Scenario: Deciding Whether To Consult An Expert For Investme

Scenario: Deciding Whether to Consult an Expert for Investment Analysis

You are deciding among three investments and considering whether to consult an expert with a highly reliable track record in predicting favorable or unfavorable market conditions. The goal is to determine whether the value of the expert’s predictions justifies paying for his advice. You need to perform a decision analysis using probabilities, expected net present values (NPVs), and the expert’s predictive accuracy to evaluate the potential benefit of consulting the expert.

The three investment options are:

• Option A: Real estate development with a high payoff of $7.5 million if the market is favorable (probability 0.5), and a lower payoff of $2 million if unfavorable (probability 0.5).
• Option B: Retail franchise for Just Hats, with a favorable NPV of $4.5 million (probability 0.75), and an unfavorable NPV of $2.5 million (probability 0.25).
• Option C: High-yield municipal bonds with a certain NPV of $2.25 million (probability 1.0).

The expert has a proven track record in predicting market conditions, with the following accuracy:

• Predicts “Favorable” when the market is favorable with probability 0.9, and predicts “Unfavorable” with probability 0.7 when the market is unfavorable.

You also have prior estimates of joint probabilities for the markets, such as the likelihood that both markets are favorable, both are unfavorable, or one is favorable and the other unfavorable. These probabilities are necessary for a comprehensive analysis, especially given that the expert's predictions relate to two different markets: real estate and retail hats.

The task involves filling in the decision tree with the relevant probabilities, calculating the expected NPVs assuming no expert consultation, then including the expert’s predictions and posterior probabilities to determine the expected value if you decide to consult the expert. The core question is whether the expected increase in value from consulting the expert justifies paying his fee.

Paper For Above instruction

In uncertain investment environments, decision-makers must weigh the benefits of gathering additional information against the costs associated with obtaining it. The scenario at hand involves evaluating three investment opportunities—the real estate development, retail franchise for Just Hats, and municipal bonds—while considering the potential value of an expert’s market predictions. This paper explores how utilizing a decision tree analysis incorporating prior probabilities, expert prediction accuracy, and updated posterior probabilities can inform whether consulting the expert adds value to the investment decision-making process.

Understanding the initial expected values of investments forms the baseline for this analysis. The real estate development offers a 50% chance of a high payoff of $7.5 million, and a 50% chance of $2 million if the market turns unfavorable. The retail franchise presents a higher likelihood (75%) of a favorable outcome with an NPV of $4.5 million, and a 25% chance of an unfavorable return of $2.5 million. Municipal bonds are straightforward, offering a certain NPV of $2.25 million, reflecting low risk and certainty in returns.

The primary consideration involves the expert’s predictive accuracy, which is notably high when forecasting favorable markets (90%) but less reliable when predicting unfavorable markets (70%). Given these figures, the value of perfect or imperfect information can be quantified within the decision tree. Initial priors suggest a 45% probability that both markets will be favorable as predicted by the expert, with respective probabilities for other prediction combinations (e.g., "Favorable-Favorable," "Favorable-Unfavorable," etc.) derived from joint probabilities.

The decision analytic process proceeds by constructing the decision tree with branches representing different market conditions, the expert’s predictions, and associated posterior probabilities. The calculation involves updating the probabilities based on the expert’s predictions using Bayes’ theorem, and then computing the expected NPVs for each possible decision node.

Inserting the posterior probabilities into the decision tree reveals how much additional value the expert’s forecast provides. If the expected NPV of choosing to consult the expert exceeds that of making an immediate decision without consultation, then the consultation is justified financially. Conversely, if the expected value does not increase sufficiently to cover the expert’s fee, then relying solely on prior estimates may be more advantageous.

The results from the analysis generally suggest that expert opinions – especially when highly reliable – can significantly alter decision outcomes. When the expert correctly predicts favorable markets, the expected NPVs increase, potentially leading to more aggressive investment strategies such as real estate development. Conversely, if the expert’s predictions tend to be uncertain or incorrect, the value of additional information diminishes.

In conclusion, the decision to consult the expert should hinge on a quantitative assessment of the expected value of their predictions compared to the cost incurred. This analysis demonstrates that, in scenarios where expert predictions are highly accurate, leveraging such information can enhance investment decisions significantly—potentially increasing expected NPVs—thus justifying the consultation fee. When the predictive accuracy is less assured, the benefit diminishes, and reliance on original priors may be more sensible. Ultimately, decision-makers should employ these probabilistic analyses to optimize their choices under uncertainty, ensuring resources are allocated efficiently to maximize investment returns.

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