Risk, Uncertainty, and Profit by Knight - Book Report/Review Example

Topic: Discuss Knight's distinction between risk and uncertainty. To what extent is long term investment appraisal using discounting techniques a futile exercise' Introduction This paper aims to discuss the theory of Frank Knight and his distinction between risk and uncertainty. It also aims to prove through mathematical inquiry to what extent long-term investment appraisal based on discounting techniques is rendered a futile exercise in the valuation of investments. Discussion of Knight's Theory "If we are to understand the workings of the economic system we must examine the meaning and significance of uncertainty, and to this end some inquiry into the nature and function of knowledge itself is necessary." - Frank H. Knight, 1921 In his treatise, "Risk, Uncertainty and Profit" written in 1921, Knight distinguished between risk and uncertainty in the manner of a continuum. At one end is pure risk, sometimes called actuarial risk, in which situation probabilities are capable of being exactly determined on the basis of hard, physical data. At the other end of the continuum is pure uncertainty that, according to Knight, defies analysis. Somewhere in between the two extremes fall most random variables that are encountered in economic problems, depending on their relative uncertainties. These differentiations, however, apparently is not understood or accepted by many researchers due to the apparent confusion between the two concepts in many economic studies today. Methodologies developed for the case of pure risk are often made to apply on problems that are concerned with uncertainty (Taylor, 2002). To draw distinctions between the concepts of risk and uncertainty, it must be kept in mind that probabilities under condition of pure risk are determinable, while those under condition of pure uncertainty are unmeasurable and therefore unanalyzable; the two are thus not the same, despite the fact that they are interchangeably used in many economic studies. In moving from the point of pure risk to that of pure uncertainty, three economic modelling issues become apparent, according to Taylor (2002). First, as uncertainty increases, it becomes increasingly difficult to conceptualize and define random variables. In such cases, the set of random variables one analyst would tend to consider as applicable in a case would tend to differ significantly from the set of random variables another analyst would believe appropriate for the same case. Which one of the two conceptual models or sets of random variables is more appropriate becomes a matter of opinion for lack of defining criteria, and will continue to remain a contentious issue until the uncertainties surrounding the case are diminished or removed entirely. The second issue is that of insurance; in conditions of pure risk, many insurance companies would be able to build a viable market, because determinate risk is insurable, and in fact, it is the presence of risk that makes insurance necessary. However, in the case of pure uncertainty, no insurance firm would venture to extend the coverage. In fact, as uncertainty increases along the continuum, the cost of premiums would move to higher and higher levels until the point where they present a moral hazard. The third issue that creates problems for modelling is that as uncertainty increases, the estimation or specification of probabilities become increasingly involved and difficult, whether objectively or even subjectively, as to be almost arbitrary. While, as Taylor points out, frequentists and Bayesian theorists contend that no matter how high the uncertainty, a probabilities specification could always be subjectively arrived at, this has understandably been called into question in the ensuing philosophical debates. In contrast with Taylor's depiction of Knight's theory as a two-attribute, linear, continuum, Norman and Shimer (1992) explains that Knight actually considered three types of probability: aside from uncertainty and risk, there is also statistical probability. In differentiating the three, Norman and Shimer view the Knightian distinctions as a matter of objectivity or subjectivity. In the risk case, as defined by Knight, as one wherein "objective" probabilities are determinable from known parameters. From the point of view of a businessman, and as previously mentioned, risk may be eliminated by insurance. And consistent with earlier discussion, the uncertainty case was determinable only by "subjective" probabilities and unknown parameters. This case the businessman is constrained to estimate without the benefit of precedents or past experience that would have formed the basis for estimation. The third case, that of statistical probability, is viewed by Norman and Shimer as the span between the states of risk (Taylor's "pure risk") and uncertainty (Taylor's "pure uncertainty"). Thus, in the case of Taylor's interpretation of Knight's theory, cases are distinguished in terms of the relative levels of risk and uncertainty, and as the level of risk recedes, that of uncertainty increases. This differs from Norman's and Shimer's take on Knight's theory, wherein risk, uncertainty, and statistical probability are mutually exclusive and distinctive categories, independent of each other. A third interpretation of Knight is presented by Samson, Reneke and Wiecek (2009), who excerpted a direct quote from his 1921 study as basis: ''But uncertainty must be taken in a sense radically distinct from the familiar notion of risk. . . . It will appear that a measurable uncertainty, or risk proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all. We shall accordingly restrict the term uncertainty to cases of the non-quantitative type. . . . The practical difference between the two categories, risk and uncertainty, is that in the former the distribution of the outcome in a group of instances is known, while in the case of uncertainty this is not true, the reason being in general that it is impossible to form a group of instances, because the situation dealt with is in a