hello so i got a question and have two different answers one of them is mine i just wanna know which one is accurate or more accurate then the othen:

question:

A financial investor builds a portfolio that is worth an expected $35$mil. The investor knows that his analysts can build a model to boost the potential return from the portfolio investment. The additional return has a Normal Distribution with mean $3$mil and standard deviation $0\mathrm{.}5$mil. The investor wishes to sell his financial services at a price that guarantees his expected profit will be $5\%$ of the total return from the portfolio.

$1)$ Simulate $($with a min of $200$ repetitions$)$ the average and the standard deviation of the profit the financial advisor realizes when setting the price for his services between $1\%$ and $10\%$ of the total expected return from the portfolio. Then discuss your findings.

answer $1$:

Price $(\%$ of portfolio return$)|$ Average Profit $($mil$)|$ Standard Deviation $($mil$)$

$1\%|0\mathrm{.}8|10\mathrm{.}191$

$2\%|1\mathrm{.}3|10\mathrm{.}245$

$3\%|1\mathrm{.}8|10\mathrm{.}288$

$4\%|2\mathrm{.}3|10\mathrm{.}327$

$5\%|2\mathrm{.}8|10\mathrm{.}362$

$6\%|3\mathrm{.}3|10\mathrm{.}393$

$7\%|3\mathrm{.}8|10\mathrm{.}421$

$8\%|4\mathrm{.}3|10\mathrm{.}446$

$9\%|4\mathrm{.}8|10\mathrm{.}468$

$10\%|5\mathrm{.}3|10\mathrm{.}487$

These results demonstrate that the average profit rises with the price of the financial service, which is to be expected given that the investor keeps a higher portion of the total return. But the standard deviation also rises, suggesting that there is more uncertainty or risk involved in the profits. This implies that the investor must strike a balance between controlling the risk brought on by profit volatility and setting a higher price to maximise profit.

answer $2)$

We will use:

$$ Portfolio value: $35$ million

$$ Mean of additional return: $3$ million

$$ Standard deviation of additional return: $0\mathrm{.}5$ million

$$ Total expected return: $38$ million

Let's proceed with the simulation for each price point from $1\%$ to $10\%$ of $38$ million, calculate the average profit, and standard deviation, then compare to your table.

The simulation results show a significant deviation from the table you provided. Here's a summary of our simulated results:

Price $(\%$ of portfolio return$)$ Average Profit $($mil$)$ Standard Deviation $($mil$)$

$1\%2\mathrm{.}70\mathrm{.}511$

$2\%2\mathrm{.}20\mathrm{.}472$

$3\%1\mathrm{.}80\mathrm{.}516$

$4\%1\mathrm{.}40\mathrm{.}486$

$5\%1\mathrm{.}10\mathrm{.}470$

$6\%0\mathrm{.}80\mathrm{.}461$

$7\%0\mathrm{.}30\mathrm{.}483$

$8\%0\mathrm{.}00\mathrm{.}502$

$9\%-0\mathrm{.}40\mathrm{.}504$

$10\%-0\mathrm{.}80\mathrm{.}465$

Key Observations:

$$ As the price percentage increases from $1\%$ to $10\%,$ the average profit initially decreases from $2\mathrm{.}7$ to $0\mathrm{.}8$ million, and then becomes negative. This is different from your results where the average profit continuously increases as the percentage price increases.

$$ Standard deviations are generally around $0\mathrm{.}5$ million, showing some level of variability but not dramatically increasing with the price as suggested in your table.

Conclusion:

$$ The findings from the simulation suggest a different trend compared to what was indicated in your answer. Instead of profits increasing with higher price percentages, profits actually decrease and become negative as the price surpasses the additional return's mean $(3$ million$),$ reflecting the diminishing returns and the set prices cutting into the potential profit.

$$ The original answer's assertion that profits increase as the pricing percentage increases does not align with our simulations, which may be due to assumptions about the variability and distribution of the additional returns, or a misunderstanding of how the price affects net profits when additional returns are normally distributed with a fixed mean and standard deviation.