Global Value Investing |

A multifaceted approach to value investing with stock valuation based on intrinsic value estimated from cash returns, appraised value of assets, and other facets of value. |

**Risk and
Uncertainty**

Risk refers to the occurrence of uncontrollable undesirable outcomes including unknown and unexpected possibilities. Thus, in order to know what constitutes risk for any particular investor in any given situation, it is necessary to first know what the investor seeks or desires as a favorable outcome.

For long-term investors seeking the maximum total real return on their equity investment subject to the preservation of the purchasing power of their invested capital, generally the single greatest and longest enduring risk is general price level inflation. U.S. inflation is measured by the Consumer Price Index (CPI) at the retail or finished goods level and by the Producer Price Index (PPI) at the wholesale or raw materials and intermediate goods levels.

Inflation in the general price level is the most insidious form of taxation. Inflation reduces real purchasing power while simultaneously increasing the nominal face value of currencies. In addition to the general level of prices, there are particular components of the inflation indexes that merit special monitoring. Energy and food are both "high-noise" components that are relatively unstable. For that reason, the "core" rate of inflation excludes these two components. Sudden shortages of supplies of energy in the form of fossil fuels (coal, crude oil, and natural gas) and in supplies of food historically have been identified as the causes of runaway inflation, to instability in prices, to debasement of the currency, to destruction of the monetary system, to failure of the economy, to widespread societal unrest, to toppling of the government of city/states in almost every past civilization. Not surprisingly, wars between the overpopulated urbanized city/states are fought over food and energy in addition to territory for expansion. The structure of city/states is inherently unstable because it requires continuous exponential growth, and this cannot be maintain indefinitely due to the physical limits of the planet regardless of new technologies to more efficiently exploit its resources.

For investments in common stock, another major enduring risk is the agency costs of company management and, where applicable, of investment management. The interests of company owners and company management are not identical. Where there is a conflict of interest, then managers can be expected to advance their own interests at the expense of stockowners. Checks and balances are required to contain human greed for power, wealth and fame.

Uncertainty refers to the unpredictability of known possible future economic states of the world or known possible outcomes of a choice or action. Uncertainty can be included in an investment model such as the discounted cash flow model directly with a probability distribution and a random number generator. Alternatively, uncertainty can be modeled indirectly by adjusting the appropriate discount rate to apply to expected dividends or free cash flow to equity in the estimation of investment value.

Opinions about the current investment value of any particular stock will differ. Given an investor's best estimate of the current investment value of a stock, his greatest risk is paying more than this amount for the stock. Just as a hustler "makes his game" by playing only with terms that offer a likely win for him, the prudent investor "makes his game" by buying a stock only with a sufficient margin of safety that offers a likely profit to him. This is why the concept of margin of safety, the difference between quoted market price and expected investment value, is central to intrinsic value investing.

Investment Value

, John Burr Williams (see citation in the Special Books). Chapter III. Evaluation by the Rule of Present Worth. Section 1. Future Dividends, Coupons, and Principal. page 55: Let us define the investment value of a stock as the present worth of all the dividends to be paid on it. Likewise, let us define the investment value of a bond as the present worth of its future coupons and principal. In both case, dividends, or coupons and principal, must be adjusted for expected changes in the purchasing power of money.The Theory of Investment Value

Section 8. Uncertainty and the Premium for Risk. page 67: Whenever the value of a security is uncertain and has to be expressed in terms of probability, the correct value to choose is the mean value.

Section 12. Marketability. pages 74-75: Marketability, or salability, or liquidity, is an attribute of an investment to which many buyers of necessity attach great importance. Yet it would not be helpful to amend our definition of investment value in such a way as to make it take cognizance of marketability. Risk, to be sure, should be covered by the definition, as done above, but not marketability. ... Likewise,stabilityis a thing distinct from investment value, and from marketability as well. While the expected stability of the price of a security in future years is a consideration of great importance to some investors, particularly banks, yet it is not a component of investment value as the latter term ought to be defined. ... In conclusion, therefore, it may be said that neither marketability nor stability should be permitted to enter into the meaning of the terminvestment value.

Chapter XV. A Chapter for Skeptics. Section 5. Conclusion. page 191: The wide changes in stock prices ... are a serious indictment of past practice of Investment Analysis. Had there been any general agreement among analysts themselves concerning the proper criteria of value, such enormous fluctuations should not have occurred, because the long-run prospects for dividends have not in fact changed as much as prices have. Prices have been based too much on current earning power, too little on long-run dividend-paying power. Stock prices, in fact, have moved more violently than almost anything else in the business cycle. Is not one cause of the past volatility of stocks the lack of a sound Theory of Investment Value?

page 57: Earnings are only a means to an end, and the means should not be mistaken for the end. Therefore we must say that a stock derives its value from its dividends, not its earnings. In short, a stock is worth onlywhat you can get out of it.

page 72: If the investment value of an enterprise as a whole is by definition the present worth of all its future distributions to security holders, whether on interest or dividend account, then this value in no wise depends on what the company's capitalization is. ... Furthermore, nochangein the investment value of the enterprise as a whole would result from achangein its capitalization. ... Such constancy of investment value is analogous to the indestructibility of matter or energy; it leads us to speak of the Law of the Conservation of Investment Value ...

page 80: To conclude, a stock is worth the present value of all the dividends ever to be paid for it, no more, no less. The purchase of a stock represents the exchange of present goods for future goods, just as in other cases where interest arises. Dividends are the claim on future goods. Present earnings, outlook, financial condition, and capitalization should bear upon the price of a stock only as they assist buyers and sellers in estimating future dividends.

