A bank has a Mean operating Income of $78 413.99 and a Standard Deviation of the operating income is $385 962.44 thus the operating income appears to have a low mean, indicating an average on the investment profitability. however, the standard deviation suggests a significant level of variability of risk associated with the investment. Furthermore, the After Tax Income Analysis has a Mean of $90 022.98 and a Standard Deviation of After Tax Income of $1 124864.11, showing similarity to operating income, the Mean after-tax income is positive, but the high Standard Deviation indicated substantial risk and variability.

In Total, using a 95% confidence level the VaR for Operating Income is VaR OI = -$569 721.52 and the VaR for After Tax Income is = -$1800067.31. Thus, the negative VaR values, shows a significant downside risk associated with the investment.

Critically discuss each approach and recommend between the historical simulation and Monte Carlo simulation which one will better fit the above mentioned scenario in computing value-at-risk (VaR) and why. Also, explain what relevant evidence can or should be used to substantiate the responses because to fully understand the answer to the question, a full description and evaluation should be provided plus, it should be visible how they can be applied in the above mentioned scenario?