ERT is choosing between two maintenance policies for its vehicles. The outcomes of these policies are difficult to predict and so ERT has run a…

This question assesses the interpretation of statistical measures—expected value (mean) and standard deviation—in a risk management context.

(A) Risk is quantified by the variability of outcomes, for which standard deviation is a primary measure. Policy 2 has a standard deviation of $150,000, which is significantly higher than Policy 1's $80,000. Therefore, Policy 2's outcomes are more dispersed and less predictable, making it the riskier option.

(C) Assuming a normal distribution for the simulated outcomes, we can use Z-scores to compare probabilities. For Policy 2, the $500,000 cost is only 1.0 standard deviation above its mean ($150k/$150k). For Policy 1, it is 1.25 standard deviations above its mean ($100k/$80k). A lower Z-score corresponds to a higher probability of exceeding that value, making Policy 2 more likely to surpass $500,000.

(D) "Upside risk" in a cost scenario refers to the potential for costs to be significantly lower than expected. Policy 2's larger standard deviation means its outcomes are more widely spread on both sides of the mean. This creates a greater potential for very low costs (upside) as well as very high costs (downside) compared to the less volatile Policy 1.

B. Policy 1 will always be the more expensive in any given period.

This is incorrect because the expected value is an average, not a guaranteed outcome. The distributions of possible costs overlap, so a low-cost outcome for Policy 1 could be cheaper than a high-cost outcome for Policy 2.

E. Policy 2 is clearly the better policy.

This is incorrect because the choice depends on ERT's risk appetite. A risk-averse entity might prefer the certainty of Policy 1 despite its higher expected cost, while a risk-seeking entity might be attracted by Policy 2's lower expected cost, accepting the higher risk.

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1. For Standard Deviation as a Measure of Risk (A):

Drury, C. (2018). Management and Cost Accounting (10th ed.). Cengage Learning EMEA. In Chapter 19, "Quantitative methods in decision making," the standard deviation is presented as a fundamental measure of the risk or dispersion of possible outcomes around the expected value. (Specifically, see sections on decision making under conditions of risk and uncertainty).

2. For Probability Calculation using Z-scores (C):

Bertsimas, D., & Freund, R. M. (2004). Data, Models, and Decisions: The Fundamentals of Management Science. Dynamic Ideas. Chapter 6, "Simulation," discusses how to analyze the output of simulations, including using the mean and standard deviation to calculate probabilities of specific outcomes, often by assuming a normal distribution and using Z-scores. (See Section 6.5, "Analysis of Simulation Output").

3. For Upside/Downside Risk and Risk Appetite (D & E):

CIMA. (2019). CIMA P3 Risk Management Study Text. Kaplan Publishing. Chapter 3, "Risk Identification and Measurement," explains that standard deviation measures total volatility, encompassing both downside and upside potential. The text also emphasizes throughout that the selection of a course of action depends on balancing risk and return according to the organization's specific risk appetite, meaning no single option is universally "better."