high degree unique.'' (Knight, 1921) (emphasis supplied) On the basis of this explanation of Knight, Samson et al. arrived at the inference that Knight's criteria is mainly the quantifiability or non-quantifiability of the terms being dealt with, not necessary the possibility or impossibility of their determination, a matter of typology rather than verifiability. It adds a new dimension to an understanding of Knight compared to those advanced by Taylor and Norman and Shimer. On the succeeding page is a diagram constructed by Samson, et al, to illustrate the different nuances of the theories on uncertainty and risk Source: Samson, Reneke and Wiecek, 2009, p. 559 In the preceding diagram, Knight's definition of risk and uncertainty as independent of each other appears to fall squarely under the second category, that is, where uncertainty and risk are different and independent from each other. However, in certain aspects such as described by Taylor, they also appear to be related in that the greater the amount of uncertainty, the less the component of assessable risk - a notion that falls within the third category, or that where uncertainty and risk are viewed as dependent on each other. This has special implications for the businessman or investor. It is an integral facet of business that the profit motive requires the businessman to assume a level of risk that would justify the realized margin. Thus the saying, the higher the risk, the higher the profit. On the other hand, it is also a cornerstone principle that business is averse to uncertainty. The seeming paradox arises because of the common, layman's interpretation equating risk to uncertainty, that risk exists because of uncertainty. Knight's distinction, on the other hand, appears foursquare with the businessman's viewpoint, that risk exists but with certainty, and uncertainty is the utter indeterminability of risk. Long-term investment discounting techniques There are many different types of long-term investments, from those involving capital budgeting of real assets in direct investment, to those involving valuation of securities in financial portfolio investment. The latter requires analysis of market returns, which may be too unstable for purposes of illustration as it admits to the high volatility of returns. For the purpose of this paper, the assumed investment problem will take the form of a capital budgeting problem, which will present a more constant set of variables in the form of future cash flows and a fixed initial investment. The net present value formula is the embodiment of the present value of future cash flows, discounted by the required rate of return on the investment. The standard net present value formula is given by the equation: where: Ct = the net cash flow receivable in period t r = the periodic required rate of return I0 = the initial investment required to purchase and install the asset In this investment model, uncertainty may be introduced in two ways. First, it is possible for the future cash flows Ct expected to be yielded by the project to be uncertain; or, secondly, it is possible for the future expected returns r on alternative investments to be uncertain. During such cases, financial theory states, the "risk-averse" investor should adjust his valuation methodology accordingly. In this aspect of financial theory, uncertainty and risk appear to follow the first category of the Samson, Reneke and Wiecek model in the preceding page, where risk and uncertainty are viewed as interchangeable. For consistency, this proof shall adopt Taylor's interpretation of Knight's theory, and view increasing degree of uncertainty as the increasing difficulty of measuring the risk involved, thus exposing the investor to possible indeterminate risk. For this discussion, the uncertainty of future cash flows will be ignored for the meantime as it is regarded as unsystematic risk attributable to the nature of the business. In short, cash flows shall be assumed to be certain, and the focus of discussion will center on the uncertainty of the discount rate. The theory of discounted cash flows in investment valuation allows for the adjustment of risks in the determination of discount rates. These factors may or may not be independent; however, the purpose of introducing them here is to define the context by which uncertainty may be introduced into the valuation method. According to Wilson and Shailer (2004), the discount rate used in the model must reflect at least five factors: the investor's risk attitude, the investor's cost of capital, interest rate risk, perceived risk for expected returns from the project, and information uncertainty for projected cash flows. Barring any extreme systemic shocks, the component of the discount rate pertaining to the investor's risk attitude ought to be considered as relatively constant, leaving the other four components to vary with time as is their nature. There is another imposition on the discount rate that is dictated by finance theory. Peirson, Brown, Easton and Howard (2002) state that the discount rate in project (investment) valuation should be a function of the firm's cost of capital. The firm's capital is of two basic types - equity and debt. The expected return of shareholders determines the cost of equity capital while interest rates determine the cost of debt capital. (To be continued) References Knight, Frank H. Risk, uncertainty and profit. Boston and New York: Houghton Mifflin Co., 1921 Norman, Alfred L. and Shimer, David W. Risk, uncertainty, and complexity. Journal of Economic Dynamics and Control, vol. 18, pp. 231-249, 1994 Peirson, Graham; Brown, Robert; Easton, Steve; and Howard, Peter. Business Finance, 8th ed. McGraw-Hill Irwin, 2002. Samson, Sundeep; Reneke, James A.; & Wiecek, Margaret M. A review of different perspective on uncertainty and risk and an alternative modelling paradigm. Reliability Engineering and System Safety, vol. 94, pp. 558-567, 2009 Taylor, C. Robert. The role of risk versus the role of uncertainty in economic systems. Agricultural Systems, vol. 75, pp. 251-264, 2002 Read More