The average, plus or minus 2 x the std. dev. = 95% of the outcomes, leaving 2.5% of good years and 2.5% of bad years on each extreme side of the bell curve.) For a simulated S&P 500 Index, over 81 years (1927- 2008), there has been 2 calendars years greater than 50% (1933=53.8% and 1954=52.5%) and 3 calendar years with losses great than 30% (1931= -43.4%, 1937= -35.1%, and 2008= -36.8%.)

The expected return and standard deviation (descriptors of the probability distribution) for diversified index portfolios can be best estimated by looking at the past distribution of simulated returns over a very long period, like the last 50 years, or using the Fama/French Five Factor Model for equities and fixed income, as explained here and seen below in Figure 1. If you would like to include the Great Depression in your probability distribution estimate, you can go back 83 years.

Figure 1

Market prices change so that buyers will be comfortable that they will earn the expected rate of return commensurate with the risk of their investment, based on current information about factors that affect capitalism, which could be characterized as an uncertainty of obtaining that expected return over the appropriate time horizon.

Investors should assume that the expected return is essentially constant (see The Theory of Finance, Fama and Miller, p. 339) based on the Five Factor Model or a long term (approximately 50 years) historical annualized return and standard deviation of a given investment, regardless of market conditions. The expected return at the time of investment, based on historical data, changes slightly as one data point is dropped from the front of the historical data and one data point is added at the end, to get the new average or annualized return and standard deviation.

As an example, the charts below are histograms of 50 years of monthly returns of 20 Index Portfolios. The data box includes 3 important characteristics of each index portfolio for the time period.

Figure 2

The Hebner Model of why prices change can be stated as a formula: the Current Price of an Investment (Pi) equals the current Expected Return (Eri) divided by the market's assessment of the current Uncertainty of that Expected Return (UEri):

Price (Pi) is expressed in currency ($). Expected Return (Eri) in % Return per Period of Time for a specific investment, held constant, with an implied Standard Deviation, based on your method of determination. Uncertainty (UEri) is a calculated index number with no units, derived from Pi and Eri. Depending on your Price and Expected Return, you may want to multiply Uncertainty by 100 or some constant for charting purposes, see charts below.

Risk is actually represented twice in the model, with a certain level of risk embedded in the investment (such as Index Portfolio 50) and an additional layer of perceived risk determined by the current news, the state of the world, or the Uncertainty of the Expected Return based on the news at the time the price is agreed to by seller and buyer.

In a really simplified version and a liberal interpretation of the model, you could say that:

Price = Expected Return/Risk
Risk = Expected Return/Price
Expected Return = Price x Risk

To visualize how markets work, imagine an essentially constant Expected Return for a given investment portfolio set at the fulcrum of this teeter-totter. The Uncertainty of the Expected Return would be on the left side and the Price would be on the right side. The price is moving inversely proportional to the uncertainty of expected returns. When price (set by willing sellers agreeing with willing buyers in a free market) has fallen 2%, you can imply that uncertainty (guided by unexpected and random new information about the systematic or market risk, i.e. news about capitalism) went up 2%. When the price has increased 2%, uncertainty fell 2%, allowing the investors assumptions of Expected Return at the time of buying the investment to remain essentially constant.

Figure 3

Listen to Ken French discuss the market in terms of this model. "Expect to get a normal [expected] rate of return for the risk taken"

See Index Portfolio 60 overlaid on Galton Board and how 780 months of simulated historical monthly data matches up to the random dropping of beads through a pattern of pins which represent risk.

Figure 3a:

As illustrated in Figure 4 below, news (uncertainty), prices and returns are generated in a random series as time goes by, but within ranges (standard deviations) that are tied to the risk level of Index Portfolio 50.

IFA suggests that investors who score a 50 on the Risk Capacity Survey should invest in Index Portfolio 50 and that they should have an average holding period of about 7 years.

Figure 4 estimates 7 years (84 months) of news, prices and monthly returns, or a Simulated Passive Investor Experience (SPIE). The 84 monthly returns are simulated by the dropping of beads from the center of the fulcrum. The beads eventually form a bell shape curve, with a shape that resembles what was expected: an Average Return of near 0.9% /month and a Standard Deviation (2.5%). These characteristics are appropriate for Index Portfolio 50, based on 600 monthly returns. The 600 months of data are represented by the black outline of the distribution in the fulcrum. This bell curve is our best estimate of the probability distribution of future returns or Eri.

