**Statistical Techniques for Risk Analysis**

Statistical techniques are analytical tools for handling risky investments. These techniques, drawing from the fields of mathematics, logic, economics and psychology, enable the decision-maker to make decisions under risk or uncertainty.

The concept of probability is fundamental to the use of the risk analysis techniques. Hoe is probability defined? How are probabilities estimated? How are they used in the risk analysis techniques? How do statistical techniques help in resolving the complex problem of analyzing risk in capital budgeting? We attempt to answer these questions in our posts.

**Probability defined**

The most crucial information for the capital budgeting decision is a forecast of future cash flows. A typical forecast is single figure for a period. This referred to as “best estimate” or “most likely” forecast. But the questions are: To what extent can one rely this single figure? How is this figure arrived at? Does it reflect risk? In fact, the decision analysis is limited in two ways by this single figure forecast. Firstly, we do not know the changes of this figure actually occurring, i.e. the uncertainty surrounding this figure. In other words, we do not know the range of the forecast and the chance or the probability estimates associated with figures within the range. Secondly, the meaning of best estimates or most likely is not very clear. It is not known whether it is mean, median or mode. For these reasons, a forecaster should not give just one estimate, but a range of associate probability- a probability distribution.

Probability may be described as a measure of someone’s option about the likelihood that an event will occur. If an event is certain to occur, we say that it has a probability of one of occurring. If an event is certain not to occur, we say that its probability of occurring is zero. Thus, probability of all events to occur lies between zero and one. A probability distribution may consist of a number of estimates. But in the simple form it may consist of only a few estimates. One commonly used form employs only the high, low and best guess estimates, or the optimistic, most likely and pessimistic estimates.

**Assigning probability**

The classical probability theory assumes that no statement whatsoever can be made about the probability of any single event. In fact, the classical view holds that one can talk about probability in a very long run sense, given that the occurrence or non-occurrence of the event can be repeatedly observed over a very large number of times under independent identical situations. Thus, the probability estimate, which is based on a very large number of observations, is known as an

**objective probability**.

The classical concept of objective probability is of little use in analyzing investment decision because these decisions are non-respective and hardly made under independent identical conditions over time. As a result, some people opine that it is not very useful to express the forecaster’s estimates in terms of probability. However, in recent years another view of probability has revived, that is, the personal view, which holds that it makes a great deal of sense to talk about the probability of a single event, without reference to the repeatability, long run frequency concept. Such probability assignments that reflect the state of belief of a person rather than the objective evidence of a large number of trials are called personal or

**subjective probabilities**.

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