Lecture Notes 2 Ec 403

LECTURE NOTES 2 EC 403

RISK ANALYSIS

Introduction

Managers are expected to come up with good decisions. A good decision is one that is based on logic, considers all available data and possible alternatives and applies the quantitative approach. Occasionally, a good decision results in an unexpected or unfavourable outcome. If it is made properly it still is a good one.

A bad decision is one that is not based on logic, does not consider all alternatives and does not employ appropriate quantitative techniques. If a manager makes a bad decision, but is luck and a favourable outcome occurs, he still has made a bad decisions.

Steps in Decision making

There are ten steps

(i)  Realize that there is a problem and clearly define the problem at hand.

(ii)  Obtain suitable information on all aspects of the problem.

(iii)  Judge the relevance and validity of all information obtained.

(iv)  List the possible alternatives and Evaluate these alternatives.

(v)  Identify the possible outcomes.

(vi)  List the pay-off or profit of each combination of alternatives and outcomes in a decision table.

(vii)  Select one of the mathematical decision theory models. Selection of the model depends the environment the firm is operating in and the amount of risk and uncertainty involved.

(viii)  Mobilize the resources required.

(ix)  Apply the model and make your decision.

(x)  Check to determine if the problem has been solved.

Types of Decision making Environments

There are alternative states of information or decision making environments.

1.  Certainty- Decision making under this environment, the decision-maker knows with certainty the consequences of every alternative or decision choice. The decision-maker is perfectly informed in advance about the outcome of his decisions. For each decision there is only one possible outcome which is known to the decision-maker. Under conditions of certainty there is accurate, measurable reliable information available on which to base a decision. For example a man who has $100 to invest for one year may open a savings account paying 5% interest and the second is to invest same amount in treasury bills paying 10% interest, there is certainty the treasury bill will be a better investment and will be chosen.

2.  Risk- Risk is probability that an outcome will not be as expected. Decision making under risk is where predictability is lower. Complete information is unavailable. A situation of risk is when either of two or more events (outcomes) may follow an act (decision) and where all of these events and the probability of each occurring, are known to the decision-maker. In other words in this situation of risk a decision may have more than one possible outcome, so that certainty no longer exists and the decision maker is aware of all possible outcomes and knows the probability of each one occurring. In this environment, the decision-maker will attempt to maximize his/her expected well being. In this environment decision theory models for business problems typically employ two equivalent criteria- maximization of expected monetary value and minimization of expected loss.

3.  Uncertainty- Decision environment here, very little is known. In this situation a decision may have more than one outcome and the decision-maker does not know the precise nature of these outcomes, nor can he objectively assign a probability to the outcomes. In other words not all outcomes may be accurately foreseen and the probabilities cannot be deduced or based on empirical data. The decision maker has to use intuition, judgement and experience to assign the probabilities to the outcomes considered possible in such a situation. Assignment of probabilities is on a subjective basis. Instead of immediately identifying the appropriate course of action, or solution to a problem,(because of limited knowledge and experience), actions and solutions are arrived at through a process of searching through sequences of possible alternatives, using past experience and rules of thumb as guidelines.

Techniques for decision making under risk.

Decision making under risk is a probabilistic situation. Several states of nature may occur, each with a given probability. The probabilities are known.

Measures of risk

(i)  Standard deviation- the lower the standard deviation the lower the risk.

where is probability of outcome i; is value of outcome i; is the mean value or expected value of all outcomes. When considering choices between alternative courses of action, decision markets may be thought of as deciding on different combinations of return on the one hand, measured by the expected value of returns and risk on the other, measured by the standard deviation of those returns. The smaller the standard deviation, the lower the riskiness of the alternative.

Suppose there are two projects A and B whose returns are as stated below and probabilities of states of nature also given.

Project A

Project B

The standard deviations are calculated as shown below for the two projects

Project A

Standard deviation =

Project B

Standard deviation =

The standard deviation of Project A is $63.25; that of B is $316.23. By the standard deviation criterion, project B is riskier since its standard deviation is much larger than the standard deviation for project A. Since the expected values for the returns from the two projects are equal at $500, project A would be preferred. The standard deviation as a measure of risk has problems where projects have the same standard deviation but different expected returns, the standard deviation alone cannot bee used hence the risk per dollar is a much better measure. The project with a lower risk per dollar will be selected.

(ii)  Coefficient of Variation- this can be used as an alternative measure to the standard deviation. It handles the problem mentioned above. It divides the standard deviation by the mean deviation by the mean or expected value of the net cash flows, to obtain the coefficient of variation (CV).

