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 where 1000 simulated returns from a Normal distribution with mean 0 and a very small standard deviation (likely 1%), and all 1000 draws turn out positive. Now, evaluate each option in turn.

Option 1: 'It is bad luck. Let me re-run code and sample another 1000 numbers.' This stance treats the observed outcome as a matter of chance and suggests re-sampling. While randomness exists in simulations, getting all 1000 draws positive from a distribution centered at zero with a small standard deviation is extremely unlikely. This option misses the potential need to diagnose whether the simulation setup (mean, variance, or data generation) is correct, and it delays ensuring the model is implemented properly. The expectation under normal sampling would be some negative values as well, so this option leans toward treating an improbable event as routine luck without inspection.

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 respondent accepts the unusual outcome as bad luck but chooses to proceed with VaR calculations based on an all-positive sample. Using a sample that shows no negatives will bias percentile estimates (e.g., the 5th percentile would be near the minimum of the sample, which is not representative of the true distribution). In risk management, relying on an unrepresentative sample can lead to severely underestimating risk. This option fails to address the fundamental anomaly and risks propagating a biased result.

Option 3: 'It is abnormal. I should go back and check the code or Excel formula.' This statement directly flags the improbable event and advocates a diagnostic step to verify the data generation process. Given a normal model with mean zero and small volatility, the probability that all 1000 draws are positive is astronomically small (the event is far into the tail of the distribution). Such an outcome strongly suggests a bug or mis-specification (e.g., using absolute values, mis-specified parameters, truncation, or incorrect application of the normal distribution). This option correctly prioritizes verification of the model, calculation, and data pipeline before drawing conclusions or proceeding with risk metrics.

In summary, Option 1 attributes the result to luck without investigation, which is misleading given the extreme rarity of the event. Option 2 accepts the unlikely sample and proceeds with potentially biased risk estimates, which is unsafe in practice. Option 3 appropriately identifies the abnormal result and recommends checking the underlying code or formula to ensure the simulation accurately reflects the intended distribution. The reasoning emphasizes the importance of validating data generation in quantitative analyses before relying on the results for decision-making.

BU.230.730.52.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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