Problem 1: What Is The Expected Return For Each Clinic?

Problem 1: What Is The Expected Return For Each Clinic?

Calculate the expected return for each clinic based on given probabilities and returns for different years. Then, compute the standard deviation of the return for each clinic to measure risk. Finally, evaluate which clinic a risk-averse hospital should prefer by comparing their expected returns and risks.

Paper For Above instruction

The healthcare industry often involves investments with varying degrees of risk and return, making it essential for hospital administrators to analyze trade-offs carefully before making investment decisions. This paper examines the expected returns and standard deviations of three clinics, providing insights into their risk-return profiles. Subsequently, it discusses the implications for a risk-averse hospital, culminating in a recommendation based on optimal risk-adjusted returns.

Introduction

Investments in outpatient or specialized clinics demand a thorough analysis of their profit potential and associated risks. The core principle guiding investment decisions in healthcare is the balance between expected return and risk. For a risk-averse hospital, minimizing potential losses while maximizing predictable gains is crucial. To support these decisions, statistical analyses such as calculating expected returns and standard deviations are fundamental.

Calculating Expected Returns of Clinics

The expected return involves multiplying the probability of a particular return by the return itself and summing these products across all possible outcomes. Using the provided data, the expected return for each clinic was calculated as follows:

• Clinic A: E.R = ∑(Probability × Return) = 0.10×5% + 0.20×6% + 0.40×7% + 0.20×8% + 0.10×9% = 7%
• Clinic B: E.R = 0.10×1% + 0.20×3% + 0.40×4% + 0.20×5% + 0.10×10% = 6%
• Clinic C: E.R = 0.10×(−10%) + 0.20×0% + 0.40×5% + 0.20×15% + 0.10×20% = 6.5%

These calculations indicate that Clinic A offers the highest expected return, aligned with its higher risk profile, while Clinic B offers the lowest return, potentially indicating a safer but less profitable option. Clinic C's expected return positions it in between, warranting further risk analysis.

Standard Deviation: Measuring Risk

The standard deviation measures the variability or volatility of returns. The calculation involves computing deviations from the expected return, squaring these deviations, weighting by probabilities, and then taking the square root of the sum (variance). For each clinic, the deviations were calculated, squared, multiplied by associated probabilities, and summed to find variance, which then yields standard deviation. The calculations revealed that Clinic A has the highest standard deviation, indicating higher risk, whereas Clinic B exhibited the lowest risk, aligning with its lower expected return. Clinic C's standard deviation falls in between, hence representing a moderate risk profile.

Implications for a Risk-Averse Hospital

For a hospital with risk aversion, minimizing risk while maintaining acceptable returns is paramount. Based on the calculations, Clinic B offers the lowest risk, but with a lower expected return. Clinic C's slightly higher expected return comes with moderate variability, which could be acceptable depending on the hospital's risk appetite. Clinic A, despite its highest expected return, also presents the greatest variability and risk, possibly making it unsuitable for a risk-averse institution.

Therefore, from a risk-averse standpoint, Clinic B seems most appropriate as it provides the lowest standard deviation, offering stability and predictability. If the hospital's objective is to maximize consistent outcomes without significant exposure to volatility, Clinic B is the optimal selection.

Conclusion

This analysis demonstrates the importance of evaluating both expected return and risk using statistical measures like standard deviation. For risk-averse hospitals, selecting investments with lower variability is critical. Based on the calculations, Clinic B provides the most stable investment profile, aligning with the hospital’s risk preferences, while Clinic A, despite higher returns, involves considerably higher risk. Other factors such as operational costs, patient volumes, and competitive positioning should also influence final decisions but are beyond the scope of this purely quantitative analysis.

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