page 84: The Evaluation of Net Quick Assets. A word as to financial position and its bearing on the price of a company's stock may be added here. If a company has cash holdings, for instance, in excess of what are needed to maintain its earning power, it is in a position to pay an extra, non-recurrent dividend, equal in amount to the excess cash per share. Likewise, if its receivables, inventories, or other quick assets are redundant, an extra dividend can be paid whose amount will depend upon what the excess of quick assets can be liquidated for. On the other hand, if net quick assets are too small, either because of low cash, inventories, or receivables, or high bank loans, the company will have a deficiency in net quick assets that will curtail dividends while current assets are being built up out of earnings.

page 113: The foregoing equation shows how the price of a common stock is affected by changes in (1) the purchasing power of money, (2) the interest rate for the entire enterprise, and (3) the interest rate for the senior securities. The factors listed above, rather than the growth of the country and the profitable reinvestment of earnings, largely account for the persistent rise in stocks ... This fact greatly weakens their whole claim that the growth of the country tends to make stocks in general go up year after year indefinitely, save for temporary reactions.

pg. 244: It is a mistake to say that the greater variability of dividends that would result from changing the rate of dividend from year to year as earnings changed would make stock prices go up and down more. To begin with, stocks could hardly be more volatile than they are now!

Expected Value

The concept of expected value is mathematical and based on probability. Expected monetary value or expected investment value refer to the same underlying concept. The calculation of expected value requires an appropriate probability distribution and an acceptable-quality pseudo-random number generator or a genuine random number generator. See the

DCF Valuatorand theexamplecalculation of investment value under certainty. Such calculations are referred to as deterministic in contrast to calculations with uncertainty that are referred to as stochastic (probabilistic). In addition, calculations that include more than one holding period are referred to as dynamic in contrast to single holding periods that are referred to as static. A holding period is the duration of time between opening and closing a position in an investment, usually from the buy time to the sell time.

As an example, the expected value of the roll of one true die that does not stand on edge is the mean of all the possible known but uncertain outcomes 1 through 6, which is 3.5. Nevertheless, there is a risk that the dice may be loaded intentionally or otherwise be unfair.

Paradoxes

The well-known Petersburg Paradox (see listing for Durand in the General Books) has a history of publication going back to the Bernoulli brothers in 1738. The lesser-known Allais Paradox (see the listing for Allais in the General Books) is part of an explication of the St. Petersburg Paradox that was published in 1952. We quote below from the cited Allais article.

Allais Paradox is a simple illustration of Allais' general theory of random choice proposed as a counter-example to the neo-Bernoullian formulation of the St. Petersburg Paradox. His observations are based on very careful persons, well aware of the probability calculus and considered as rational in the economic sense.

For game theory and economic models, risk is often defined and measured mathematically. The principle of the mathematical expectation of monetary gains has proven to be open to question in the case of the St. Petersburg Paradox outlined by Nicolas Bernoulli. To explain this paradox, Daniel Bernoulli considered the mathematical expectation of cardinal utilities instead of the mathematical expectation of monetary gains. He added the psychological monetary value of the random prospect to the player's capital for the utility function and proposed to take the logarithmic expression as cardinal utility.

Allais shows that limiting consideration to the mathematical expectation of the utility function or a utility-index function involves neglecting the basic element characterizing psychology vis-a-vis risk, namely the distribution of cardinal utility about its mathematical expectation, and in particular, when very large sums are involved in comparison with the psychological capital of the subject, the strong dependence between the different eventualities and the very strong preference for security (risk aversion) in the neighborhood of certainty.

Because the cardinal utility and the neo-Bernoullian index of utility are necessarily identical up to a linear transformation, the neo-Bernoullian formulation reduces to considering the mathematical expectation of cardinal utility alone, neglecting its dispersion about the average. In so doing, it neglects what may be considered as the specific element of risk. The mistake made by proponents of the neo-Bernoullian formulation is the want to impose restrictions on the preference index. Imposing other restrictions would, in the case of certain goods, reduce to imposing special restrictions on the preference index which no author has ever envisaged.

From the St. Petersburg Paradox to the Allais Paradox. In sum, just as the St. Petersburg paradox led Daniel Bernoulli to replace the principle of maximization of the mathematical expectation of monetary values by the Bernoullian principle of maximization of cardinal utilities, the Allais Paradox leads to adding to the Bernoullian formulation a specific term characterizing the propensity to risk which takes account of the distribution as a whole of cardinal utility.

Neither the St. Petersburg nor the Allais Paradox involves a paradox. Both correspond to basic psychological realities: the non-identity of monetary and psychological values, and the importance of the distribution of cardinal utility about its average value.

For nearly forty years the supporters of the neo-Bernoullian formulation have exerted a dogmatic and intolerant, powerful and tyrannical domination over the academic world; only in very recent years has a growing reaction begun to appear. This is not the first example of the opposition of the 'establishments' of any kind to scientific progress, nor will it be the last.

The Allais Paradox does not reduce to a mere counter-example of purely anecdotal value based on errors of judgment, as too many authors seem to think without referring to the general theory of random choice which underlies it. It is fundamentally an illustration of the need to take account not only of the mathematical expectation of cardinal utility, but also of its distribution as a whole about its average, basic elements characterizing the psychology of risk.

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