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Strategic Performance Management and Business Valuation · Risk Management

Risk Measurement and Assessment Techniques for CMA Final

Updated 11 October 2026 · Fact-checked

Risk measurement means putting numbers on uncertainty. You use probabilities to get expected value, standard deviation or coefficient of variation to show spread, sensitivity and scenario analysis to test changes in inputs, and Value at Risk (VaR) to state a likely worst-case loss. Compare options, then recommend one.

Understand Risk Measurement and Assessment Techniques

Risk is the chance that actual results differ from what you expected. You cannot manage it until you measure it. Measurement turns a vague worry into a number you can compare across projects, products or portfolios.

The starting point is probability analysis. You list possible outcomes and assign each a probability. The probability-weighted average is the expected value (EV). It tells you the central result, but not how uncertain it is.

To show uncertainty you use standard deviation (σ), which measures how far outcomes spread around the EV. A larger σ means higher risk. When projects have different EVs, use the coefficient of variation (CV), which is risk per rupee of expected return.

Sensitivity analysis changes one input at a time (say, selling price or volume) and shows how much the result, such as NPV, moves. Scenario analysis changes several inputs together to build a coherent case, such as best, base and worst. Sensitivity finds the key variable. Scenario shows the combined effect.

Value at Risk (VaR) states the maximum loss you expect not to exceed over a set period at a set confidence level. For example, a one-day 95% VaR of ₹10 lakh means that on 95 days out of 100 you expect the loss to be ₹10 lakh or less. It does not say how bad the loss can be in the remaining days. For qualitative risks, a risk matrix rates likelihood and impact to rank risks.

Key rules to remember

Expected value
EV = Σ (p × x)
Probabilities must add up to 1. x is the outcome for each case.
Variance
σ² = Σ p × (x − EV)²
Use deviations from the EV, weighted by probability.
Standard deviation
σ = √σ²
Same unit as the outcome. Higher σ means higher absolute risk.
Coefficient of variation
CV = σ ÷ EV
Use to compare options with different EVs. Lower CV means less risk per unit of return.
Sensitivity (margin of safety in a variable)
% change tolerable = NPV ÷ PV of that variable's cash flows × 100
Shows how far the variable can fall before NPV becomes zero. Apply to one variable only.
Parametric VaR (normal distribution)
VaR = Z × σ × Value of position, scaled for time by √t
Z is about 1.65 at 95% and about 2.33 at 99% (one-tailed). Assumes normal returns.
Risk score in a matrix
Risk score = Likelihood rating × Impact rating
Use the rating scale given in the question. Higher score means higher priority.

How to solve Risk Measurement and Assessment Techniques questions

Use this order for any numerical or descriptive question on risk measurement.

  1. 1Identify what is asked: EV, spread, comparison, sensitivity, scenario or VaR.
  2. 2List outcomes and probabilities. Check that probabilities add up to 1.
  3. 3Compute the EV first, as every other measure depends on it.
  4. 4Compute deviations, variance and σ. Add CV if the EVs differ.
  5. 5For sensitivity or scenario questions, recompute the result (such as NPV) for each changed input and show the change.
  6. 6For VaR, pick Z from the confidence level, then multiply by σ and the position value, adjusting for time if needed.
  7. 7Compare and give a clear recommendation, stating the risk-return trade-off.
  8. 8State the key limitation, such as the normal-distribution assumption or one-variable-at-a-time change.

Quickest way: Table-first method for EV and σ

When to use it: Use for any question with a probability distribution of outcomes and a request for EV, σ or a choice between options.

  1. Draw columns: x, p, p×x, (x − EV)², p×(x − EV)².
  2. Fill p×x and total it to get EV.
  3. Fill the deviation columns using that EV and total to get variance.
  4. Take the square root for σ.
  5. If EVs differ, divide σ by EV for CV and choose the lower CV.
  6. If EVs are equal, choose the lower σ.

Common mistakes in Risk Measurement and Assessment Techniques

  • Using σ to compare projects with different expected values.

    σ looks like the complete risk figure.

    Fix: Calculate CV = σ ÷ EV and compare that. Use σ alone only when EVs are equal.