In formula terms, CV= where is the mean or expected value of net cash flows.

Since D has a lower coefficient of variation, of variation, it has less risk per unit of return than investment C.

(iii)  EXPECTED MONETARY VALUE (EMV)

The expected monetary value (EMV) of an event is the payoff, should that event occur, multiplied by the probability (the probability is known) that the event will occur. In other words, the EMV for an alternative is just the sum of possible pay-offs of the alternative, each weighted by the probability of that pay-off occurring. It is the mean of the probability distribution in question.

Formula: where Ri is return or pay-off of the ith event, and Pi is the probability of the ith event.

Case study: Mr. Thambolenyoka is a director of a profitable firm. He has identified the problem whether to expand his product line by manufacturing and marketing a new product, backyard storage sheds. He has three options; to construct:

(1)  A large new plant to manufacture the storage sheds.

(2)  A small plant or

(3)  No plant at all.

Thambo has determined that there are only two possible outcomes: the market for the sheds could be favourable (high demand for the sheds) or unfavourable (low demand for the sheds) He has already evaluated the potential profits associated with the various outcomes. With a favourable demand he thinks a large facility would result in a net profit of $200 000, to his firm. This profit is conditional upon building a large factory and there is a good (favourable) market. If the market is unfavourable there would be a net loss of $180 000. A small plant would result in a net profit of $100 000 in a favourable market but a net loss of $20 000 would occur if the market was unfavourable. Finally doing nothing would result in a $0 profit in either market. Using the EMV what should Thambo do?

To solve the problem, construct a decision table, also called a pay-off table or pay-off matrix. A pay-off matrix is a table that shows the possible outcomes or results of each strategy under each state of nature. 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.

Decision table with conditional values

The alternatives listed in the first column can also be referred to as strategies. A strategy is one of several alternative courses of action that a decision maker can take to achieve a goal. The alternative that gives the highest EMV is the one to go for.

Alternative 1 :Large facility

Alternative 2: Small facility

Alternative 3 :Do nothing

Since the largest EMV ($40 000) results from the second alternative, building a small facility, Thambo should to put up a small plant to manufacture the sheds.

Limitations of expected values

1.  Expected value is an average and therefore only really applicable when there are repeated trials or decisions. Many business decisions are one-offs however.

2.  The probabilities employed will often be subjective estimates by managers and therefore influenced by their personalities (optimistic, pessimistic) and objectives of the individuals making the estimates.

3.  Although the EMV provides an average of the future values, it does not measure the degree of possible spread around the average (i.e. risk of the decision).

4.  It does not reflect the personal attitudes to risk of either individual managers or a group of managers.

5.  Individuals will not accept fair bets involving large amounts of money because they ‘care’ more about the possibility of loss than they do about the possibility of an equal gain. (Davies and Lam(2001:242).

EXPECTED VALUE OF PERFECT INFORMATION (EVPI)

Suppose a KMO Marketing Company claims that its technical analysis will tell Mr. Thambo with certainty whether or not the market is favourable for his proposed product. In other words KMO claims it can change his environment from one of decision making under risk to one of decision making under certainty. This information could prevent Thambo from making a very expensive mistake. For this service (information), KMO will charge $65 000. The question now is whether Thambo should hire the firm or not and whether even if the information is accurate, it is worth the amount. The value of such perfect information can be useful as it places an upper bound on what Thambo would be willing to spend on information such as being sold by KMO.

The Expected Value of Perfect Information (EVPI) and the Expected Value With Perfect Information (EVWPI) can help Thambo make his decision about the marketing consultant.

Expected Value With Perfect Information (EVWPI)

Is the average or expected value of the decision if you know what would happen ahead of time. You have perfect knowledge before a decision has to be made. In order to calculate this value choose the best alternative for each state of nature and multiply its pay-off times the probability of occurrence of that state of nature.

Expected Value With Perfect Information = (Best outcome for 1st state of nature) x (Prob. of 1st state of nature) + (best outcome for 2nd state of nature) x (Prob. of 2nd state of nature)------+ (Best outcome for last state of nature ) x (Prob. of last state of nature)

The Expected Value of Perfect Information, EVPI is the expected outcome with perfect information minus the expected outcome without perfect information, the maximum, EMV.

EVPI= Expected value with perfect information – maximum EMV or

EVPI=EVWPI-EMVmax

Under favourable market the best outcome is a pay-off of $200 000 (when he constructs a large facility) while under the unfavourable market condition the best is a pay-off of $0 when he does nothing.