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Measurement Of Risk

Sensitivity Analysis Assignment / Homework Help
Methods of Calculating Total Risk

The risk associated with a single asset is measured from both a behavioural and a statistical (quantitative) point of view.

The behavioural risk view is measured using:
  • Sensitivity analysis and
  • Probability distribution
The statistical risk view is measured using:
  • Standard deviation and
  • Coefficient of variation.

Behaviour Risk views:
  • Sensitivity analysis
    Sensitivity analysis is one of the simplest ways of handling risk. It consists of examining the magnitude of change in the rate of return for the project, for a small change in each of its components which are uncertain. The best possible way is to select these variables whose estimated value may contain significant errors or element of uncertainty and then to calculate the effect of errors of different sizes on the present value of the project. Some of the key variables are cost, price, project life, market share etc. Sensitivity analysis takes into account a number of possible outcome estimates while evaluating an asset risk. In order to have a sense of the variability among return estimates, a possible approach is to estimate the worst(pessimistic), the expected(most likely) and the best(optimistic) returns associated with the asset. The difference between the optimistic and the pessimistic outcomes is the range, which according to the sensitivity analysis is the basic measure of risk. The greater the range, the more is the risk and vice versa.

    Example:

    Particulars Asset X Asset Y
    Initial investment(t=0) 50 50
    Annual return(%)
    Pessimistic 13 7
    Most likely 15 14
    Optimistic 17 21
    Range 4 14

    Asset Y is more risky than Asset X on the basis of annual returns.
  • Probability distribution
    Probability may be described as the measure of likelihood of an eventís occurrence. The risk associated with an asset can be assessed more accurately by the use of probability distribution than sensitivity analysis. For example, if the expectation is that a given outcome or return will occur six out of ten times, it can be said to have sixty percent chance of happening; if it is certain to happen, the probability of happening is 100%. An outcome which has a probability of zero will never occur. So, on the basis of the probability distributed or assigned to the rate of return, the expected value of the return can be computed. The expected rate of return is the weighted average of all possible returns multiplied by their respective probabilities and those probabilities of the various outcomes are used as weights. The expected return(R),

    R = ∑ n Ri x Pri
          i=1
    Where:
    Ri = Return for the ith possible outcome
    Pri = Probability of its outcome / return
    n = Number of outcomes considered

    Example:
    Let us calculate the expected return of two assets X & Y, whose probability of generating pessimistic returns of 13% and 7% is 30%, most likely returns of 15% and 14% is 30% and optimistic returns of 17% and 21% is 40%, respectively.

    Possible outcomes Probability Returns Expected Returns
    ASSET X (P) (R) (P x R)
    Pessimistic 0.30 13% 3.9
    Most likely 0.30 15% 4.5
    Optimistic 0.40 17% 6.8
       Expected return 15.2
    ASSET Y
    Pessimistic 0.30 7% 2.1
    Most likely 0.30 14% 4.2
    Optimistic 0.40 21% 8.4
       Expected return 14.7

    From the above risk analysis, Asset X seems to have a higher expected return and would be preferred over Asset Y.
Statistical risk views:
  • Standard Deviation:
    The most common statistical measure of risk of an asset is the standard deviation from the mean or expected value of return. It represents the square root of the average squared deviations of the individual returns from the expected returns. The standard deviation can be represented as thus:
                                           
    σ = n (Ri - R)2 x Pri
              i=1

    Where:
    Ri = Return for the ith possible outcome
    R = mean of the returns ( Pri and n as given above)

    Example: Let us calculate the standard deviation for the returns of assets X & Y. (data as given above)

    i Ri R Ri - R ( Ri - R)2
    A
    Pri
    B
    A X B
    1 13% 15% (-2)% 4% 0.30 1.20%
    2 15% 15% 0 0 0.30 0
    3 17% 15% 2% 4% 0.40 1.60%
    Total (x) 2.80%
    1 7% 14% (-7)% 49% 0.30 14.7%
    2 14% 14% 0 0 0.30 0
    3 21% 14% 7% 49% 0.40 19.6%
    Total (Y) 34.3%

    Standard deviation of Asset X = √2.80 = 1.67%
    Standard deviation of Asset Y = √34.3 = 5.86%

    If the standard deviation is greater, the variability and thus risk is also greater and vice versa. According to this measure, Asset Y is riskier than Asset X.

  • Coefficient of variation:
    It is a measure of relative dispersion or a measure of risk per unit of expected return. It converts standard deviation of expected values into relative units and thus facilitates comparison of risks associated with assets having different expected values. It is calculated by dividing the standard deviation of an asset by its expected value.

    CV = σrR

    Example: Let us calculate the coefficient of variations for the assets X and Y(data as given above).

    CV of asset X => 1.67 / 15 => 0.111

    CV of asset Y => 5.86 / 14 => 0.419

    If the coefficient of variation is greater, the risk is greater and vice versa. According to this measure, Asset Y is riskier than Asset X. As this measure considers the expected value of assets, it is considered the best method for comparing risks.

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