A first approach to dealing with risk is to seek more information about the decision alternative. Additional information often reveals that the range of outcome variability is narrower than at first thought, and that the decision alternative is thus less risky than earlier imagined. But information itself is a scarce resource which is costly to acquire. The determination to acquire additional information is a administrative decision which is based on a comparison of the benefits of the additional information relative to the cost of acquiring it. At some point, the benefits of acquiring additional information must be judged as not outweighing the costs, and the decision must be made under conditions of uncertainty or risk. The decision maker must then find some way to deal with (i.e., manage) the remaining risk, possibly by insuring against it, offsetting it (possibly by hedging), or by simply accepting it. One of the essential functions of an entrepreneur is to assume risk in undertaking new ventures or in changing the operation of the enterprise.
Since it has not been found practical to specify utility functions, I shall take a more intuitive approach to how decision makers might deal with risk.
A potentially useful concept for short-run decision analysis is that of the certainty equivalent. In this approach, the decision maker must ask himself what certain sum he would be willing to accept in lieu of the risky outcome at issue. The risk-averse decision maker can be expected to indicate a lesser certain sum than the risky possibility (“a bird in the hand is worth two in the bush”), whereas the risk preferrer would have to have a larger certain sum as a compensation for the insult of removing the gamble from his consideration. The certainty equivalent, CE, of the risky outcome, EV, is then substituted in the numerators of the ratios in the expected value (1) and present value (2) formulas:
For a risk averse decision maker, CE < V; where the decision maker is risk indifferent, CE = V; and in the case of a risk preferrer, CE > V.
Although it may not be practical to specify preference functions, the certainty equivalent approach may be by the hypothetical risk-return indifference map. The preference function illustrated in this map is for a normally risk-averse decision maker. Suppose that a decision opportunity promises a return of $6000, but entails a risk of v1. This particular combination of risk and return lies at point C on indifference curve I3. If I now follow indifference curve I3 downward to the right until the vertical axis is reached, we find that it intersects the vertical axis (where risk is zero) at $3000. The sum of $3000 is thus the certainty equivalent of the $6000 return which entails risk v1. The certainty equivalent of any other risky sum may be found in similar fashion. The reader may imagine the appearance of an indifference curve map for a decision maker who prefers risk.
Another approach is possible in the analysis of risk in the long run. In the present value formula (2), a subjectively determined risk premium, a, is added to the interest rate discount in the denominator,
The premium A constitutes a risk adjustment to the discount rate, i. The risk-adjusted present value will be smaller than before risk adjustment in reflection of the larger denominator. The risk-adjustment factors will differ from one decision opportunity to another, but their present values, adjusted for risk, will be more realistic selection criteria.
The determination of a risk adjustment factor may be illustrated by an indifference map which is a variation. A decision maker’s indifference map with risk on the horizontal axis can be leveraged, but with percentage rates of return (rather than dollar amounts of returns) on the vertical axis. In this case, the procedure is first to find on the right-hand vertical axis the cent riskless return on something like a government bond, say 8 percent. This identifies the relevant indifference curve, I4, which may be followed. Then, when the risk factor, v1, for the decision opportunity is computed, a vertical may be erected at v1 on the horizontal axis to intersect indifference curve I4 at point D. At point D the decision maker is indifferent between the low return on the riskless government bond and the higher return on the risky decision opportunity.
A horizontal may be drawn from D to the right-hand vertical axis to find the higher return, 10 percent as illustrated. In the denominator of the present value formula, the value of i is taken to be 8 percent, and the risk premium a is 2 percent (i.e., 10 percent minus 8 percent). If the market interest rate on government bonds changes, then some other indifference curve would become relevant and a new risk premium found in similar fashion.
The illustrated procedure for determining the risk adjustment factor is operational only if the decision maker’s preference function can be specified (heroic at best), but this model does illustrate the thought process which must be used by a rational decision maker in selecting a risk adjustment factor. There is no scientific way to specify a schedule of either certainty-equivalent or discount rate adjustment factors. These are such highly subjective matters that they must be left to the personal judgment of each decision maker. This is one reason that different decision makers, confronted with the same scenarios and information, can reach such different investment conclusions. The naive or inexperienced decision maker may have no ability at all to determine either certainty equivalents or discount adjustment factors. The ability to determine either will come only with time and the accumulation of a stock of experience in considering risky alternatives.
Finally, I should note that neither discounting to allow for the time value of money nor risk-adjustment of the discount rate constitutes an allowance for the risk of inflation. If over the n-period life of a decision opportunity inflation is expected to ensue, a deflation factor (i.e., an inflation risk adjustment factor), d, may be included in the denominators of the terms of the present value equation,
Each deflation factor is a decimal equivalent, e.g., .04, of an anticipated rate of inflation, e.g., 4 percent. The deflation factors may differ from term to term if inflation is thought likely to accelerate or decelerate over the life of the decision opportunity.
In the previous section I considered the utility implications of different probability assessments, but suppose that a decision maker simply cannot in any meaningful way assess the probabilities of the possible outcomes. How can the decision maker decide whether or not to invest in the venture described in the above example? Under the maximin decision rule, the decision maker would examine the worst-case scenarios, $0 for not investing and -$1 million if the investment is undertaken and fails; the choice under this rule would be not to invest because it yields the least of the worst scenarios.
The minimax regret rule, however, yields a different conclusion. A so-called “payoff matrix” may help to illustrate the computations. According to the minimax regret rule, the alternative with the least regret of not selecting the best outcome should be chosen. In the example above, a much larger regret ($4 million) would be suffered from not investing if the investment turns out to be successful than would be realized ($1 million) from investing which is not successful. Therefore, under this rule the decision maker should choose to invest.
This series is a lot of parts that I am quasi-using pieces of for a academic research paper stance so bear with me if it gets too esoteric. Or read the other governance articles available within the SharePoint Security category within the main site (available through the parent menu).