RISK AND UNCERTAINTY IN MANAGERIAL DECISION MAKING
Managerial decisions are made under conditions of certainty, risk, or uncertainty. Certainty refers to the situation where there is only one possible outcome to a decision and this outcome is known precisely. For example, investing in Treasury bills leads to only one outcome (the amount of the yield), and this is known with certainty. The reason is that there is virtually no chance that the federal government will fail to redeem these securities at maturity or that it will default on interest payments. On the other hand, when there is more than one possible out-come to a decision, risk or uncertainty is present.
Risk refers to a situation where there is more than one possible outcome to a decision and the probability of each specific outcome is known or can be estimated. Thus, risk requires that the decision maker knows all the possible outcomes of the decision and have some idea of the probability of each outcome's occurrence. For example, in tossing a-coin, we can get either a head or/a rail, and
In the analysis of managerial decision making involving risk, we will use such concepts as strategy, states of nature, and payoff matrix.
A strategy refers to one of several alternative courses of action that a decision maker can take to achieve a goal.
States of nature refers to conditions in the future that will have a significant effect on the degree of success or failure of any strategy, but over which the decision maker has little or no control. For example, the economy may be in boom normal, or in a recession in the future. The decision maker has no control over states of nature that will prevail in the future but the future states of nature certainly affect the outcome of any strategy that he or she may adopt.
a payoff matrix is a table that shows the possible outcomes or results of strategy under each state of nature. For example, a payoff matrix may show the level of profit that would result if the firm builds a large or a small plant and if economy will be booming, normal, or recessionary in the future.
MEASURING RISK WITH PROBABILITY DISTRIBUTIONS
Risk is the situation where there is more than one possible outcome to a decision and the
probability of each possible outcoik is known or can be estimated.
Probability Distributions
The concept of probability distributions is essential in evaluating and comparing investment projects. In general, the outcome or profit of, an investment project is highest when the economy is booming and smallest when the economy is in a recession. If we multiply each possible outcome or profit of an investment by its probability of occurrence and add these products, we get the expected value or profit of the project. That is,
' Expected profit =
where tt, is the profit level associated with outcome i, P, is the probability that outcome / will occur, and i' = 1 to n refers to the number of possible outcomes or states of nature. Thus, the expected profit of an investment is the weighted average of all possible profit levels that can result from the investment under the various states of the economy, with the probability of those outcomes or profits used as weights. The expected profit of an investment is a very important consideration in deciding whether or not to undertake the project or which of two or more projects is preferable.
Probability Distribution of States of the Economy
State of the Economy Probability of Occurrence
Boom 0.25
Normal 0.50
Recession 0.25
Calculation of the Expected Profits of Two Projects
Expected profit from project A $500
State of economy | Probabiity of occurance | Outcome of investment | Expected value |
Boom | 0.25 | $600 | 150 |
Normal | 0.50 | $500 | 250 |
Recession | 0.25 | $400 | 100 |
Expected Profit from project (A) | 500 |
Expected profit from project B
State of economy | Probabiity of occurance | Outcome of investment | Expected value |
Boom | 0.25 | $800 | 200 |
Normal | 0.50 | $500 | 250 |
Recession | 0.25 | $200 | 50 |
Expected Profit from project (B) | 500 |
Tablespresent the payoff matrix of project A and project B and shows how the expected value of each project is determined. In this case the expected value of each of the two projects is $500, but the range of outcomes for project A (from $400 in recession to $600 in boom) is much smaller than for project B (from $200 in recession to $800 in boom). Thus, project A is less risky than and, therefore, preferable to project B.
The expected value of a probability distribution need not equal any of the possible outcome (although in this case it does). The expected value is simply a weighted average of all the possible outcomes if the decision or experiment were repeated a very large number of times. Had the expected value of project A been lower than of project B, the manager would have had to decide whether the lower expected profit from project A was compensated by its lower risk.
An Absolute Measure of Risk: The Standard Deviation
We know that the tighter or the less dispersed is a probability distribution, the smaller is the risk of a particular strategy or decision. The reason is that there, is a smaller probability that the actual outcome will deviate significantly from the expected value. We can measure the tightness or the degree of dispersion of a probability distribution by the standard deviation, which is indicated by the symbol δ , Thus, the standard deviation (δ) measures the dispersion of possible outcomes from the expected value. The smaller the value of (t, the tighter or less, dispersed is the distribution, and the lower the risk.
To find the value of the standard deviation (δ) of a particular probability distribution, we follow the three steps outlined below.
- Subtract the expected value or the mean () of the distribution from each possible outcome () to obtain a set of deviations (d) from the expected value. That is,
(1)
2. Square each deviation, multiply the squared deviation by the probability of its expected outcome, and then sum these products. This weighted average of squared deviations from the mean is the variance of the distribution (δ2), That is,
Variance = δ2 =
3. Take the square root of the-variance to find the standard deviation (o-):
Standard deviation =δ2 =
If we calculate the standard deviation of the probability distribution of profits for any two project A and project B. If the standard deviation of the probability distribution of profits for project A is Rs. 100, while that for project B is Rs. 200. These values provide a numerical measure of the absolute dispersion of profits from the mean for each project and confirm the greater dispersion of profits and risk for project B than for project A.
A Relative Measure of Risk: The Coefficient of Variation
The standard deviation is not a good measure to compare the dispersion (relative risk) associated with two or more probability distributions with different expected values or. means. The distribution with the largest expected value or mean may very well have a larger standard deviation (absolute measure of dispersion) but not necessarily a larger relative dispersion. To measure relative dispersion, we use the coefficient of variation (v). This is equal to the standard deviation of a distribution divided by its expected value or mean. That is,
Coefficient of variation =v=
The coefficient of variation, thus, measures the standard deviation per Rupee of expected value or mean. As such, it is dimension-free, or, in other words, it is a pure number that can be used to compare the relative risk of two or more projects. The project with the largest coefficient of variation will be the most risky.
