2. NATURE OF RISK
Risk exists because of the inability of the decisionmaker to make perfect
forecasts.
In formal terms, the risk associated with an likely to occur in the future returns
from the
investment may be defined as the variability that is investment.
Three broad categories of the events influencing the investment forecasts:
General economic conditions
Industry factors
Company factors
3. TECHNIQUES FOR RISK ANALYSIS
1. Statistical Techniques for Risk Analysis
a) Probability
b) Variance or Standard Deviation
c) Coefficient of Variation
2. Conventional Techniques of Risk Analysis
a) Payback
b) Risk-adjusted discount rate
c) Certainty equivalent
4. PROBABILITY
A typical forecast is single figure for a period. This is referred toas “best
estimate” or “most likely” forecast:
Firstly, we do not know the chances of this figure actually occurring, i.e., the
uncertainty surrounding this figure.
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 associated probability–a probability distribution.
Probability may be described as a measure of someone's opinion about the
likelihood that an event will occur
5. ASSIGNING PROBABILITY
The probability estimate, which is based on a very large number of
observations, is known as an objective probability.
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.
6. RISK AND UNCERTAINITY
Risk is referred to a situation where the probability distribution of the cash flow of an investment
proposal is known.
If no information is available to formulate a probability distribution of the cash flows the
situation is known as uncertainty.
EXPECTED NET PRESENT VALLUE
Once the probability assignments have been made to the future cash flows the next step is to
find out the expected net present value.
ENPV= 𝑡=0
𝑛
ENCF/(1 + 𝐾) 𝑛
Expected net present value = Sum of present values of expected net cash flows.
𝐸𝑁𝐶𝐹𝑡 = 𝑁𝐶𝐹𝑗𝑡 + 𝑃𝑗𝑡
7. EXAMPLE:
Suppose an investment project has a life of three years, and it would involve an initial cost of Rs
10,000
If the discount rate is 15 per cent, calculate the expected NPV
8.
9. VARIANCE OR STANDARD DEVIATION
Variance measures the deviation about expected cash flow of each of the possible cash flows.
Standard deviation is the square root of variance.
𝜎2 𝑁𝐶𝐹 = 𝑗=1
𝑛
(𝑁𝐶 𝐹𝑗 - ENCF)2 𝑃𝑗
Absolute Measure of Risk.
COEFFICIENT OF VARIATION
Coefficient of variation is relative Measure of Risk.
It is defined as the standard deviation of the probability distribution divided by its expected
value:
Coefficient of variation = standard deviation / expected value
10. COEFFICIENT OF VARIATION
The coefficient of variation is a useful measure of risk when we are comparing the projects
which have
• same standard deviations but different expected values, or
• different standard deviations but same expected values, or
• different standard deviations and different expected values.