Figure 4: As Time Goes By


The equilibrium price agreed to by willing buyers (demand) and sellers (supply) embeds the expected return and the uncertainty of it for that moment in time. For this reason, investors can expect to be properly compensated for the risks they accept, every day they buy, regardless of price or market conditions because a free market reaches a price that is an equilibrium point between the two factors. Don't forget that the greater the risk, or volatility, of the investment, the longer the investor should be prepared to wait to achieve their annualized expected return. It is time, not timing that will determine your investing success.

As long as markets are free to trade, Adam Smith's invisible hand should work. The best assumption for investors is to assume that prices are fair at all times. Fair prices are prices where investors are properly compensated for the risk they bear over a reasonable period of time. If you think the price is wrong, you won't know for sure until long after the fact. So once you are invested in a risk exposure that matches your risk capacity, forget about the changing prices and find something more useful to do with your time.

The following charts show several periods or Simulated Passive Investor Experiences (SPIEs), with 7 randomly selected starting times, simulated starting prices based on a price of $1 on Jan 1, 1958, and how the price, uncertainty and simulated average cumulative monthly return changed over a 7 year period for Index Portfolio 50. Note that the cumulative return converges on the Expected Return (0.88%) over the holding period. Seven years is the IFA recommended average holding period (AHP) for investors who score a 50 on the risk capacity survey. The AVP is the SPIE (period of time) where the Standard Deviation of annualized returns are about 4 or less and there are no negative annualized returns over the SPIE. See this table of data and click the roll button on top of the table to compare the 20 Index Portfolios. AVPs are highlighted in the color of the portfolio.

Figure 5

When will the buyers be right, again?
About 10 Billions shares of about 20,000 stocks are bought and sold every day around the world. At each new price, buyers think it is a good time to buy and sellers disagree. Since prices are set at fair market value, there is about a 50/50 chance that future daily returns will be higher or lower than the approximate average of 0.035%/day for Index Portfolio 90 (based on 50 year experience ending Dec. 2007.) Even in 2008, when the S&P 500 was down 37%, out of the 253 trading days, 126 were positive, 126 were negative, and 1 was break-even. The average up day was up 1.58%, and the average down day was down 1.90%. The average day was down only 0.16% in 2008.

This is illustrated in the chart below. In fact, a fair market value should be a price where the buyer and seller are equally likely to gain or lose in the short term. Click on the 90 button below. As you can see, on a daily basis, it is a close split between days with gains and days with losses (51.6% gains and 48.4% losses). This must be or one side of the trade would not be agreeing to a fair price. Of course there are some unwilling buyers and sellers and some uninformed buyers and sellers, but I estimate that these get offset or diversified away when looking at volumes of 10 Billion shares per day. If 70% of the days were positive, few shareholders would sell unless the price went up and if 70% of the days were negative, there would very few buyers, unless the price went down. However, the very cornerstone of a free market is that the prices would quickly adjust up or down so that future daily gains and losses would be close to 50%/50% again. Over the longer term, you can see that the job of the free market was successful, because prices were set so that investors (buyers) were compensated for the risk of capitalism over an appropriate holding period of 5 to 10 years. Or otherwise stated, the cost of capital of the sellers was paid to the buyers or you could also say the investors (buyers) were paid a return (premium) commensurate with the 5-factor risk they took. That small 0.035% average daily return for Index Portfolio 90 accumulates to an average annualized return of 13.36% over the 481 10-year Simulated Passive Investor Experiences.
Figure 6: Well, chances are your chances are awfully good.

A French mathematician Louis Bachelier, published a now famous paper, The Theory of Speculation, way back on March 29, 1900. He wrote, "the determination of these [price] fluctuations depends on an infinite number of factors; it is, therefore, impossible to aspire to mathematical prediction of it. Contradictory opinions concerning these changes diverge so much that at the same instant buyers believe in a price increase and sellers in a price decrease." Nothing has changed.

Here are some other interesting charts about past market declines (source: - Here are some more interesting charts showing recoveries since 1950. See data here and back tested data disclosures at


The Austrian School and Joseph Schumpeter maintained that in the short term equilibrium is never attained as everyone was always trying to take advantage of the pricing system and so there was always some dynamism in the system. The free market's strength was not creating a static or a general equilibrium but instead in organizing resources to meet individual desires and discovering the best methods to carry the economy forward.