I simulate tomorrow’s return from the distribution
𝑁
𝑜
𝑟
𝑚
𝑎
𝑙
(
0
,
(
1
%
)
2
)
1000 times. All 1000 simulated returns are positive. What do you think?

Question

I simulate tomorrow’s return from the distribution 
𝑁
𝑜
𝑟
𝑚
𝑎
𝑙
(
0
,
(
1
%
)
2
)
 1000 times. All 1000 simulated returns are positive. What do you think?

BlackTom AI · Accepted Answer

The question presents a scenario of simulating tomorrow’s return from a normal distribution with mean 0 and standard deviation 1%? (the text shows N(0, (1%)^2) and 1000 trials), and notes that all 1000 simulated returns are positive. This prompts evaluation of whether such an outcome is plausible under the stated model and what action to take.

Option 1: 'It is bad luck. Let me re-run code and sample another 1000 numbers.' This response treats the all-positive outcome as mere unlucky sampling. While repeating simulations can help assess randomness, if the underlying model is correct and the distribution is Normal with symmetric support around zero, obtaining 1000 all-positive samples is extraordinarily unlikely (probability of all positive is 0.5^1000, effectively zero). This suggests a potential bug or mis-specification rather than just bad luck. However, the option also frames a plan to re-run without first diagnosing the root cause, which is not unreasonable but incomplete as a diagnostic step.

Option 2: 'It is bad luck, but ok. I should not re-run code. I should move on with the VaR by calculating the percentile of 1000 simulated numbers.' Here, the responder accepts the improbable outcome as luck and proceeds to VaR (Value at Risk) estimation using the current sample. This ignores the fundamental issue that a completely positive sample is inconsistent with a symmetric normal model unless the mean is heavily skewed or there is a data handling error. Relying on the flawed sample to compute VaR can lead to severely biased risk estimates. Thus, this option is flawed because it endorses proceeding despite a serious red flag.

Option 3: 'It is abnormal. I should go back and check the code or Excel formula.' This choice identifies the core problem: an all-positive set of 1000 draws from a symmetric normal distribution is highly improbable under a correctly specified model, indicating a possible bug in code, data transformation, or Excel formula (e.g., misinterpreting standard deviation, missing a sign, or applying absolute value somewhere). This option correctly elevates the need to diagnose the pipeline before trusting results or proceeding to risk calculations. It reflects sound data quality and model-checking practice.

In terms of reasoning nuances, note that the normal distribution N(0, (1%)^2) is symmetric around zero, so roughly half the draws should be negative. An outcome with zero negatives among 1000 observations should trigger a sanity check. If you discover a bug—such as taking absolute values, incorrectly scaling, or clipping values—the fix is essential before any interpretation or VaR computation. In general, when simulation outputs violate fundamental distributional properties, the responsible action is to inspect the data generation, sampling, and transformation steps, not to accept the result as legitimate or to proceed unadjusted.

Summarizing: Option 3 correctly flags the abnormality and prescribes debugging the generation process. Option 1 suggests re-running without diagnosis, which is not ideal given the red flag, though it’s not entirely unreasonable if the goal is to verify randomness. Option 2 endorses ignoring the issue and moving forward with VaR, which is inappropriate given the evidence of a potential problem. The safest and most methodologically sound first step is to check the code or Excel formula to locate and fix any bug or mis-specification.

BU.230.730.53.SP25 Final Exam- Requires Respondus LockDown Browser

I simulate tomorrow’s return from the distribution 𝑁 𝑜 𝑟 𝑚 𝑎 𝑙 ( 0 , ( 1 % ) 2 ) 1000 times. All 1000 simulated returns are positive. What do you think?

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