Expected Rate Of Return And Risk For BJ Gautney Enter 399051

Expected Rate Of Return And Risk Bj Gautney Enterprises Is Evaluati

Expected Rate Of Return And Risk Bj Gautney Enterprises Is Evaluati

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This assignment involves calculating the expected rate of return and the associated risk (standard deviation) for two investment scenarios. The first scenario considers an individual security, while the second involves an investment fund related to economic conditions. The core of the task is to analyze potential returns alongside their probabilities and determine whether these investments appear financially promising based on calculated metrics.

Paper For Above instruction

Introduction

Investment decision-making hinges critically on understanding both the expected returns and the associated risks associated with potential assets. The expected rate of return reflects the anticipated profitability of an investment, while risk measures its variability or volatility, often expressed as the standard deviation. Accurate estimation of these metrics enables investors to make informed decisions aligning with their risk tolerance and investment objectives. This paper thoroughly analyzes two investment scenarios: one involving a security evaluated against treasury bills, and another concerning a fund tied to economic outcomes, to assess their expected returns and risks.

Part 1: Expected Return and Risk of a Security

This scenario involves evaluating a security with a set of possible returns, each associated with a specific probability. The given data includes the probabilities and corresponding returns:

  • Probability 0.05, Return -4%
  • Probability 0.45, Return 1%
  • Probability 0.45, Return 7%
  • Probability 0.05, Return 9%

The goal is to compute the expected return using the formula:

Expected Return (ER) = Σ (Probability × Return)

Calculating each component:

  • 0.05 × (-4%) = -0.2%
  • 0.45 × 1% = 0.45%
  • 0.45 × 7% = 3.15%
  • 0.05 × 9% = 0.45%

Adding these up gives:

Expected Return = -0.2% + 0.45% + 3.15% + 0.45% = 3.85%

This indicates that the security’s expected return is approximately 3.85%.

Next, to determine the risk, we calculate the standard deviation of returns. The variance (σ²) is determined by summing the squared deviations weighted by probability:

Variance = Σ [Probability × (Return - ER)²]

Calculating each squared deviation:

  • For -4%: (-4% - 3.85%) = -7.85%; squared = 61.62
  • For 1%: (1% - 3.85%) = -2.85%; squared = 8.12
  • For 7%: (7% - 3.85%) = 3.15%; squared = 9.92
  • For 9%: (9% - 3.85%) = 5.15%; squared = 26.52

Weighted sum:

Variance = 0.05 × 61.62 + 0.45 × 8.12 + 0.45 × 9.92 + 0.05 × 26.52 = 3.08 + 3.65 + 4.46 + 1.33 = 12.52

The standard deviation is the square root of variance:

Standard Deviation = √12.52 ≈ 3.54%

Therefore, the security offers an expected return of approximately 3.85%, with a risk (standard deviation) of about 3.54%. Given these figures, if the risk level aligns with the investor’s appetite, and considering the risk-free rate of 4.6% from treasury bills, the security’s return does not outperform the risk-free alternative, suggesting limited attractiveness unless other factors are considered.

Part 2: Expected Return and Risk of an Investment Fund Based on Economic Outcomes

This scenario involves a fund whose performance depends on the state of the economy, with four possible outcomes:

  • Rapid expansion and recovery: Probability 10%, Return 100%
  • Modest growth: Probability 35%, Return 45%
  • Continued recession: Probability 50%, Return 20%
  • Falls into depression: Probability 10%, Return -100%

The expected return is calculated as:

ER = Σ (Probability × Return)

Calculating each component:

  • 0.10 × 100% = 10%
  • 0.35 × 45% = 15.75%
  • 0.50 × 20% = 10%
  • 0.10 × -100% = -10%

Sum total:

Expected Return = 10% + 15.75% + 10% - 10% = 25.75%

This indicates that the average expected return is approximately 25.75%, which appears attractive relative to the risk-free rate, assuming the probabilities accurately reflect real-world chances.

Next, the risk (standard deviation) is computed through the variance, involving squared deviations from the expected return:

Variance = Σ [Probability × (Return - ER)²]

Calculations of deviations squared:

  • (100% - 25.75%) = 74.25%; squared = 5518.56
  • (45% - 25.75%) = 19.25%; squared = 370.56
  • (20% - 25.75%) = -5.75%; squared = 33.06
  • (-100% - 25.75%) = -125.75%; squared = 15829.56

Weighted sum for variance:

Variance = 0.10 × 5518.56 + 0.35 × 370.56 + 0.50 × 33.06 + 0.10 × 15829.56 = 551.86 + 129.70 + 16.53 + 1582.96 = 2281.05

The standard deviation, reflecting the risk, is:

Standard Deviation ≈ √2281.05 ≈ 47.78%

This high level of risk indicates substantial volatility, which might be acceptable to aggressive investors but unsuitable for risk-averse individuals.

Conclusion

Analyzing both options demonstrates the importance of considering both expected return and risk in investment decisions. The security's expected return of 3.85% with a low risk profile suggests limited appeal, especially when risk-free treasury bills yield 4.6%. Conversely, the economic outcome-based fund offers a significantly higher expected return but also comes with substantial variability, emphasizing the necessity of aligning investment choices with one’s risk tolerance. Investors must evaluate whether the potential returns justify the considerable risk exposure. Proper assessment of these metrics allows investors to optimize their portfolios for maximum efficiency and suitability to their financial goals.

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