Question

Risk analysis question-

(a) Explain in words how the math is supposed to work for calculating the number of scenarios. (b) Show the arithmetic behind calculating the final value. (c) Why is it important to be able to estimate the number of scenarios before beginning your full assessment?

Answer 1

Mathematics, as an analytical tool, is one of the best methods to evaluate the quantum of risk and return associated with a particular investment in due course of time. Mathematics and Statistics play an important role in determining the probable cases of return of loss associated with a particular investment. The mathematical based analysis provide an estimate of the expected value of a portfolio after a given period of time, assuming specific changes in the values of the portfolio's securities or key factors take place, such as a change in the interest rate.
And the Scenario analysis is commonly used to estimate changes to a portfolio's value in response to an unfavorable event, and may be used to examine a theoretical worst-case scenario. A common method is to determine the ‘standard deviation’ of daily or monthly security returns/risks associated and then computing the expected value for the portfolio if the security generates returns that are two or three standard deviations above and below the average return. Scenarios being considered can relate to a single variable, such as the relative success or failure of a new product launch, or a combination of factors. Estimation of risk is one of the most important stages of risk management and it is necessary to analyze and evaluate the probable scenarios associated with an investment. Statistical evaluation methods allow obtaining the most complete quantitative picture of the level of risk, and often it is used in the practical activity of financial management, and determines the probability of loss based on statistical data of the previous period and the establishment of the area (zone) of risk, risk factor, etc. Analogy evaluation methods are allowing to define the probable scenarios or level of probability of the risk of some of the most frequently used operations of the company. Furthermore, to be able to adequately understand the terms of a loan or an investment account and risk associated, a basic understanding of higher math such as Algebra would be required.
The arithmetic behind calculating the final value of Risk or the return associated with the investment includes usage of various mathematical formulae and functions which may be given as:-
-   Standard deviation calculates the probable scenarios of risk and its frequency of occurrence.
-   Arithmetic or Geometric Mean, Weighted Average Return, etc. determines the average return or risk associate with an investment.
-   Normal Distribution function provides an estimate of portfolio mix and associated risk and return.
-   Value At Risk (VAR) Models (Variance/Covariance, Monte Carlo Simulation, Historical Simulation, etc) assist the management about the risk profile of the firm and to protect it against unacceptably large losses resulting from concentration of risks.
It is important to estimate the number of scenarios before beginning for the full assessment of the risk associated with an investment, as the diversity of the probable scenarios provide a standard about the quantum of Risk associated with a particular investment under different business conditions. The methods used in determining the scenarios of the amount of risk, helps in project planning and gives an estimate of returns and various profitability ratios related to the investment.