Expected Rate Of Return And Risk At Bj Gautney Enterprises

Expected Rate Of Return And Risk Bj Gautney Enterprises Is Evalu

Evaluate the expected rate of return and associated risk for various investment opportunities based on provided probabilities, returns, and economic scenarios. This includes calculating the expected return and standard deviation for a security similar to one-year Treasury bills, and assessing potential investments in a new fund linked to national economic outcomes, considering their probable returns and associated risks.

Paper For Above instruction

Investment decisions fundamentally revolve around understanding the expected returns and associated risks of various assets. Two primary components of investment analysis are the expected rate of return and the risk, which can be quantified through measures like standard deviation. This paper explores these concepts by analyzing a security similar to one-year Treasury bills and evaluating two different investment opportunities presented by scenarios involving economic states and associated returns.

Analysis of Treasury Bill-Like Security

Treasure bills are considered among the safest short-term investments, especially when government-backed. The current yield on one-year Treasury bills is indicated as 4.6%, serving as a baseline for comparison. To calculate the expected return and standard deviation of an investment similar to these bills, we generally need the probability distribution of potential returns. Despite the vague data provided in the initial prompt, a typical method involves assigning probabilities to different return scenarios and calculating the weighted average returns (expected return) alongside the variance and standard deviation, which gauge the risk.

Given that the investment mirrors Treasury bills, the expected return would likely hover around 4.6%, assuming the probability of returns being exactly the current Treasury yield. However, if there's additional variance due to inflation, interest rate fluctuations, or slight market risks, these would increase the standard deviation beyond zero. It is essential to note that Treasury bills are regarded as risk-free or minimal risk investments, implying their standard deviation is very low.

Therefore, assuming a simplified scenario where the expected return equals the current yield and the risk is minimal, one could estimate the expected return as approximately 4.6%, with a standard deviation approaching zero, aligning with their status as risk-free assets. More precise calculations would require explicit probability distributions of potential returns, which are not fully provided here.

Investment in a New Fund Based on Economic Scenarios

The second scenario involves evaluating an investment fund whose performance depends on the future state of the economy. The fund's returns are contingent on economic growth or recession, with specific probabilities assigned to different scenarios. The core goal is to calculate the expected rate of return and the associated risk — measured as standard deviation — based on these probabilities and returns.

Scenario 1: First Set of Outcomes

In the first case, we are provided with the following data:

  • Rapid expansion and recovery: Probability = 10%, Return = 100%
  • Modest growth: Probability = 35%, Return = 40%
  • Continued recession: Probability = 45%, Return = 20%
  • Falls into depression: Probability = 10%, Return = -100%

The expected return (E) is calculated using the formula:

E = ∑ (Probability × Return)

Applying the data:

Expected Return = (0.10 × 100%) + (0.35 × 40%) + (0.45 × 20%) + (0.10 × -100%)

= 10 + 14 + 9 - 10 = 23%

Thus, the estimated expected return for this set of economic scenarios is approximately 23%.

Risk Assessment: Standard Deviation

To assess the risk, we calculate the variance and then the standard deviation. The variance is the weighted average of squared deviations from the expected return:

Variance = ∑ (Probability × (Return - E)^2)

Calculating each component:

  • (0.10 × (100% - 23%)^2) = 0.10 × (77%)^2 = 0.10 × 5929 = 592.9
  • (0.35 × (40% - 23%)^2) = 0.35 × (17%)^2 = 0.35 × 289 = 101.15
  • (0.45 × (20% - 23%)^2) = 0.45 × (-3%)^2 = 0.45 × 9 = 4.05
  • (0.10 × (-100% - 23%)^2) = 0.10 × (-123%)^2 = 0.10 × 15129 = 1512.9

Sum of variances = 592.9 + 101.15 + 4.05 + 1512.9 = 2211

The standard deviation (σ) is the square root of variance:

σ = √2211 ≈ 47.04%

The high standard deviation indicates substantial risk associated with this investment given the wide distribution of potential outcomes.

Investment Viability

With an expected return of approximately 23% and a standard deviation of about 47%, this investment appears to offer high potential gains but also significant risk. An investor with a high-risk tolerance might find this attractive, particularly if they believe the economic scenarios align with optimistic outcomes. Conversely, risk-averse investors might be cautious due to the possibility of large losses in adverse economic states, such as depression.

Scenario 2: Second Set of Outcomes

The second set of data is as follows:

  • Rapid expansion and recovery: Probability = 10%, Return = 9%
  • Modest growth: Probability = 45%, Return = 7%
  • Continued recession: Probability = 45%, Return = 1%
  • Falls into depression: Probability = 5%, Return = -4%

Calculating the expected return:

Expected Return = (0.10 × 9%) + (0.45 × 7%) + (0.45 × 1%) + (0.05 × -4%)

= 0.9 + 3.15 + 0.45 - 0.2 = 4.3%

The expected return for this diverse set of economic outcomes is approximately 4.3%, considerably lower than the previous scenario, indicating a more conservative outlook.

  • Variance components:

(0.10 × (9% - 4.3%)^2) = 0.10 × (4.7%)^2 = 0.10 × 22.09 = 2.209

(0.45 × (7% - 4.3%)^2) = 0.45 × (2.7%)^2 = 0.45 × 7.29 = 3.28

(0.45 × (1% - 4.3%)^2) = 0.45 × (-3.3%)^2 = 0.45 × 10.89 = 4.9

(0.05 × (-4% - 4.3%)^2) = 0.05 × (-8.3%)^2 = 0.05 × 68.89 = 3.44

Sum of variances = 2.209 + 3.28 + 4.9 + 3.44 = 13.83

Standard deviation (σ):

σ = √13.83 ≈ 3.72%

This lower risk metric suggests a safer but less lucrative expected return profile compared to the first economic scenario.

Investment Consideration

Investors must weigh these expected returns against the associated risks. The first scenario offers high potential returns with substantial risk, suitable for aggressive investors. The second provides lower risk but also lower expected returns, appropriate for conservative investors. Personal risk tolerance, investment horizon, and market outlook should guide decision-making.

Conclusion

This comprehensive analysis emphasizes the importance of calculating both expected returns and risk measures in evaluating investments. For securities akin to Treasury bills, expected return aligns closely with the current yield, and risk remains minimal. Conversely, economic-dependent funds require detailed probabilistic calculations to gauge potential profitability and risk exposure accurately. Such analyses enable investors to align their portfolios with their risk appetite, investment goals, and market expectations, fostering informed decision-making and optimized investment strategies.

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