  • Taking deviations from a simple average instead of the EV.

    Students ignore the probabilities.

    Fix: Always weight by p and measure deviation from the probability-weighted EV.

  • Forgetting to take the square root, and reporting variance as σ.

    Rushing at the last step.

    Fix: End every table with σ = √variance and label the unit.

  • Changing several variables at once in sensitivity analysis.

    Confusing it with scenario analysis.

    Fix: Change one variable and hold the rest constant. Move several together only in scenario analysis.

  • Reading VaR as the maximum possible loss.

    The word 'maximum' in the definition is misread.

    Fix: Say the loss is not expected to exceed VaR at the stated confidence level. Losses beyond it can occur.

Worked examples

Example 1

Project A has cash inflow outcomes of ₹40,000, ₹60,000 and ₹80,000 with probabilities 0.3, 0.5 and 0.2. Project B has an EV of ₹90,000 and σ of ₹27,000. Which project has lower risk per rupee of return?

Show the solution
  1. EV of A = (0.3 × 40,000) + (0.5 × 60,000) + (0.2 × 80,000) = 12,000 + 30,000 + 16,000 = ₹58,000.
  2. Deviations from 58,000: −18,000, +2,000, +22,000.
  3. Variance = 0.3 × 18,000² + 0.5 × 2,000² + 0.2 × 22,000² = 0.3 × 324,000,000 + 0.5 × 4,000,000 + 0.2 × 484,000,000 = 97,200,000 + 2,000,000 + 96,800,000 = 196,000,000.
  4. σ of A = √196,000,000 = ₹14,000.
  5. CV of A = 14,000 ÷ 58,000 = 0.241.
  6. CV of B = 27,000 ÷ 90,000 = 0.300.
  7. A has the lower CV.

Answer: Project A: EV ₹58,000, σ ₹14,000, CV 0.241. Project B: CV 0.300. Project A carries less risk per rupee of expected return and is preferable on this measure.

Example 2

A firm holds a portfolio worth ₹5,00,00,000. Daily return σ is 1%. Using the normal distribution with Z = 1.65 for 95% confidence, compute the one-day VaR and the 4-day VaR, and explain what the one-day figure means.

Show the solution
  1. One-day VaR = 1.65 × 1% × ₹5,00,00,000.
  2. 1% of ₹5,00,00,000 = ₹5,00,000.
  3. One-day VaR = 1.65 × 5,00,000 = ₹8,25,000.
  4. 4-day VaR = one-day VaR × √4 = 8,25,000 × 2 = ₹16,50,000.
  5. Interpretation: on 95 days out of 100, the one-day loss is expected to be ₹8,25,000 or less.

Answer: One-day 95% VaR is ₹8,25,000 and 4-day 95% VaR is ₹16,50,000. On the remaining days losses may exceed VaR, and VaR does not say by how much.

Exam tips

  • Show the table layout for EV and σ. Marks are given for each step even if the final figure slips.
  • End numerical answers with a recommendation. Examiners reward the decision, not only the figure.
  • In sensitivity versus scenario questions, state the difference in one line: one variable at a time versus several together.
  • For VaR theory, always mention confidence level, time horizon and the normality limitation.
  • In MCQs, check whether the question gives variance or σ before substituting into CV.

Practice questions from Risk Management

Risk Measurement and Assessment Techniques in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Risk Measurement and Assessment Techniques: frequently asked questions

What is the difference between sensitivity analysis and scenario analysis?

Sensitivity analysis changes one variable at a time to see its effect on the result. Scenario analysis changes several variables together to form cases such as best, base and worst. Sensitivity finds the critical variable, while scenario shows the combined impact.

When should I use coefficient of variation instead of standard deviation?

Use CV when the options have different expected values. It gives risk per unit of expected return. If EVs are equal, standard deviation alone is enough.

What does a 95% VaR mean in simple words?

It is the loss you expect not to exceed on 95 out of 100 periods. In the other periods the loss could be higher. It is a threshold, not a worst-case limit.

How does a risk matrix work?

You rate each risk for likelihood and for impact, often on a scale such as 1 to 5. Multiplying the two gives a score. Higher scores are treated first.